*Article* **Event-Driven Online Machine State Decision for Energy-E**ffi**cient Manufacturing System Based on Digital Twin Using Max-Plus Algebra**

#### **Junfeng Wang 1,\*, Yaqin Huang 1, Qing Chang 2 and Shiqi Li 1**

Received: 17 August 2019; Accepted: 12 September 2019; Published: 14 September 2019

**Abstract:** Energy-efficient manufacturing is an important aspect of sustainable development in current society. The rapid development of sensing technologies can collect real-time production data from shop floors, which provides more opportunities for making energy saving decisions about manufacturing systems. In this paper, a digital twin-based bidirectional operation framework is proposed to realize energy-efficient manufacturing systems. The data view, model view, and service view of a digital twin manufacturing system are formulated to describe the physical systems in virtual space, to perform simulation analysis, to make decisions, and to control the physical systems for various energy-saving purposes. For online energy-saving decisions about machines in serial manufacturing systems, an event-driven estimation method of an energy-saving window based on Max-plus Algebra is presented to put the target machine to sleep, considering real-time production data of a system segment. A practical, simplified automotive production line is used to illustrate the effectiveness of the proposed method by simulation experiments. Our method has no restriction on machine failure mode and predefined parameters for energy-saving decision of machines. The proposed approach has potential use in synchronous and asynchronous manufacturing systems.

**Keywords:** energy efficient operation; manufacturing system; stochastic event; digital twin; Max-plus Algebra; MATLAB-Simulink

#### **1. Introduction**

Industrial activities are the most important factor that leads to carbon dioxide (CO2) emissions in the world. The manufacturing industry in China accounts for 58.27% of the total CO2 emissions, which increased by approximately 220.77% in the past twenty years [1]. With the increased sustainable consensus, many emission reduction policies were issued to undertake environmental responsibility and duty in China. More and more manufacturers take effort to reduce energy costs. Energy-efficient manufacturing has been paid more attention considering productivity, flexibility, efficiency and environmental effect in production management [2].

A discrete manufacturing system is a kind of complex, stochastic, and dynamic system with interactions among machines and buffers. It is very common that many machines stay in an idle state, resulting from starvation or blockage during a working day. Statistically, the machine at an idle state consumes about 70% energy of their processing state [3]. Many modern Computerized Numerical Control (CNC) machines and robots have multiple idle states with different energy consumptions. An important strategy for energy-saving operations is to put the idle machine to sleep and to wake it up again at an appropriate time point without sacrificing the system productivity. The machine control

requires real-time production data. New, emerging Internet of Things (IoT) technology, e.g., smart sensors and meters, provide multilevel monitoring of manufacturing system (almost) in real time [4]. The collected data provide more opportunities for energy-saving decisions at the machine, process, and system levels.

Usually, discrete event simulation can be used to evaluate system performances including energy cost [5]. However, discrete event simulation is computationally expensive and time consuming, which is not suitable for online decision-making. As a new, emerging technology for modeling, simulation, and optimization, digital twin can reflect real-time states of physical systems [6]. Based on various models, digital twin not only can carry out simulations in virtual space before production but also can deliver decisions from virtual space to physical space during production, which realizes closed-loop feedback and interactions between physical systems and virtual systems. In this paper, a framework of digital-twin-based energy-efficient operation of manufacturing systems is proposed to support bidirectional interactions between virtual and physical systems. An event-driven Max-plus Algebra method is presented and validated online to predict the dynamic sleep duration of a machine for energy-saving operations at the system level.

The rest of this paper is organized as follows. The literature review is given in Section 2. Section 3 describes an operation framework for energy-efficient manufacturing systems based on digital twin technology. An event-driven energy-saving window approach for online machine state decision is proposed using Max-plus Algebra in Section 4. In Section 5, a practical serial manufacturing system is used to demonstrate the effectiveness of our method and discussions are given. Conclusions and future works are drawn in Section 6.

#### **2. Literature Review**

#### *2.1. Modeling and Simulation of Energy-E*ffi*cient Manufacturing*

Modeling and simulation are important methods for performance evaluation and optimization of energy-efficient manufacturing [7]. The simulation models of machine tools, processes, systems, or products can be used to carry out various what-if analyses. The production manager can understand the impacts of different manufacturing parameters on energy consumption and, thus, make decisions to optimize the parameters for energy-efficient manufacturing.

From the machine tool and process view, Lee et al. [8] proposed a simulation method based on a virtual machine tool to estimate the machining condition considering the energy consumption function or component model. Based on dynamic and kinematic behaviors of machine tools, Bi et al. [9] explored relations of machining parameters (cutting force, depth, and feed rate) and energy consumption. Kim et al. [10] proposed an additive regression algorithm to formulate the relationships between CNC machine energy consumption and machining parameters. From the product aspect, Seow et al. [11] built a simulation model to evaluate the total embodied product energy based on direct and indirect consumed energy.

At the production or manufacturing system levels, simulation-based prediction of energy consumption can support a manager in making decisions considering dynamic changes of production plans, energy prices, and environmental impact. Process chain simulation was an energy-oriented manufacturing system simulation approach [12]. The EnergyBlocks simulation method integrated energy-efficiency criteria with evaluation and decision processes during production system planning and scheduling [13]. Prabhu et al. [14] presented a simulation model that continuously integrated variable power consumption at the machine level and discrete nature at the production level to characterize energy dynamics in discrete manufacturing systems. By integrating a sustainability-enabled product lifecycle management information model with energy-consumption metrics, Zhao et al. [15] estimated the impact of energy control on actual energy consumption of a heating, ventilation, and air conditioning system; a ventilation system; and a production system.

The current modeling and simulation approaches focused on offline evaluation, prediction, and optimization for energy-efficient manufacturing. In order to incorporate real-time production data of shop floors, a data-driven method was always adopted for alleviating the burden of modeling and simulation [16].

#### *2.2. Energy-Aware Manufacturing System Scheduling and Control*

Taking energy consumption as one objective in scheduling; a multi-objective optimization problem can be formalized, and near-optimal job sequences can be searched by heuristic algorithms or exact methods [17]. Shrouf et al. [18] presented a mathematical model to minimize energy costs for a single machine system, and genetic algorithm technology has been used to obtain optimal solutions. For a two-machine system, Fang et al. [19] proposed a mathematical programming model that considered peak power load, energy consumption, and associated carbon footprint in addition to cycle time. In a flow shop with a reference schedule, Bruzzone et al. [20] built a mixed integer programming model where the reference schedule was modified to account for energy consumption without changing the jobs' assignment and sequencing. An energy-efficient flexible job shop scheduling model considering total production energy consumption and makespan was formulated in Reference [21], and a non-dominated sorting genetic algorithm-II was adopted to solve the model. Luo et al. [22] developed an ant colony optimization meta-heuristic to optimize both makespan and electric power cost with the presence of time-of-use electricity prices in a hybrid flow shop.

