Control System design using classical techniques

Feb 3rd, 2012
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California Polytechnic State University-San Luis Obispo
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Control system modelling, Characteristics of control system, Control System design using classical techniques like root locus plot, bode plot nyquist plot, nichols plot, sensitivity and stability of system

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Computation of K : Design methodsDr. Abdul Qayyum KhanRoom No. SE-302Department of Electrical Engineering,Pakistan Institute of Engineering and Applied Sciences,P.O. Nilore Islamabd PakistanEmail: aqkhan@pieas.edu.pkhttp://www.pieas.edu.pk/aqayyum/()Copyrighted@AQKhan. All rights reserved1 / 22Lecture OutlineDiscussed so far: how controllability is necessary and sufficientcondition for design of state feedback controllerToday; we shall discussComputation methods for state feedback gain matrix KDesign of K using the transformation methodDesign of K using the Direct substitution methodDesign of K using Ackermann formula()Copyrighted@AQKhan. All rights reserved2 / 22Design of K using the method of Transformation matrix TIConsider the systemx = Ax + Bu(1)where x n , A nn matrix and B n1 . Consider the control ofthe form u = Kx. Thenx = (A BK ) x(2)Let 1 , 2 , n be the desired eigenvalues.K must be computed such away that the closed loop eigenvalues shouldbe 1 , 2 , , n()Copyrighted@AQKhan. All rights reserved3 / 22Design of K using the method of Transformation matrix TIIThe following algorithm is used to compute K .Algorithm 1Step I. Check the controllability, if the system is controllable, then go tostep II. Otherwise exit.Step II. From the characteristics polynomial of A, i.e.;|sI A| = s n + a1 s n1 + a2 s n2 + + an1 s + an(

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