《计算机控制系统课件第四章》由会员分享，可在线阅读，更多相关《计算机控制系统课件第四章（245页珍藏版）》请在金锄头文库上搜索。
1、1,Design of Discrete-Time Control System by Conventional Methods,Chapter 4,2,4-1 Introduction,Firstly, we present mapping from the s plane to the z plane and then discuss stability of closed-loop control systems in the z plane. Mapping between the s plane and the z plane Stability analysis of closed
2、-loop systems in z plane Transient and steady-state response analysis,3,4-1 Introduction,Next we treat the following different design methods for single-in-single-output discrete-time control systems. Root-locus technique using pole-zero configurations in the z plane (established in 1950s) Design co
3、ntrollers for system with time delay with Smith predictor Design controllers for system with time delay using Dahlin algorithm Analytical method to obtain a desired behavior of the closed-loop system by manipulating the transfer function of a digital controller,4,Outline,4-1 Introduction 4-2 Mapping
4、 between the s plane and the z plane 4-3 Stability analysis of closed-loop systems in z plane 4-4 Transient and steady-state response analysis 4-5 Design based on the root-locus method 4-6 Design controllers for system with time delay 4-7 Analytical design method,5,4-2 Mapping between the s plane an
5、d the z plane,The absolute stability and relative stability of the linear time-invariant continuous-time closed-loop control system are determined by the locations of the closed-loop poles in the s plane Complex closed-loop poles in the left half of the s plane near the j axis will exhibit oscillato
6、ry behavior Closed-loop poles on the negative real axis will exhibit exponential decay The complex variables z and s are related by z=esT The pole and zero locations in the z plane are related to the pole and zero locations in the s plane, depending on the sampling period T The pole and zero locatio
7、ns in the z plane determine the stabilities and response behaviors of a DCS,4-2 Mapping between the s plane and the z plane,1. Mapping of the left half of the s plane into the z planeFrequencies, differ in integral multiples of the sampling frequency 2/T, are mapped into the same locations in the z
8、plane, which means that there are infinitely many values of s for each value of z.The left half-s-plane:The j of s-plane: the imaginary axis in the s plane (the line =0) corresponds to the unit circle in the z plane, and the interior of the unit circle corresponds to the left half of the s plane.,7,
9、4-2 Mapping between the s plane and the z plane,2. Primary strips and complementary strips,8,4-2 Mapping between the s plane and the z plane,3. Constant attenuate loci (1) Constant-attenuation line (=constant),Constant-attenuation line (=constant) in the s plane maps into a circle of radius z=eT cen
10、tered at the origin in the z plane.,9,4-2 Mapping between the s plane and the z plane,(2) Settling time ts: The settling time is determined by the value of attenuation of the dominant closed-loop poles.,10,4-2 Mapping between the s plane and the z plane,(3) Constant frequency loci-a radial line of c
11、onstant angle T1,Left half-s-plane, : z-plane 0-(-1) negative real axis Right half-s-plane, : z-plane 1- positive real axis Negative real axis in s-plane : z-plane 0-1 positive real axis,11,4-2 Mapping between the s plane and the z plane,12,4-2 Mapping between the s plane and the z plane,13,4-2 Mapp
12、ing between the s plane and the z plane,(4) Constant damping ratio loci- a spiral line,14,4-2 Mapping between the s plane and the z plane,15,4-2 Mapping between the s plane and the z plane,16,4-2 Mapping between the s plane and the z plane,Note that if a constant-damping-ratio line is in the second
13、or third quadrant in the s plane then the spiral decays within the unit circle in the z plane. However, if a constant-damping-ratio line is in the first or fourth quadrant in the s plane (which corresponds to negative damping), then the spiral grows outside the unit circle.,17,4-2 Mapping between th
14、e s plane and the z plane,Remark: For discrete-time control system, it is necessary to pay particular attention to the sampling period T. This is because, if the sampling period is too long and the sampling theorem is not satisfied then frequency folding occurs and the effective pole and zero locati
15、ons will be changed.,18,4-2 Mapping between the s plane and the z plane,19,4-2 Mapping between the s plane and the z plane,20,4-2 Mapping between the s plane and the z plane,21,4-2 Mapping between the s plane and the z plane,22,4-3 Stability analysis of closed-loop systems in z plane,1. Stability an
16、alysis of a closed-loop system Consider the following closed-loop pulse transfer function system,23,4-3 Stability analysis of closed-loop systems in z plane,24,4-3 Stability analysis of closed-loop systems in z plane,25,4-3 Stability analysis of closed-loop systems in z plane,2. Methods for testing absolute stability (1) The Jury Stability Test,