Quantitative policies and fuzzy rules can describe the operation knowledge of machine/system for energy-efficient manufacturing. Mouzon et al. [23] described several switch-off dispatching policies to minimize total energy consumption in a one-buffer, one-machine system. For a single machine system with stochastic inter-arrival times, the N-policy, Upstream Policy, and Downstream Policy were defined to switch the machine off when the conditions of the policies were satisfied [24]. By formulating four ON–OFF control rules in serial production lines with Bernoulli machines, Jia et al. [25] analyzed system performance measures in order to achieve high energy efficiency while maintaining high productivity. Wang et al [26] designed a fuzzy controller considering real-time data of buffers/machines in order to switch machine states and realize energy-efficient production.

Some works used an analytical method to study energy-saving opportunities of manufacturing systems. Chang et al. [27] proposed an energy opportunity window of a machine, which was predicted based on an approximated analytical model considering random downtime events. Sun and Li [28] presented an analytical estimation of energy control opportunities considering buffer utilization. Zou et al. [29] developed a stochastic analytical model which could predict shutdown time and recovery time of machines based on discrete-time Markov Chains in a stochastic production system. Li et al. [30] developed an analytical approach to quantitatively predict the system level production loss resulting from an energy-saving control event.

The multi-objective scheduling methods of energy-aware manufacturing are usually used to optimize operation plans before actual production. The complex and stochastic events of real shop floors are simplified or ignored in scheduling algorithms. It is noted that the control policies or rules for real-time energy-saving operation of production systems have many parameters to be determined and adjusted with time-consuming work. The advantage of the analytical models is its mathematical theory. Most of the analytical models did not consider the associated events during energy-saving operation, and only a constant energy opportunity window was predicted.

#### *2.3. Digital Twin of Cyber-Physical Manufacturing and Production System*

Digital twin [31], a near-real-time virtual representation of a physical component, product or system enriched with sensing data, is a digital and dynamic model in the cyber-space that is Digital twin [31], a near-real-time virtual representation of a physical component, product, or system enriched with sensing data, is a digital and dynamic model in cyberspace that is completely consistent with its physical ones in real space. It is considered a key technology in realizing cyber–physical production systems (CPPS) for Industry 4.0 [32]. Digital twin can simulate the characteristics, behavior, and performance of its physical counterpart in a timely fashion, which shows gigantic application potential in manufacturing system analysis and control [33,34].

In the aspects of production management, optimization, and control, Zhuang et al. [35] proposed a framework of digital-twin-based smart production management and control approach for complex product-assembly shop-floors. By using Plant simulation software, Vachálek et al. [36] built a digital twin for the optimization of production plans, which was designed in a way that it triggered physical and virtual productions as well. Coronado et al. [37] described the development and implementation of a new manufacturing execution system that combines MTConnect data with production data collected from operators. The work was integral to realizing a complete digital model of the shop floor for production control and optimization.

Considering digital-twin-based energy consumption evaluation and optimization of a production plan, Karanjkar et al. [38] presented an IoT-driven digital twin for energy optimization in an automated printed circuit-board assembly line. A digital twin of the line was built, and a buffering-based solution for improving energy efficiency was evaluated using simulations. Lu et al. [39] proposed an open system architecture for energy-efficient cyber–physical production network for facilitating distributed manufacturing. A cyber twin of a physical manufacturing asset was built, and the energy consumption of feature-based machining process models were evaluated in connected virtual factories. Zhang et al. [40] proposed a framework of equipment energy consumption management for a digital-twin shop floor. The data and models were discussed for monitoring, analysis, and optimization of equipment energy consumption.

It can be concluded that the most current works on digital twin of manufacturing or production system are used to monitor, evaluate, and visualize the real system based on unidirectional mapping from physical space to digital space. There is little research on models of online real-time production control from digital space to physical space, which is the main contribution in this paper considering energy consumption and productivity.

#### **3. Digital Twin Based Operation Framework of Energy-E**ffi**cient Manufacturing System**

Energy-efficient operation decisions of production systems require data from shop floors, carries out evaluations in virtual space, and makes control actions on the shop floor. Digital twin is the digital representation of a physical object. The main purpose of a production system digital twin is to facilitate decision-making activities based on simulation or computation before, during, and after production. The real-time monitoring, simulation, prediction, and control of production systems are vital to improving productivity, efficiency, and flexibility. At present, the interaction between physical and digital production systems is mainly offline interactions, lacking continuous and online interaction [33]. In this section, an operation framework with a three-view representation (Figure 1), i.e., data view, model view, and service view, is proposed to digitalize a manufacturing system, which enables us to perform simulations, to make decisions, and to control the physical system for different energy-saving purposes.

In the physical space of Figure 1, the real manufacturing/production system is a complex, diverse, and dynamic system with sensible ability in the context of Industry 4.0. The multisource and heterogeneous data (e.g., behavior, event, and state) of physical objects (e.g., machines, materials, and parts) are monitored and transmitted to databases based on IoT sensors (e.g., smart meters, radio frequency identification reader, and tags), which enhance the perception ability for physical manufacturing systems. The energy-efficient decisions made in virtual space based on digital twin are implemented through actuators of machines on the shop floor. A three-view digital twin of manufacturing systems for energy-saving operations is described as follows, which enables two-way direct or indirect mapping and interaction between the physical and the virtual manufacturing systems.

**Figure 1.** Framework of digital-twin based energy efficient operation of manufacture systems. eKPIs = energy-related key performance indicators.

#### *3.1. Data View*

The data of energy-efficient manufacturing collected from different sources has the "4V" characteristics (i.e., volume, velocity, variety, and value) of big data considering the spatial and time dimensions. The big data for energy-efficient operation of manufacturing system includes real-time and non-real-time data. The real-time data, such as electrical power of device, location of parts, buffer level, and machine throughput, is monitored and collected during production, which is the most important data source for online energy-saving decisions. The layout data, process plan, maintenance plan, and job schedule are the non-real-time data of the system collected or generated from the physical and cyber space before production. The energy-related key performance indicators (eKPIs), such as energy demand, energy cost, and energy efficiency, are also non-real-time data mined or acquired based on simulation after production. The energy big data can be structured or semi-structured. For example, the data of a machine, such as rated power, spindle speed, and cutting rate, is structured data. The process plan of a part is semi-structured data which has several flexible aspects (e.g., feature sequence, operation type, and machine selection).

The methods for cleaning, reduction, integration, and storage of energy-efficient manufacturing data can be referenced in Reference [41] and is not the focus of the paper. The high real-time processing ability of the storm real-time computing framework [42] can be adopted to process the time-series energy data. The Hadoop computing framework [43] can be used to process the non-real-time data. In order to efficiently store the big data of energy-efficient manufacturing, the Not only Structured Query Language [44] can be chosen for these large-scale structured and semi-structured datasets.

