线性控制课件 module 21 08-4-27-english_new.ppt

Sample Problem 21.1 Sample Problem 21.3 Problem: Consider the system, Design a PID controller using a Ziegler Nichols method for tuning the coefficients, and compute the resulting step response of the closed loop system. * Linear Control Systems Engineering线性控制系统工程 Module 21 Multimode Controllers (多模控制器)  21 Multimode Controllers Multimode control design: change the type of the system to meet desired performance requirements. Mode control – Design the controller in the loop. ＋ － Controller Plant Feedback transducer Fif.21.1 Definition of controller R C Proportional Control The output is proportional to the input. ＋ - － ＋ ＋ e K K×e Controller Fig.21.2 Proportional controller R K T C Fig.21.3 First-order type 1 system with disturbance. For first order system. R is unit step input: T is unit step disturbance: If K is made large, the output for input approach 1 and for disturbance approach 0. But the K is finite. For second order system. R is unit step input T is unit step disturbance. If K is made large, the disturbance approach 0. But the large K should cause an oscillatory response. Conclusion: P control is of limited success in trying to obtain good performance in terms of steady state error, disturbance rejection and transient response. C ＋ － ＋ ＋ K T Fig.21.4 Second-order type 1 system with disturbance. × Im Re Fig.21.5Root locus of second-order system. × R Proportional-Plus-Integral Control (PI) The output is proportional to the input plus the integral of the input. C Fig.21.7 PI control of first- order sysrem. ＋ ＋ ＋ － ＋ ＋ R Fig.21.6 PI controller T The transfer function of the controller: For first order system: R is unit step input: T is unit step disturbance: The system type has been change from 0 to 1, due to the controller. For second order system: R is unit step input: T is unit step disturbance: Draw the root locus using: To make the system stable, the zer