Dynamic response of control systems, Electrical Engineering

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Q. Dynamic Response of Control Systems?

The existence of transients (and associated oscillations) is a characteristic of systems that possess energy-storage elements and that are subjected to disturbances. Usually the complete solution of the differential equation providesmaximuminformation about the system's dynamic performance.

Consequently, whenever it is convenient, an attempt is made to establish this solution first. Unfortunately, however, this is not easily accomplished for high-order systems. Hence we are forced to seek out other easier and more direct methods, such as the frequency-response method of analysis.

Much of linear control theory is based on the frequency-response formulation of the system equations, and several quasi-graphical and algebraic techniques have been developed to analyze and design linear control systems based on frequency-response methods. Although frequency-response techniques are limited to relatively simple systems, and apply only to linear systems in the rigorous mathematical sense, they are still most useful in system design and the stability analysis of practical systems and can give a great deal of information about the relationships between system parameters (such as time constants and gains) and system response.

Once the transfer function of Equation is developed in terms of the complex frequency variable s, by letting s = jω, the frequency-response characteristic and the loop gain GH(jω) can be determined. The Bode diagram, displaying the frequency response and root-locus techniques, can be used to study the stability analysis of feedback control systems. The dc steady-state response, which becomes one component of the step response of the control system, can also be determined by allowing s to be zero in the transfer function. The step response, in turn, can be used as a measure of the speed of response of the control system. Thus, the transfer function obtained from the block diagram can be used to describe both the steady-state and the transient response of a feedback control system.


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