#### *3.2. Model View*

In digital space, the parameter correlations of the objects/systems are represented in simulation or computation models, which are core components of digital twin and the base of the application services. The models describe the working principle of machines with power supply, the energy consumption resources of the machining process, and the state space evolution of production systems. The models at three different levels are built for energy-efficient decisions in this framework.

At the device level, the physics-based energy model is required to formulate power consumption and dynamic behavior of industrial robot and CNC machine [40,45], and thus the energy-efficient trajectory planning, operating parameters, and power state of machine components can be completed. At the process level, the machining parameters, e.g., spindle speed, feed rate, and depth of cut, have a notable influence of energy consumption for the same job features [9]. The mathematical cutting equations or learning algorithms should be constructed for energy-consumption calculation and prediction of machining process.

The models at the system level depict the interaction among the objects in production systems. Various models such as knowledge-based models, mathematical models, and discrete event simulation models are established for different decisions of energy-efficient manufacturing. The policies/rules [23–25] and fuzzy logic [26] are expert knowledge for the energy-saving operation of production systems. The big data analysis models [46], e.g., neural networks, rough set theory, and deep learning, can mine implicit relationships of production parameters considering energy cost and productivity. The stochastic process [28] and algebra mathematical models [47] usually are used to evaluate the system eKPIs. The heuristic models (e.g., simulated annealing, genetic algorithm, and particle swarm optimization algorithm) for multi-objective optimization [17] are important for production scheduling. The discrete event simulation models are very popular for system evaluation and optimization as stated in the review section. The complex relations among entities, events, and activities of a production system are scheduled based on queuing theory in simulation models.

#### *3.3. Service View*

At the top of Figure 1, many kinds of application services are provided for online and offline scheduling, evaluating, forecasting, visualizing, monitoring, and controlling of energy-efficient manufacturing based on simulation or computation models.

The offline services are usually initiated on-demand by managers to determine the appropriate energy-efficient process parameters or job sequences in advance before production. The simulation services allow managers to perform what-if analyses on various production plans and to optimize schedules for minimizing total energy cost while maintaining higher productivity. After production, the future energy management [48,49], such as energy policy, energy benchmark, energy recycle, and manufacturing process/production schedule, can also be analyzed based on the collected data. The data-mining application services [46] can be formulated to discover hidden valuable information and knowledge from the enormous production datasets with energy indicators.

From the online services view, a near-real-time dynamic visualization application of productionand energy-related information can be generated based on discrete event simulation models with collected data, which provide more direct perceptions of the physical shop floor status. By creating the latest snapshot of the physical manufacturing system status based on the data-driven simulation method [16], the forecasting application is adaptive and flexible to any change in terms of actual production settings and can provide prediction services of system performances and eKPIs using online forward simulation experiments. Feedback control based on decisions in virtual space is the distinct characteristic of digital twin. The energy-saving opportunities during production come from the transient states of manufacturing system [27]. An online, event-driven energy-saving decision service for machine state control is proposed in this paper to execute short-term analysis by mapping the exact state of a physical system into the digital world at run time. The decision results will be sent to physical machines for realizing energy-efficient production.

#### **4. Event-Driven Online Decision Model of Energy Saving Window Using Max-Plus Algebra**

#### *4.1. Physical Manufacturing System and Modeling Assumptions*

In this paper, a typical serial production system (Figure 2) is used to illustrate energy efficient operation at the system level based on the above described digital twin framework. In order to build the mathematical model of the physical system for energy saving decision and control, the following assumptions are made.

**Figure 2.** Typical serial production system.

#### *4.2. Methodology of Event-Driven Online Energy Saving Decision and Control of Machine States*

Usually, time-based scheme is adopted at shop floor to collected production data with predefined sampling intervals and data-driven method is used to make operation decisions [41]. Generally speaking, the idle activities during production bring energy-saving opportunities. The idle activities generate from the events of blockage or starvation. Thus, event-based scheme can be more effective and economical considering the big data processing burden of time-based scheme [50]. Event-driven decision has shown many potential applications in manufacturing, such as manufacturing information system architecture [51], make-to-order production [52], and manufacturing execution system [53]. The most related research of event-based energy efficient production control is conducted by Li et al. [30,54], where a sequence of disruption events was defined to estimate the production loss for energy saving operation. In this paper, four traditional events of a machine, i.e., blockage event (BE), starvation event (SE), failure event (FE) and recover event from failure (RE), are monitored at the physical shop floor, which trigger energy-saving decision in digital space and control machines in physical system.

Based on previous works [27,55–57], an energy-saving window (ESWi) of a target machine *Mi* is defined as a time length of *Mi* being purposely put to sleep without bringing production loss to the system in this study. A system segment (SGi) of a target machine *Mi* is defined as the partial system including all machines and buffers between the target machine and bottleneck machine. The estimation of ESW in the next section will consider the bottleneck machine of the system, of which the production interruption will most likely result in system production loss [57]. The main flow of event-driven online energy-saving decision and control is shown in Figure 3 and explained as follows.

**Figure 3.** Event-driven online machine energy saving decision and control flow. Note: Abbreviations defined before Figure 2.

As shown in Figure 3, the main decision flow (rectangle 1) will be triggered if there is a BE or SE of a target machine Mi during production. The ESW of this target machine is estimated based on the current states of SGi. Then, the physical machine is switched into sleep mode. During the sleep duration of a target machine, different events of machines will be monitored and machine states will be controlled for energy-saving operation. In the flow of rectangle 2, the FE and then the RE of a machine in SGi are monitored. If an RE occurs on a machine, the main decision flow is retriggered to estimate a new ESW of the target machine. The underlying principle is that the failure of a machine in SGi can provide more energy-saving time for the target machine. In the flow of rectangle 3, different machines of the system are monitored according to the place of SGi, considering the bottleneck Mb. If the target machine Mi is before Mb, a new system segment before SGi is named as BSGi. The BE of machines in BSGi and the SE of machines in SGi are monitored. For each machine, from near to distant, related to the target machine, the machine in BSGi or SGi will be put to sleep if it is blocked or starved. If the target machine Mi is after Mb, a new system segment after SGi is named ASGi and similar decisions are made on each machine before the target machine ends its sleep. All the machines that were put to sleep will be woken when the ESW of the target machine is exhausted and a decision round ends.

Compared with time-based data sampling in the fuzzy logic method [26], our event-driven method greatly eases the burden of data collection and conforms to the stochastic of the system. The dynamic updating of the ESW of the target machine during one round decision is more reasonable compared with the constant opportunity windows [27,29,55–57] and will be illustrated in Section 5.

From the flow in Figure 3, our event-driven energy-saving decision method is also different from the event-based energy-efficient production control in References [30,54], which used predefined energy-saving control events to analyze the system performances.

