CONTROL SYSTEM PERFORMANCE: ORDER/TYPE OF SYSTEM, STEADY-STATE ERROR

Any dynamic control system can be subjected to analysis to see if it meets certain performance criteria. The performance of the control system is studied in terms of its transient – and steady-state behavior. The first is the response to the initial conditions and the latter the response when the transients are settled. Since these two require­ments are often conflicting, a trade-off is required. The responses of a system are studied in terms of unit step-, unit ramp-, and unit-parabolic inputs. As seen in Chapters 7 and 9, the responses of a dynamic system can be obtained by applying short pulse, doublet, 3-2-1-1, and other multi-step inputs for studying the specific behavior of such systems. Often a steady-state error in standard inputs to a control system is computed. The highest power of s in the denominator of the TF is equal to the order of the highest derivative of the output, and if this highest power is equal to n, the system is an order ‘‘n.’’ A system could have a pole at origin of multiplicity N. Then it is of type N. This signifies the number of integrations involved in the open loop system. If N = 1, then the system is of type 1, if N = 0, then it is type zero, and so on. The steady-state error in terms of the gain K of the system is given in Table C1. If the type number of the system is increased, the accuracy for the same type of input is increased, but the stability of the system is aggravated progressively.

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