Main components o control systems

· Sensor(s), which measure some physical state such as temperature or liquid level.

· Responder(s), which may be simple electrical or mechanical systems or complex special purpose digital controllers or general purpose computers.

· Actuator(s), which effect a response to the sensor(s) under the command of the responder, for example, by controlling a gas flow to a burner in a heating system or electricity to a motor in a refrigerator or pump.

Building Basic Principles: From Classical to Modern.

Our goal is to present a clear exposition of the basic principles of frequency- and time-domain design techniques.

The classical methods of control engineering are thoroughly covered:

- Laplace transforms and transfer functions;

- root locus design;

- Routh-Hurwitz stability analysis;

- frequency response methods, including Bode, Nyquist, and Nichols;

- steady-state error for standard test signals;

- second-order system approximations;

- phase and gain margin;

- control system bandwidth.

In addition, coverage of the state variable method is significant. Fundamental notions of controllability and observability for state variable models are discussed. Full state feedback design with Ackermann's formula for pole placement is presented, along with a discussion on the limitations of state variable feedback. Observers are introduced as a means to provide state estimates when the complete state is not measured.

System classifications

Linear Systems control

For MIMO systems, pole placement can be performed mathematically using a state space representation of the open-loop system and calculating a feedback matrix assigning poles in the desired positions. In complicated systems this can require computer-assisted calculation capabilities, and cannot always ensure robustness. Furthermore, all system states are not in general measured and so observers must be included and incorporated in pole placement design.

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