#### *4.3. Estimation of Energy Saving Window Based on System Segment using Max-Plus Algebra*

Discrete event simulation is usually time consuming and cannot be used as the online tool for real-time decisions. Max-plus Algebra is a mathematical tool that can model discrete event systems in linear equations analogous to traditional state space dynamic equations [58] and has higher computation efficiency. Some works used Max-plus Algebra to model and analyse manufacturing systems, such as parametric analysis of mixed-model assembly lines [59], makespan calculation of a job-shop [60], and flow shop scheduling problems [61]. In this section, Max-plus Algebra is used to estimate the ESW of a target machine for energy saving operation based on previous work [62].

As aforementioned, ESW represents the sleep time of the target machine without affecting the production of Mb. If the target machine Mi is located before the bottleneck Mb (1 ≤ i < b), the sleep of the target machine will result in the starvation of the Mb. We define TEi as the time length that all work-in-processes (WIP) in buffers of SGi are cleared out. In order to recover the production of Mb immediately after waking the target machine, the time length from entering the target machine to arriving at buffer Bb−1 must be eliminated and donated as TRi. If the target machine Mi is located after the bottleneck Mb (b < i ≤ m), putting the target machine to sleep will cause a blockage of the Mb if all buffers in SGi are full. We define TFi as the time duration that all buffers in SGi are filled from their current levels. The ESW of the target machine Mi is estimated as follows:

$$ESW\_i = \begin{cases} \begin{array}{l} TE\_i - TR\_i \quad (1 \le i < b) \\ TF\_i \end{array} \\ \begin{array}{l} (b < i \le m) \\ \end{array} \tag{1}$$

The time length TEi, TRi, and TFi can be estimated using the Max-plus Algebra method, which can calculate the time instant of a system state. Here, the estimation of TEi is illustrated as an example. The following variables are defined to describe the system states for target machine Mi (1 ≤ i < b).

Apparently, we can get the following formula if the current time clock is zero.

$$TE\_i = \mathfrak{x}\_b(n) \tag{2}$$

where xb (*n*) means the time instant that bottleneck machine Mb starts processing the last part in SGi.

At a decision time point, there are Ij−1 parts in buffer Bj−1 that are available to machine Mj. After the processing activity of Mj, a new part will be sent to Bj and will be available to machine Mj+1. The vector uj is formulated as follows:

$$\mu\_{i+1} = \underbrace{[0,0,\ldots,0]}\_{I\_i}^T \tag{3}$$

$$\mathfrak{u}\_{l+2} = \underbrace{[0, 0, \dots, 0, \mathbf{x}\_{l+1}(1) + \mathbf{P}\_{l+1}, \mathbf{x}\_{l+1}(2) + \mathbf{P}\_{l+1}, \dots, \mathbf{x}\_{l+1}(I\_l) + \mathbf{P}\_{l+1}]^T}\_{I\_{l+1}} \tag{4}$$

$$\mathbf{u\_{b}} = \underbrace{\left[0, 0, \dots, 0, \mathbf{x\_{b-1}}(1) + \mathbf{P\_{b-1}}, \mathbf{x\_{b-1}}(2) + \mathbf{P\_{b-1}}, \dots, \mathbf{x\_{b-1}}(I\_{l} + I\_{l+1} + \dots + I\_{b-2}) + \mathbf{P\_{b-1}}\right]^T \tag{5}$$

For each part in buffers of SGi, the time instant that Mj starts processing the part is as follows:

$$\mathbf{x}\_{i+1}(\mathbf{k}) = \max(\mu\_{i+1}(\mathbf{k}), \mathbf{x}\_{i+1}(\mathbf{k} - 1) + P\_{i+1}, \mathbf{x}\_{i+2}(\mathbf{k} - 1 + I\_{i+1} - \mathcal{C}\_{i+1})) \tag{6}$$

$$\max\_{i+2}(\mathbf{k}) = \max(\mu\_{i+2}(\mathbf{k}), \mathbf{x}\_{i+2}(\mathbf{k}-1) + \mathbf{P}\_{i+2}, \mathbf{x}\_{i+3}(\mathbf{k}-1 + I\_{i+2} - \mathbf{C}\_{i+2})) \tag{7}$$

$$\mathbf{x}\_{b-1}(k) = \max(\boldsymbol{u}\_{b-1}(k), \mathbf{x}\_{b-1}(k-1) + P\_{b-1}, \mathbf{x}\_b(k-1 + I\_{b-1} - \mathbf{C}\_{b-1})) \tag{8}$$

$$\mathbf{x}\_{\mathbf{b}}(k) = \max(\boldsymbol{u}\_{\mathbf{b}}(k), \mathbf{x}\_{\mathbf{b}}(k-1) + \boldsymbol{P}\_{\mathbf{b}}) \tag{9}$$

In state space form, it can be described as follows:

$$\begin{array}{l} \mathbf{x}(k) = & \mathbf{A} \otimes \mathbf{u}(k) \oplus \mathbf{D} \otimes \mathbf{x}(k-1) \oplus \mathbf{F}^1 \otimes \mathbf{x}\_{l+2}(k-1 + I\_{l+1} - \mathbf{C}\_{l+1}) \\ & \oplus \mathbf{F}^2 \otimes \mathbf{x}\_{l+3}(k-1 + I\_{l+2} - \mathbf{C}\_{l+2}) \oplus \dots \oplus \mathbf{F}^{b-1} \otimes \mathbf{x}\_b(k-1 + I\_{b-1} - \mathbf{C}\_{b-1}) \end{array} \tag{10}$$

The coefficient matrices A, D and F are formulated as follows:

$$\mathbf{A} \in \mathbf{R}\_{\varepsilon}^{(b-i+1)\times(b-i+1)}, \; D \in \mathbf{R}\_{\varepsilon}^{(b-i+1)\times n}, \; \mathbf{F}^{l} \in \mathbf{R}\_{\varepsilon}^{(b-i+1)\times(b-i+1)}$$

$$\mathbf{A} = (a\_{lj}) = \begin{cases} \begin{array}{l} \mathbf{e} & \mathbf{i} = j; \\ \varepsilon & \text{otherwise} \end{array} \end{cases} \tag{11}$$

$$D = (d\_{i\dot{\jmath}}) = \begin{cases} \ P\_i & \text{ $i = j$ ;} \\ \varepsilon & \text{otherwise} \end{cases} \tag{12}$$

$$\mathbf{F}^l = (f\_{ij}) = \begin{cases} \mathbf{e} & \mathbf{i} = l, j = l+1 \ (l = 1, 2, \dots, b-\mathbf{i})\\ \boldsymbol{\varepsilon} & \text{otherwise} \end{cases} \tag{13}$$

where *e* is the null element and ε is the identity element in Max-plus Algebra.

