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Control System Design - Index | Book Contents |
| Section 2.4
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.
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
and we will say that the plant is under automatic control
when the control objectives are achieved
with infrequent human intervention.