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2. Introduction to the Principles of Feedback

2.4 Definition of the Problem

The example presented in section §2.3 motivates the following more formal statement of the nature of the control problem:

Definition 2.1 The fundamental control problem

The central problem in control is to find a technically feasible way to act on a given process so that the process adheres, as closely as possible to some desired behavior. Furthermore, this approximate behavior should be achieved in the face of uncertainty of the process and in the presence of uncontrollable external disturbances acting on the process.

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The above definition introduces several ideas:

  • Desired behavior. This needs to be specified as part of the design problem.
  • Feasibility. This means that the solution must satisfy various constraints, which can be of technical, environmental, economic, or other nature.
  • Uncertainty. The available knowledge about a system will usually be limited and of limited accuracy.
  • Action. The solution requires that action be somehow applied to the process, typically via one or more manipulated variables which command the actuators.
  • Disturbances. The process to be controlled will typically have inputs other than those that are manipulated by the controller. These other inputs are called disturbances.
  • Approximate behavior. A feasible solution will rarely be perfect. There will invariably be a degree of approximation in achieving the specified goal.
  • Measurements. These are crucial to let the controller know what the system is actually doing and how the unavoidable disturbances are affecting it.

In the sequel, we will refer to the process to be controlled as the plant, and we will say that the plant is under automatic control when the control objectives are achieved with infrequent human intervention.