Based on the above method, the state equations of the system segment will be quickly initialized using real time production data collected from shop floor and the ESW of a machine can be estimated for online energy saving decision and control.

#### **5. Simulation Experiments and Discussion**

#### *5.1. Simulation Case of a Serial Manufacturing System*

The event-driven energy saving decision model in our digital twin of an energy efficient manufacturing system can be used to control the physical system online under Industry 4.0 environment in the future, which realizes the communication from virtual space to physical space. In order to imitate the operation procedure of the physical production system, the model of the real production line is built in MATLAB-Simulink [63]. The running process of the modeled system generates real-time production data and events, which are monitored, collected and sent to digital twin. The energy-saving decision based on Max-plus Algebra is built in digital space as a service. The decision is driven based on defined events and the decision results are sent to the mimetic physical production system in MATLAB-Simulink, where the machines are controlled for energy-saving operation. The whole process simulates the bidirectional communication between physical space and virtual space.

A typical serial manufacturing system including six machines and five buffers (6M5B) in References [26,29] is taken to illustrate the effectiveness of our method. This system is a simplified version of a real automotive production line. The parameters are presented in Tables 1 and 2, where mean time between failure (MTBF) and mean time to repair (MTTR) are assumed as exponential distribution for this case. The simulation duration is three weeks, i.e., 30,240 min. The electricity rate is assumed to be \$0.2/kWh. It is assumed that no power is consumed in machine sleep mode for comparing performances with the methods in References [26,29].

**Table 1.** Machine parameters of the 6M5B serial automotive production line.

**Table 2.** Buffer parameters of the 6M5B serial automotive production line.

Three scenarios are simulated as follows: baseline scenario with no energy saving decision and control (S1), only one machine being controlled for energy saving (S2), and multi-machine except the bottleneck machine being controlled for energy saving (S3). These three scenarios are simulated for 20 trials-each. After simulation of baseline scenario S1, machine M4 is recognized as the system bottleneck.

#### *5.2. Experiment Results and Analysis*

The simulation results of system performances, i.e., System throughput (STP), System throughput Loss (STPL), Total system energy cost (TSEE), Energy cost per part (ECPP), and Energy cost saving per part (ECSPP), are shown in Table 3 with 95% confidential interval (CI). It can be seen that the energy cost saving per part is remarkable based on an event-driven digital twin model of the machine control method. When multiple-machines are controlled in S3, there is almost 57.24% energy-cost saving and only 2.20% system throughput is lost compared with baseline scenario S1.

**Table 3.** Simulation results of the three scenarios.

Figure 4 shows the machine states time in three scenarios, where the machine states include processing (PR), blockage (BL), starvation (ST), failure (FL), and sleep (SL). For machine M1, M2, and M3 before the BN (M4), the blockage time gradually decreases and the sleep time (energy-saving time) gradually increases in S2 and S3 compared with S1. The processing time of the machines almost remain unchanged, which means the energy-saving control does not affect processing work and converts the blockage time to sleep time. For machines M5 and M6 after the BN (M4), the energy-saving decision and control method can effectively change the starvation time into sleep time. For example, the total starvation time of M5 in S1 is 86.37% of simulation time. In S3, the starvation time of M5 is entirely converted to sleep time. The total processing time of M5 in S1 (3438.2 min) and S3 (3376.6 min) almost remain the same, while the sleep time of M5 is 86.57% of simulation time in S3. The control of machine states results in the energy-cost reduction as shown in Table 3.

We recorded the data of an event-driven energy-saving decision process during simulation experiments. Table 4 shows some data from S3, and the meanings are explained as follows.

An SE of M3 is monitored at 19,772.1 min, and M3 is taken as the target machine. An energy-saving decision is triggered based on the system segment SG3 (i.e., M3-B3-M4), and the ESW of M3 is estimated as 110.1 min. At the same time, the M3 is put to sleep. No energy-saving event is monitored following 110.1 min, and then M3 is woken at 19,882.2 min. For M5, an SE is monitored at 20,679.6 min and the target machine is set as M5. The ESW5 is calculated as 470.0 min, considering system segment SG5 (i.e., M4-B4-M5) in record No.4. Before the end of sleep time, there is a failure event of M4 at time 20,757.8 (No.5) and then a recover event of M4 at time 20,813.3 (No.6). Therefore, the energy-saving decision process of M5 is retriggered at time 20,813.3 and a new ESW5 is estimated as 385.4 min. The ESW5 is updated dynamically based on the event-driven method. Later, M6 in ASG5 (i.e., B5-M6) has an SE and is put to sleep at time 20,944.8. The sleep states of M5 and M6 are ended at time 21,198.7 (No.9). M5 and M6 have another decision round shown in record No.10, 12, and 14. For M3, a BL is monitored at 21,065.4 min and taken as the target machine. The ESW3 is calculated as 1501.3 min (No.8). At the later procedure, M2 and M1 are put to sleep in succession because of the BE in BSG3 (i.e., M1-B1-M2-B2). At

the end of the sleep time of M3 (i.e., 22,566.7 min), M1, M2, and M3 are woken up together. It can be seen that multiple machines can be controlled for energy-saving operation based on the event-driven method considering online production data.

**Figure 4.** The state time distribution of machines in three scenarios.

**Table 4.** Event-driven energy-saving decision process in scenario S3.

Figure 5 shows the changing process of machine states (M5) in S1 and S3, which is randomly selected from the experiments between 20,000 to 24,000 min. In baseline S1 with no energy-saving decision and control, there are many interval starvations and processing times of M5 due to the empty state of buffer B4. For example, there is one part in B4 at time 20,158.6 (S1) and in M5 that begins to process the part for 1.1 min. After time 20,159.7, the frequent starvation and processing state occurs alternately. Therefore, many normal starvation states of M5 with short duration consume a lot of non-value-added energy. In controlled scenario S3, the M5 is put to sleep until time 20,619.2. At time 20,619.2, M5 is woken up and processes parts continuously for 61.6 min until time 20,680.7. Then, M5 is put to sleep again in a new event-driven decision round. Comparing the states of M5 in S1 and S3, it can be concluded that control of machine energy-saving states brings energy-cost reduction of manufacturing systems.

**Figure 5.** The machine state changing process of M5: (a) S1 and (b) S3.

The eKPIs of the system under multi-machine control scenario in this paper are compared with fuzzy logic method [26] and mathematical model [29] in Table 5. The three methods of energy-saving control all result in reduction of system throughput less than 3%, which is acceptable in practical manufacturing systems. Our method achieves the most energy-cost reduction per part (57.23%) compared with the other two methods, and the effectiveness of this paper is proved.

