ABSTRACT

The performance of a closed-loop system can be described in terms of Mm, ωm, and the system error coefficient Km. The value of Mm (or γ) essentially describes the damping ratio ζ and therefore the amount of overshoot in the transient response. For a specific value of Mm, the resonant frequency ωm (or ωϕ) determines the undamped natural frequency ωn that in turn determines the response time of the system. The system error coefficient Km is important because it determines the steady-state error with an appropriate standard input. The design procedure is usually based on selecting a value of Mm and using the methods described in Chapter 12 to find the corresponding values of ωm and the required gain Km. If the desired performance specifications are not met by the basic system after this is accomplished, compensation must be used. This alters the shape of the frequency-response plot in an attempt to meet the performance specifications. Also, for those systems that are unstable for all values of gain, it is mandatory that a stabilizing or compensating network be inserted in the system. The compensator may be placed in cascade or in a minor feedback loop. The reasons for reshaping the frequency-response plot generally fall into the following categories:

1. A given system is stable, and its Mm and ωm (and therefore the transient response) are satisfactory, but its steady-state error is too large. The gain Km must therefore be increased to reduce the steady-state error (see Chapter 9) without appreciably altering the values of Mm and ωm. It is shown later that in this case the high-frequency portion of the frequencyresponse plot is satisfactory, but the low-frequency portion is not.