Computer Controlled Systems by Astrem, Wittenmark

By Astrem, Wittenmark

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H{k) = Ck-'lf =CT-l(TT-1)k-1Tr ::: CT-1T~-lr ;:: h(k) • f:. 0 for only a finite number of k, then the system is called a finite impulse-response (FIR) system. This implies that the output only will be influenced hy a fiuite number of inputs. Discrete-Time Systems 48 Chap. 2 Shift-Operator Calculus Differential-operator calculus is a convenienttool for manipulating linear differential equations with constant coefficients. An analogous operator calculus can be developed for systems described by linear difference equations with constant coefficients.

10 20 ..... 10 Simulation of the disk ann servo with analog and computer control. 5, and there is a. 1 sin 12t. (a) Continuous-time system; (b) sampled-data system. that the steady-state response to sinusoidal excitations is sinusoidal with the frequency of the excitation signal. It will be shown that computer-controlled systems behave in a much marc complicated way because sampling will create signals with new frequencies. This can drastically deteriorate performance if proper precautions are not taken.

The inverse problem offinding the continuous-time system that corresponds to a given discrete-time system is also treated in Sec. 3. The general solution of forced difference equations is given in Sec. 4. 6 deal with transformation of state-space models and the connection between state-space and input-output models. Shift operators are used to describe input-output mod- in 30 Sec. 2 Sampling Continuous-Time Signals 31 els, Shift-operator calculus is equivalent to the use of differential operators for continuous-time systems.

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