**Table 5.** Comparision of the system eKPIs in different methods.

Except for the better performances, our method has some advantages for practical use in shop floors. The first advantage is that there is no restriction on the failure mode of machines in our method. The mathematical models [24,25,29] for energy-saving decision are all based on specific failure modes of machines. When the machine recovers from failure, the event-driven method will re-estimate the ESW of the machine. Non-predefined control parameter is the second advantage of our method. In fuzzy logic method [26], the threshold values and decision intervals of the machines should be defined in advance for energy-saving control. The method in Reference [29] should assume the subjective value of discount ratio and collaboration ratio. The third advantage is that our method can be used in synchronous manufacturing systems and asynchronous manufacturing systems. The method in Reference [29] can only be used in an asynchronous line.

#### **6. Conclusions**

With the development of IoTs, energy-efficient manufacturing is provided more opportunities in an Industry 4.0 environment, where the digital twin plays an important role for real-time production monitoring, simulation analysis, and feedback control of physical systems. Considering most current works focus on the uniderection mapping from physical space to virtual space, a digital-twin-based bidirectional operation framework of energy-efficient manufacturing system is proposed to digitalize the physical manufacturing systems, to perform simulations and decisions for different energy-saving purposes in virtual space, and to control the power states of physical machines. The three views, i.e., data view, model view, and service view, are described to map the physical system to digital system. An online event-driven energy-saving decision method based on Max-plus Algebra is presented to switch machines to sleep mode with consideration of maximum energy saving and minimum effect on system throughput. The Max-plus Algebra model is used to snapshot the states of system segment and to estimate the ESW of the machines. A simplified real automotive production line is taken as an example to carry out simulation experiments, and the results illustrate the effectiveness of the proposed method compared with other methods in literatures. Not relying on machine failure mode and non-predefined parameters in our method makes it simple to be used in synchronous and asynchronous systems. The potential application of our method in more complex line, e.g., parallel line, assembly line, or disassembly line, will be experimented in the future.

**Author Contributions:** The authors contribute equally to this study.

**Funding:** This research was funded by National Natural Science Foundation of China grant number No. 71571075. **Acknowledgments:** Authors thank the anonymous reviewers for their valuable comments. **Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

#### **References**

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).


**3.1 Nanolithography method**

The exposure method of near-field nanolithography that was proposed by this paper is illustrated in Figure 10. A UV transparent substrate with refractive index of n = 1.6 (@365nm) is used for supporting the mask. The object layer with line width of 60nm and pitch of 120nm, which is made of Cr with refractive index of n=2.924 (@365nm), acts as the function of mask in exposure. The air gap comes from the vacuum contact between mask and silver layer, which can be viewed as a kind of practical nanolithography technique.

Fig. 10. Sketch of Nanolithography Model.

In brief, the experiment mentioned above demonstrates the feasibility of using photon sieves as the focusing optical element. We believe in that PSAL will be used as one of the promising tools in the nanometric device and special IC areas for the purpose of high

**3. Nanolithography in the evanescent near field by using nano-filmed noble**

The sharpness of object can't be resolved by conventional lens due to the limitation by the wavelength of illumination light. J. B. Pendry had predicted that a slab of negative refractive index material has the power to focus all Fourier components of a 2D image. The super resolution of the negative index materials using silver layer, which was called 'superlens', can reconstruct the image of a pattern with line width of 40nm (Fang, et al., 2005). They made mask, silver slab and photoresist integrity in Fang's experiment, which likes the traditional contact exposure of lithography. It is not practical in real application by Fang's method of nanolithography because each wafer needs its respective mask. The experiments of super resolution using silver slab was reported, and the line width with one fifth of illumination wavelength can be successfully resolved by the silver slab

Though Blaikie's experiment made mask and silver integrity, they separated photoresist from silver slab. This kind of configuration still had limitation in practical application. In order to investigate the influence of distance between mask and noble metal slab on imaging, we designed a separated 'superlens' with silver slab 100nm away from mask. We analyzed the distribution of optical field by Finite Difference Time Domain (FDTD). The

The exposure method of near-field nanolithography that was proposed by this paper is illustrated in Figure 10. A UV transparent substrate with refractive index of n = 1.6 (@365nm) is used for supporting the mask. The object layer with line width of 60nm and pitch of 120nm, which is made of Cr with refractive index of n=2.924 (@365nm), acts as the function of mask in exposure. The air gap comes from the vacuum contact between mask and silver layer, which can be viewed as a kind of practical nanolithography technique.

results show that the images of object can be reconstructed by the structure.

resolution regardless of low yield.

**metal layers**

(Blaikie et al., 2006).

**3.1 Nanolithography method**

Fig. 10. Sketch of Nanolithography Model.

Table 1. Physical parameters of the materials in Fig. 10.

In figure 10, the spacing layer with refractive index of n=1.517 (@365nm) acts as the following two functions: 1) to match the surface plasmon polaritons resonating conditions; 2) to protect the surface of silver slab. As for the image recording, we chose the negative photoresist of i-line.

In order to explore the potential valid imaging distance between mask and photoresist, a repeat of spacing layer and silver slab layer was followed after the first silver slab. The sample was exposed in i-line light that shone from the substrate side. For the convenience of description, we defined D1 as the distance between mask and silver slab, and D2 as the distance between silver slab and photoresist.

#### **3.2 When silver slab separated 40nm from mask (i.e. D1=40nm)**

In order to save calculating time and PC resources, we computed the distribution of optical near-field intensity by the 2-D FDTD method. We chose cell size of X\*Z=2×1(nm), which is much smaller than both the exposure light wavelength and the mask's feature size. The time step, according to Courant condition, should be:

$$TimeStep = 2\sqrt{2}N^{1/3} \tag{5}$$

N is the total cells of computing area. We chose 3500, by which the amplitude of electric field already became steady. The distance of 40nm comes from the spacing layer. At this situation, it is a kind of ideal condition, because mask and spacing layer had a hard contact. The surface plasmons polaritons of two interfaces between silver slab and its surroundings can magnify the evanescent waves that carried the detailed information of object. When D1=40nm, we calculated the following 4 conditions: D2=0nm, 20nm, 40nm, 60nm. Figure 11 show the distribution of electromagnetic (abbreviated to EM afterwards in the paper) field respectively.

It was found that the image of mask can be clear resolved by the method. Figure 11(a) shows better result, however, figure 11(b)-(d) showed worse results due to the exponential decay of the evanescent waves came from the exit side of the interface between silver slab and photoresist. The strong contrast of EM field may come from the edge effect of the evanescent waves. We chose the 10nm cross-section of photoresist layer to compare the imaging result of silver slab. When D1=40nm and D2 varied from 0nm to 60nm, the distribution of optical field in the section was shown in Figure 11. When D2 changed from 0nm to 60nm, the amplitude reduced to about a half under the same condition, but the high contrast of lines still can be clearly observed in figure 12. The amplitudes of lines were relatively uniform when D2=20nm and 60nm compared with D2=0nm. If the parameters of photoresist were

Emerging Maskless Nanolithography Based on Novel Diffraction Gratings 347

Fig. 13. The final comparison when D1=60nm while D2=0, 20, 40 and 60nm.

