北京理工大学810自动控制原理考研课件5.ppt

* Chapter 4 The Stability of Linear Feedback Systems 4.1 The Concept of Stability4.2 Routh-Hurwitz Stability Criterion * 4.1 The Concept of Stability A stable system is dynamic system with a bounded response to a bounded input. Stability is the fundamental requirement of a control system. Absolute stability —— stable / not stable Relative stability —— the degree of stability * The response of a linear system to a stimulus has two component: (1). Steady state terms which are directly related to the input. (2). Transient terms which are either exponential or oscillatory with an envelope at exponential form. 　 If the exponential terms decay as time increases then the system is said to be stable; otherwise the system is said to be unstable. 理硕教育—专注于北理工考研辅导 本资料由理硕教育整理，理硕教育是全国唯一专注于北理工考研辅导的学校，相对于其它机构理硕教育有得天独厚的优势。丰富的理工内部资料资源与人力资源确保每个学员都受益匪浅，确保理硕教育的学员初试通过率89%以上，复试通过率接近100%，理硕教育现开设初试专业课VIP一对一，初试专业课网络小班，假期集训营，复试VIP一对一辅导，复试网络小班，考前专业课网络小班，满足学员不同的需求。因为专一所以专业，理硕教育助您圆北理之梦。详情请查阅理硕教育官网 * * Stability means that with no input, the output of each integrator will decay to zero eventually.　 When the transfer function of system is T(s), the output Y(s) is: * According to inverse Laplace transform, there is: the system is stable. then total response , so the system is unstable. * The conclusion will be gotten as following: The system is stable only when all the closed-loop poles are located in the left-hand position (LHP) of the s-plane. The system becomes unstable as soon as one closed-loop pole is located in the right-hand position (RHP) of the s-plane. If a system has simple roots on the imaginary axis with all other roots in the LHP, it is called marginally stable. * 4.2 Routh-Hurwitz Stability Criterion Consider the following system: * A necessary but not sufficient criterion: For a stable system, all the coefficients of the polynomial q(s) must have the same sign and be nonzero. The Routh-Hurwitz criterion is a necessary and suffi