Control of an operon is a type of gene regulation that enables organisms to regulate the expression of various genes depending on environmental conditions. Operon regulation can be either negative or positive by induction or repression.
Negative control involves the binding of a repressor to the operator to prevent transcription.
* In negative inducible operons, a regulatory repressor protein is normally bound to the operator, which prevents the transcription of the genes on the operon. If an inducer molecule is present, it binds to the repressor and changes its conformation so that it is unable to bind to the operator. This allows for expression of the operon. The lac operon is a negatively controlled inducible operon, where the inducer molecule is allolactose.
* In negative repressible operons, transcription of the operon normally takes place. Repressor proteins are produced by a regulator gene, but they are unable to bind to the operator in their normal conformation. However, certain molecules called corepressors are bound by the repressor protein, causing a conformational change to the active site. The activated repressor protein binds to the operator and prevents transcription. The trp operon, involved in the synthesis of tryptophan (which itself acts as the corepressor), is a negatively controlled repressible operon.
Operons can also be positively controlled. With positive control, an activator protein stimulates transcription by binding to DNA (usually at a site other than the operator).
* In positive inducible operons, activator proteins are normally unable to bind to the pertinent DNA. When an inducer is bound by the activator protein, it undergoes a change in conformation so that it can bind to the DNA and activate transcription. Examples of positive inducible operons include the MerR family of transcriptional activators. 
* In positive repressible operons, the activator proteins are normally bound to the pertinent DNA segment. However, when an inhibitor is bound by the activator, it is prevented from binding the DNA. This stops activation and transcription of the system.