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Modern Linear Control Design: A Time-Domain Approach by Paolo Caravani PDF

By Paolo Caravani

ISBN-10: 1461469422

ISBN-13: 9781461469421

ISBN-10: 1461469430

ISBN-13: 9781461469438

This booklet bargains a compact advent to fashionable linear regulate layout. The simplified review provided of linear time-domain technique paves the line for the learn of extra complex non-linear innovations. merely rudimentary wisdom of linear structures thought is believed - no need of Laplace transforms or frequency layout instruments is needed. Emphasis is put on assumptions and logical implications, instead of summary completeness; on interpretation and actual which means, instead of theoretical formalism; on effects and suggestions, instead of derivation or solvability. the subjects lined comprise brief functionality and stabilization through kingdom or output suggestions; disturbance attenuation and powerful regulate; neighborhood eigenvalue task and constraints on enter or output variables; asymptotic rules and disturbance rejection. Lyapunov thought and Linear Matrix Inequalities (LMI) are mentioned as key layout tools. All tools are established with MATLAB to advertise useful use and comprehension.

· presents a single-source, compact and sensible advent to trendy linear keep an eye on layout, together with speedy and potent layout methods;

· features a cutting-edge evaluate of time-domain linear methods;

· Covers tools commonly dispersed in several books, equivalent to constraints on keep watch over variables, keep watch over robustness and the Asymptotic legislation problem;

· makes use of examples from a variety of software fields with recommendations in MATLAB.

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Additional resources for Modern Linear Control Design: A Time-Domain Approach

Example text

The invariance definition involves two notions, that of a system and that of a set. Different systems have different invariant sets. An interesting and difficult mathematical question is to characterize what family of sets are invariant for a given system. In the linear case things simplify considerably because this characterization can be reduced to a parametrization in the family of ellipsoids. Although a given linear system may admit non-ellipsoidal invariant sets, this is not true for all linear systems, so ellipsoids occupy a unique position in linear systems.

15). 3 Feasibility, Optimality The discussion so far has been carried out within a “feasibility” framework. 15) (norm-bound on y) and the resulting LMI system, if feasible, provides the solution in terms of the state-feedback gain K = Y X −1 . However we have not discussed how to select one solution, should many be available. In other words, we did not pose an “optimality” problem. Let z be the unknown variables of a feasibility problem defined by inequality constraints G(z) > 0 and let f (z) be a real function to be optimized over the set of feasible z.

4. Write a MATLAB function [K,P]=stabound(A,B,C,c,r,gam,eta) checking stabilizability of (A, B) and in the affirmative case returns a state f/b gain K placing displaceable closed-loop eigenvalues within a disc of radius r and center c, while guaranteeing (if possible) input and output norm bounds γ and η , and returns in P the matrix of the invariant ellipsoid. References 1. edu/∼boyd/cvx/ 2. Boyd S, El Ghaoui L, Feron L et al (1994) LMI in systems and control theory. SIAM, Philadelphia. pdf 3.

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