By Tan Kok Kiong PhD, Wang Qing-Guo PhD, Hang Chang Chieh PhD, Tore J. Hägglund PhD (auth.)
Recently, loads of attempt has been devoted to capitalising on advances in mathematical keep an eye on idea at the side of tried-and-tested classical keep watch over buildings really with reference to the improved robustness and tighter keep watch over of contemporary PID controllers. a lot of the study during this box and that of the operational autonomy of PID controllers has already been translated into necessary new features for business controllers. This booklet covers the $64000 wisdom on the subject of the historical past, software, and layout of, and advances in PID controllers in a unified and entire therapy together with:
Evolution and elements of PID controllers
Classical and sleek PID controller design
Multi-loop keep watch over
Practical matters inquisitive about PID regulate
The ebook is meant to be beneficial to a large spectrum of readers attracted to PID regulate starting from working towards technicians and engineers to graduate and undergraduate students.
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Additional info for Advances in PID Control
Notch filter action can be achieved by a judicious choice of the controller parameters. In this case, parameters T;, and Td should, however, be chosen so that the numerator has complex roots. Uncertain systems are yet another class of difficult processes for PID control. For systems with small parameter variations , simple detuning of the PID control may suffice. For systems with larger parameter variations, it is possible to design linear controllers that allow operation over a wide parameter range.
Assume that the control system specifications are given in terms of gain margin Am and phase margin cPm. These imply that 42 Advances in PID Control r • ~®- y u Gc(s) Gp(s) - Fig. 1. 7) where Wp and Wg are the phase and gain crossover frequencies of the loop respectively. 7) are satisfied. 7). Since both equations are complex, they can be further broken down to four real equations. Since the number of unknowns equals the number of real equations, the number of solutions will be finite. Intuitively, it may be expected that since the equations for the controller parameters Kp and Ki have been readily constructed and they are known to have limited number of solutions, the problem can be easily solved.
1) will not hold for higher frequencies. The upper bound on the bandwidth is therefore determined by the validity of the model. 2) This model has three parameters. By using a PID controller, which also has three parameters, it is possible to arbitrarily place the three poles of 38 Advances in PID Control the closed-loop system. The transfer function of the PID controller can be written as Ge(s) = Ke(1 + STi + s2TiTd). STi The characteristic equation of the closed-loop system becomes: 3 s +s 2 ( 1+ T21+ KpKeTd) (1 KpKe) KpKe TIT2 +s TIT2 + TIT2 + Ti T IT 2 = Tl O.
Advances in PID Control by Tan Kok Kiong PhD, Wang Qing-Guo PhD, Hang Chang Chieh PhD, Tore J. Hägglund PhD (auth.)