Page 330 - Modern Control Systems

CHAPTER The Performance of
5 Feedback Control Systems

5.1 Introduction 305
5.2 Test Input Signals 305
5.3 Performance of Second-Order Systems 308
5.4 Effects of a Third Pole and a Zero on the Second-Order System Response 314
5.5 The s-Plane Root Location and the Transient Response 320
5.6 The Steady-State Error of Feedback Control Systems 322
5.7 Performance Indices 330
5.8 The Simplification of Linear Systems 339
5.9 Design Examples 342
5.10 System Performance Using Control Design Software 356
5.11 Sequential Design Example: Disk Drive Read System 360
5.12 Summary 364

PREVIEW
The ability to adjust the transient and steady-state response of a control system is a
beneficial outcome of the design of control systems. In this chapter, we introduce
the time-domain performance specifications and we use key input signals to test the
response of the control system. The correlation between the system performance
and the location of the transfer function poles and zeros is discussed. We will develop
relationships between the performance specifications and the natural frequency and
damping ratio for second-order systems. Relying on the notion of dominant poles,
we can extrapolate the ideas associated with second-order systems to those of higher
order. The concept of a performance index will be considered. We will present a set
of popular quantitative performance indices that adequately represent the perfor-
mance of the control system. The chapter concludes with a performance analysis of
the Sequential Design Example: Disk Drive Read System.

DESIRED OUTCOMES

Upon completion of Chapter 5, students should:
Q Be aware of key test signals used in controls and of the resulting transient response
characteristics of second-order systems to test signal inputs.
• Recognize the direct relationship between the pole locations of second-order systems
and the transient response.
O Be familiar with the design formulas that relate the second-order pole locations to per-
cent overshoot, settling time, rise time, and time to peak.
Q Be aware of the impact of a zero and a third pole on the second-order system response.
Q Gain a sense of optimal control as measured with performance indices.

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