CH05-4 stability criterion in frequency domain.pptVIP

CH.5 frequency response 5-1 Concept of frequency characteristics 5-2 Frequency response of typical elements 5-4 Stability criterion of control system in frequent domain 5-5 Relationship between the frequency characteristics of open-loop system and the performance of closed-loop system 5-3 Plotting for the open-loop transfer function 5-4 Stability criterion of control system in frequency domain Sufficient and necessary condition: All roots of the characteristic equation have negative real parts. Time domain: Routh criterion Frequency domain: Nyquist criterion A graphic method to decide the stability of a closed-loop system by using the open-loop magnitude-phase characteristics . Merits: A graphic method; No need to calculating the closed-loop characteristic roots. Instead, the open-loop frequency characteristics is utilized to decide the stability. In addition, the way to improve the stability can also be detected. Zeros of F(s) are poles of the closed-loop transfer function; Poles of F(s) are poles of the open-loop transfer function. Nyquist criterion: a graphic method to decide if the zeros of F(s) lie on the right half of s plane. Two cases: No poles of s=0 in the open-loop system; Poles of s=0 exist in the open-loop system. No poles of s=0 in the open-loop system 中各零点和极 点到点 的向量为: Closed path on s plane Closed path on the plane of F(s) Principle of argument： when s1 moves clockwise along a closed path on the s plane , the corresponding F(s1) also goes along a closed path on the F(s) plane. If Гencloses zero of F(s) only: That means Г′makes a clockwise round the original point. When s′ moves clockwise along Г, the equivalent phase angles of the zeros and poles outside Гremains unchanged. While as, there’s a variation of -2 π in the phase angle of the zero enclosed by Г. Conclusion: If Г surrounds clockwise a zero of F(s), Г′goes clockwise around the original of F(s) plane once. If Г surrounds clockwise Z