控制工程4(英文).ppt

Ch9 Stability in the Frequency Domain 9.1 Mapping contours in the s-plane Contour map Conformal mapping 9.2 The Nyquist Criterion Nyquist stability criterion A feedback system is stable if and only if the contour in the L(s)-plane does not encircle the (-1,j0) point when the number of poles of L(s) in the right-hand s-plane is zero (P=0) A feedback system is stable if and only if ,for the contour , the number of counterclockwise encirclements of the (-1,j0) point is equal to the number of poles of L(s) in the right-hand s-plane. Application of Nyquist criterion Example 1: system with 2 real poles 9.3 Relative Stability and Nyquist Criterion Absolute stability and relative stability How to determine relative stability? Gain margin and phase margin Nyquist criterion For minimum-phase system, If the system is stable. If the system is unstable. reflect the degree of relative stability. Phase margin is a frequency-domain specification. Gain margin and phase margin calculation from Bode plot Comparison of relative stability 9.4 Time-domain performance criteria specified in the frequency domain Closed-loop frequency response Constant M circles Nichols chart Constant M circles Constant N circles Nichols chart 9.5 System bandwidth The bandwidth is measured at the -3dB frequency. The speed of response to step input is proportional to , and the settling time is inversely proportional to . System with a larger bandwidth provides a faster response. Example: Liquid level control system Assignment E9.8 E9.12 E9.19 E9.21 Ch10 The Design of Feedback Control Systems 10.1 Introduction Design of a control system is concerned with the arrangement or the plan, of the system structure and the selection of suitable components and parameters. The alteration or adjustment of a control system in order to provide a suitable performance is called compensation. A compensator is an addi