Fig. 14. The final comparison when D1=80nm while D2=0, 20, 40 and 60nm.

The evanescent waves can not propagate to a long distance due to its exponential attenuation. The intensity of evanescent waves decays with a characteristic length *Z0* :

> 0 2 2 1 *t* sin

incidence angle of light from optically denser media to optically thinner media; where

In order to explore the potential imaging property of silver slab, we increased D1 as much as possible. Considering the evanescent waves may diminish when D1=100nm, so we calculated the condition of D2=0nm only, the distribution of electromagnetic filed was shown in figure 15. It was found that the image of mask still can be resolved clearly in photoresist layer with good uniformity of imaged lines. We investigated the distribution of optical field in the 10nm cross-section of photoresist layer. The distribution of optical filed in the transverse section of photoresist was shown in figure 16. The image of mask can be resolved with high contrast. With proper choice of exposure condition and materials, the information of mask can be transferred to photoresist layer, and the image of mask can be

In brief, the image of mask can be transferred to the photoresist layer by the enhancement function of surface plasmon polaritons in silver slab. We calculated the 2D distribution of electromagnetic field in our model; the results showed that the image of mask with feature

*k n*

is the wavelength of incident light. Theoretically, *Z0* can be 100nm by

(6)

1 is the

*n Z*

where *nnn* 2 1 is the relative refractive index of two surrounding media;

**3.4 When silver slab separated 100nm from mask (i.e. D1=100nm)**

2 2 *t k n* ,

calculation.

reconstructed by the silver slab layer.

under better control, the lines of images will be more uniform. However, compare with the condition of D2=0nm, the depth of lines in photoresist will be shallower at the same exposure condition.

Fig. 11. The distribution of EM field in the model. Photoresist layer lies (a) between Z=0.31μm and Z=0.41μm, (b) between Z=0.33μm and Z=0.43μm, (c) between Z=0.35μm and Z=0.45μm, (d) between Z=0.7μm and Z=0.47μm.

Fig. 12. The distribution of optical field in the 10 nm cross-section of photoresist when D1=40nm.

#### **3.3 When silver slab separated 60nm and 80nm from mask (i.e. D1=60nm, 80nm)**

When D1=60nm, 80nm, we calculated 4 conditions respectively for each D1. We still chose the 10nm cross-section of photoresist layer to investigate the optical field. In order to show the clear comparison results, we give the final comparison of the amplitude instead of EM distribution figures for each condition of different D2. Figure 13 and figure 14 showed the result respectively when silver slab separated 60nm and 80nm from mask.

It was found that there came out extra fringes in figure13 and figure 14. This kind of phenomena may be caused by the strong interference effects among evanescent waves. The image of mask still can be resolved in photoresist layer by proper choice of materials and exposure conditions. These results showed a bad conformity between mask and recorded image in photoresist layer. On the other hand, it gave us a hint to realize better resolution of optical lithography by reasonably using the interference effect.

under better control, the lines of images will be more uniform. However, compare with the condition of D2=0nm, the depth of lines in photoresist will be shallower at the same

(a) (b)

(c) (d)

Fig. 11. The distribution of EM field in the model. Photoresist layer lies (a) between

Fig. 12. The distribution of optical field in the 10 nm cross-section of photoresist when

**3.3 When silver slab separated 60nm and 80nm from mask (i.e. D1=60nm, 80nm)**  When D1=60nm, 80nm, we calculated 4 conditions respectively for each D1. We still chose the 10nm cross-section of photoresist layer to investigate the optical field. In order to show the clear comparison results, we give the final comparison of the amplitude instead of EM distribution figures for each condition of different D2. Figure 13 and figure 14 showed the

It was found that there came out extra fringes in figure13 and figure 14. This kind of phenomena may be caused by the strong interference effects among evanescent waves. The image of mask still can be resolved in photoresist layer by proper choice of materials and exposure conditions. These results showed a bad conformity between mask and recorded image in photoresist layer. On the other hand, it gave us a hint to realize better resolution of

result respectively when silver slab separated 60nm and 80nm from mask.

optical lithography by reasonably using the interference effect.

Z=0.45μm, (d) between Z=0.7μm and Z=0.47μm.

Z=0.31μm and Z=0.41μm, (b) between Z=0.33μm and Z=0.43μm, (c) between Z=0.35μm and

exposure condition.

D1=40nm.

Fig. 13. The final comparison when D1=60nm while D2=0, 20, 40 and 60nm.

Fig. 14. The final comparison when D1=80nm while D2=0, 20, 40 and 60nm.

#### **3.4 When silver slab separated 100nm from mask (i.e. D1=100nm)**

The evanescent waves can not propagate to a long distance due to its exponential attenuation. The intensity of evanescent waves decays with a characteristic length *Z0* :

$$Z\_0 = \frac{n}{k\_t \sqrt{\sin^2 \theta\_1 - n^2}}\tag{6}$$

where *nnn* 2 1 is the relative refractive index of two surrounding media; 1 is the incidence angle of light from optically denser media to optically thinner media; where 2 2 *t k n* , is the wavelength of incident light. Theoretically, *Z0* can be 100nm by calculation.

In order to explore the potential imaging property of silver slab, we increased D1 as much as possible. Considering the evanescent waves may diminish when D1=100nm, so we calculated the condition of D2=0nm only, the distribution of electromagnetic filed was shown in figure 15. It was found that the image of mask still can be resolved clearly in photoresist layer with good uniformity of imaged lines. We investigated the distribution of optical field in the 10nm cross-section of photoresist layer. The distribution of optical filed in the transverse section of photoresist was shown in figure 16. The image of mask can be resolved with high contrast. With proper choice of exposure condition and materials, the information of mask can be transferred to photoresist layer, and the image of mask can be reconstructed by the silver slab layer.

