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Refined design method for sampled-data control systems:the pseudo-continuous-time(PCT) control system design. 指導老師 : 曾慶耀 教授 組別 : 控制組 學號 :M97670023 姓名 : 王資順. 大綱. 1.Introduction 2.PCT control system 3.DIG design technique 4.Compensators 5.Conclusion. 1.Introduction .
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Refined design method for sampled-data control systems:the pseudo-continuous-time(PCT) control system design 指導老師:曾慶耀 教授 組別:控制組 學號:M97670023 姓名:王資順
大綱 • 1.Introduction • 2.PCT control system • 3.DIG design technique • 4.Compensators • 5.Conclusion
1.Introduction • The analysis and design of sampled-data SISO system,based upon step-response specifications, maybe done entirely in z-plane or s-plane
2.Pseudo-continuous-time • The DIG design method for a ampled-data system, using the complex frequency s-plane, requires a satisfactory PCT model of the sampled-data system.
The design philosophy involves the following considerations: • (a) Follow path A if the dominant poles and zeros of C( •)/R(•) lie in the shaded area of Fig. 1. [The Tustin approximation is good as the criteria of eqns. 8 and 9 are satisfied.] • (b) Follow path A when the degree of warping is deemed not to negatively affect the achievement of the desired results. If the desired system performance specifications are not achieved, try path B. • (c) Follow path B when severe warping exists.
4. Compensators • The simple passive lead (a < 1) and lag (a > 1) compensators in the s-domain have the form
where and . The corresponding first-order z-domain compensator (digital filter) via is
(Note that the value of is just the reciprocal of that of .) • Because eqns. have the same mathematical form, the z-plane compensator design procedures via the DIR techniques are essentially the same as those for designing a compensator for a continuous-time system.
5. Conclusions • By the use of the Pade approximation, the sampling effect which introduces a gain of l/T, and the Tustin transformation, a sampled-data control system may be transformed into a pseudo-continuous-time (PCT) control system
When the rules governing this transformation are satisfied, the analysis and design of a PCT system model is a practical approach for the analysis and design of a sampled-data control system.
A consequence of applying the Tustin transformation to C(s)/R(s) of the PCT system and then applying the Guillemin-Truxal method to is that an unrealisable cascade digital compensator Dc(z) results.
