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Get Linear Control Theory: Structure, Robustness, and PDF

By Shankar P. Bhattacharyya, Aniruddha Datta, Lee H. Keel

ISBN-10: 0849340632

ISBN-13: 9780849340635

Successfully classroom-tested on the graduate point, Linear keep watch over conception: Structure, Robustness, and Optimization covers 3 significant parts of keep watch over engineering (PID regulate, strong keep watch over, and optimum control). It presents balanced insurance of chic mathematical concept and worthwhile engineering-oriented results.

The first a part of the booklet develops effects with regards to the layout of PID and first-order controllers for non-stop and discrete-time linear structures with attainable delays. the second one part offers with the powerful balance and function of platforms lower than parametric and unstructured uncertainty. This part describes a number of stylish and sharp effects, equivalent to Kharitonov’s theorem and its extensions, the sting theorem, and the mapping theorem. targeting the optimum keep watch over of linear structures, the 3rd half discusses the normal theories of the linear quadratic regulator, Hinfinity  and l1 optimum keep an eye on, and linked effects.

Written via famous leaders within the box, this ebook explains how regulate thought may be utilized to the layout of real-world structures. It indicates that the suggestions of 3 time period controllers, in addition to the consequences on powerful and optimum keep an eye on, are helpful to constructing and fixing learn difficulties in lots of parts of engineering.


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Additional info for Linear Control Theory: Structure, Robustness, and Optimization

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Using Parseval’s Theorem, this is equivalent to choosing 1 ˆ Q(s) for which min [1 − G(s)Q(s)]R(s) 2 is achieved, where R(s) = s is the Laplace transform of the unit step command. Approximating the deadtime with a first-order Pad´e approximation, we have L ∼ 1− 2s . e−Ls = 1 + L2 s ˆ is given by The resulting rational transfer function of the internal model G(s) ˆ G(s) = 1− 1+ k 1 + Ts L 2s L 2s . ˆ Choosing Q(s) to minimize the H2 norm of [1 − G(s)Q(s)]R(s), we obtain Q(s) = 1 + Ts . k Since this Q(s) is improper, we choose F (s) = 1 1 + λs where λ > 0 is a small number.

2 19 Frequency Domain Shaping These methods seek a set of controller parameters that give a desired frequency response. ˚ Astr¨om and H¨ agglund [8] proposed the idea of using a set of rules to achieve a desired phase margin specification. In the same spirit, Ho, Hang, and Zhou [102] developed a PID self-tuning method with specifications on the gain and phase margins. Another contribution by Voda and Landau [199] presented a method to shape the compensated system frequency response. 3 Optimal Control Methods This new trend has been motivated by the desire to incorporate several control system performance objectives such as reference tracking, disturbance rejection, and measurement noise rejection.

This signal es (t) is fed to the input of the integrator through a gain 1/Tt . 14 Controller with antiwindup. When the actuator is within its operating range, the signal es (t) is zero. Thus, PID CONTROLLERS: AN OVERVIEW OF CLASSICAL THEORY 21 it will not have any effect on the normal operation of the controller. When the actuator saturates, the signal es (t) is different from zero. The normal feedback path around the process is broken because the process input remains constant. However, there is a new feedback path around the integrator due to es (t) = 0 and this prevents the integrator from winding up.

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Linear Control Theory: Structure, Robustness, and Optimization by Shankar P. Bhattacharyya, Aniruddha Datta, Lee H. Keel

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