计算机控制系统英文版ChaterClassicdesign.ppt

6.1 Introduction 6.2 Indirect design method 6.2 Indirect design method Concrete procedure: 1.Choose sampling period, and design pre-antialiasing filter 2.Design or discretize continuous controller 3.Test the performance of the discrete system 4. If the system cannot meet the specification, there are three ways to improve it. a. Choose the more appropriate discretized method b. Increase sampling frequency c. Modify the original continuous controller 6.2 Indirect design method The system’s transfer function is equivalent to the differential equation (6.1) where a=1/(RC) 6.2 Indirect design method 1.Numerical integration If we write Eq. (6.1) in integral form as following Many rules have been developed based on how the incremental area term is approximated. Three possibilities are sketched in Fig. 6.5 which is called forward rectangular rule, backward rectangular rule and trapezoid rule respectively. 6.2 Indirect design method 6.2 Indirect design method (1) forward rectangular rule (also known as Euler’s rule) We approximate the area by the rectangle looking forward from kT-T and take the amplitude of the rectangle to be the value of the integrand at kT-T. The width of the rectangle is T. The result is an equation in the first approximation, u1 The transfer function corresponding to the forward rectangular rule in this case is 6.2 Indirect design method 6.2 Indirect design method (2) backward rectangular rule we approximate the area by the rectangle looking backward from kT toward kT-T. The equation for u2 is The corresponding transfer function is 6.2 Indirect design method 6.2 Indirect design method (3) trapezoid rule Taking the area to be that of the trapezoid formed by the average of the previously selected rectangles. The approximating difference equation is The corresponding transfer function from the trapezoid rule is 6.2 Indirect design method 6.