In brief, the image of mask can be transferred to the photoresist layer by the enhancement function of surface plasmon polaritons in silver slab. We calculated the 2D distribution of electromagnetic field in our model; the results showed that the image of mask with feature

Emerging Maskless Nanolithography Based on Novel Diffraction Gratings 349

The characteristics of synchrotron radiation light, resolution limits and depth of focus of the lithographic system are discussed. The design and fabrication of photon sieve are illustrated with a low-numerical-aperture amplitude-photon sieve fabricated on a chrome-coated quartz plate by means of laser-beam lithographic process, which minimum size of pinhole was 5.6um. The PSF of photon sieve in terms of side-lobes strength and main lobe width may be controlled by utilizing the apodization window function. The focusing performance of the photon sieve operating at wavelength of 632.8nm was simulated and tested. In combination with the synchrotron light sources, the photon sieve array X-ray maskless nanolithography is a promising tool in the nanometric device and special IC areas for the

The second focuses on the evanescent near field in nano-filmed noble metals. Subdiffraction-limited feature size can be resolved by using i-line illumination exposure. Compared with the model of original superlens, we separated the superlens 100nm away from the mask, under the illumination of i-line light, the initial simulation shows that the sub-diffraction-limited feature as small as 60nm line width with 120nm pitch can be clearly resolved without hard contact between mask and nano-filmed noble metal. By proper design of the materials and the parameters of nano-filmed layers, better resolution can be

In brief, a plasmonic structure for imaging and super focusing is a new approach besides the concept of negative refractive index. It is possible to realize imaging resolution beyond diffraction limit with a certain working distance within several wavelengths range. To realize this target, one of technical challenges is that how to transfer the high spatial frequency near-field signals from evanescent wave to propagation wave. The other challenge is that how to amplify the near-field evanescent wave from conventional ~200 nm

This work was supported by the grants from the Guangdong Natural Science Foundation (S2011040000711), the Key Lab of Robotics & Intelligent System, Guangdong Province (2009A060800016), the Guangdong & Chinese Academy of Sciences Cooperation Project (2009B091300160), National Natural Science Foundation of China (60904031; 60776029), Shenzhen Science & Technology Research Funds (2009-203), the Main Direction Program of the Knowledge Innovation of Chinese Academy of Sciences (KGCX2-YW-166), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars of Ministry of

Blaikie, R.J., Melville, D.O.S. & Alkaisi, M. M. (2006). Super-resolution near-field lithography

Cao, Q., & Jahns, J. (2002). Focusing analysis of the pinhole photon sieve: individual far-field model. *J. Opt. Soc. Am. A*, Vol.19, No.12, pp.2387-2393, ISSN 0740-3232 Cao, Q., & Jahns, J. (2003). Nonparaxial model for the focusing of high-numerical-aperture photon sieves. *J. Opt. Soc. Am. A*, Vol.20, No.6, pp. 1005-1012, ISSN 0740-3232

using silver lens: a review of recent developments. *Microelectronic Engineering*,

purpose of high resolution regardless of low yield.

*m* or even several wavelengths in free space.

Vol.83, No.4-9, pp.723-729, ISSN 0167-9317

realized.

to be ~ 1

**5. Acknowledgment**

Education, China (2008-890).

**6. References**

size of 60nm line width can be resolved in photoresist layer when silver slab separated 100nm from mask. By proper design and choice of material, nanolithography with better resolution can be realized by the very function of silver slab, and this technique will be a possible alternative nanolithography technique for the next generation lithography.

Fig. 15. The distribution of electromagnetic field in the model (Both X and Z is in unit of μm. Photoresist layer lies between Z=0.37μm and Z=0.47μm).

Fig. 16. The distribution of optical field in the 10nm cross-section of photoresist when silver slab separated 100nm from mask.

### **4. Conclusion**

Two types of maskless lithography are discussed in this chapter. The first uses an array of high-numerical-aperture photon sieves as focusing elements in a scanning X-ray maskless nanolithography system. The system operating at wavelength of 0.5~2nm synchrotron light sources radiated, each of a large array of photon sieves focuses incident X-ray into a diffraction-limited on-axis nanoscale spot on the substrate coated photoresist. The X-ray intensity of each spot is modulated by means of a spatial light modulator. Patterns of arbitrary geometry are exposed and written in a dot matrix fashion while the substrate on a stepping stage is precisely driven in two dimensions according to the computer program. The characteristics of synchrotron radiation light, resolution limits and depth of focus of the lithographic system are discussed. The design and fabrication of photon sieve are illustrated with a low-numerical-aperture amplitude-photon sieve fabricated on a chrome-coated quartz plate by means of laser-beam lithographic process, which minimum size of pinhole was 5.6um. The PSF of photon sieve in terms of side-lobes strength and main lobe width may be controlled by utilizing the apodization window function. The focusing performance of the photon sieve operating at wavelength of 632.8nm was simulated and tested. In combination with the synchrotron light sources, the photon sieve array X-ray maskless nanolithography is a promising tool in the nanometric device and special IC areas for the purpose of high resolution regardless of low yield.

The second focuses on the evanescent near field in nano-filmed noble metals. Subdiffraction-limited feature size can be resolved by using i-line illumination exposure. Compared with the model of original superlens, we separated the superlens 100nm away from the mask, under the illumination of i-line light, the initial simulation shows that the sub-diffraction-limited feature as small as 60nm line width with 120nm pitch can be clearly resolved without hard contact between mask and nano-filmed noble metal. By proper design of the materials and the parameters of nano-filmed layers, better resolution can be realized.

In brief, a plasmonic structure for imaging and super focusing is a new approach besides the concept of negative refractive index. It is possible to realize imaging resolution beyond diffraction limit with a certain working distance within several wavelengths range. To realize this target, one of technical challenges is that how to transfer the high spatial frequency near-field signals from evanescent wave to propagation wave. The other challenge is that how to amplify the near-field evanescent wave from conventional ~200 nm to be ~ 1*m* or even several wavelengths in free space.


**8. Personalization in teaching**

The use of digital tools is also important because it allows greater attention to the students.

Each student, in fact, is the bearer of unique characteristics. Therefore, teaching should be personalized, so as to get the best out of each of them. For students with learning disabilities, this type of attention care is even more important. Forcing them to face the same tasks as other classmates can in fact be a source of stress for them and become counterproductive.

Similarly, acting toward them in a standardized way, adapting solutions chosen for other students, can prove equally counterproductive.

In this situation the use of new technologies can help a lot. This is because the use of certain tools allows the teacher to focus attention precisely on the individual student, to prepare lessons designed specifically for him. In fact, technology offers the possibility of continuously adapting supports (such as the content of digital books), so that they can be adapted from time to time to whoever is in front of them. In addition, it allows to use multiple sensory channels and switch from one language to another, looking for the best way to present a topic, adapting it to the characteristics of the students.

Obviously caring for students with learning disabilities requires great care on the part of teachers. Technology alone is not enough. It requires teachers to use the tools to respond to the needs of individual students, in the name of that personalization of teaching that the school increasingly requires [47].

Some technological tools, however, may be fine for lessons aimed at the whole class. For example, there are softwares for presentations, which offer various possibilities for less boring, stimulating, even funny lessons. In fact, they allow to associate multiple sensory channels, therefore different ways to convey a concept, combining drawings, music, etc. Therefore, they are suitable for different students because they can stimulate different cognitive styles.

For example, augmented reality [48] can be useful both for the whole class and for SEN, to help them in the learning process. In fact, it is used to show in 3D everything that in the mind, or even just on the book, can be visualized with difficulty. It has several advantages:

Other positive aspects are the fact that the learning medium is linked to the real world, that students have an active role in the learning process, that this type of activity helps memorization, that students can access resources independently, and the fact that this activity stimulates cooperative learning.