Digital PID Controller DesignDigital PID Controller Design

Digital PID Controller Design 1. Digital PID Controller Design [n]. r[n] e[n] u[n] y[n]. C(z) P (z). Plant and Controller N(z). ( ) NC ((z)). G( ) =. G(z) ; C( ) =. C(z) : D(z) DC (z). The characteristic polynomial of the closed loop system (z) := DC (z)D(z) + NC (z)N (z). 2. Digital PID Controller Design TCHEBYSHEV REPRESENTATION AND. ROOT CLUSTERING. Tchebyshev representation of real polynomials Consider a real polynomial P (z) = an z n + an 1 z n 1 + + a1 z + a0. The image of P (z) evaluated on the circle C of radius , centered at the origin is: j .. P (z) : z = e ; 0 2 : jj . j . j . As the coe cients ai are real P e and P e are conjugate complex numbers, and so it su ces to determine the image of the upper half of the circle: j .. P (z) : z = e ; 0 : 3. Digital PID Controller Design . Since z k z= ej = k (cos k + j sin k );. k ). j . P e = (an n cos n + + a1 cos + a0 ) +j (an n sin n + + a1 sin ).

Digital PID Controller Design TCHEBYSHEV REPRESENTATION AND ROOT CLUSTERING Tchebyshev representation of real polynomials ² Consider a real polynomial P(z)=a nzn +a n¡1zn¡1 +¢¢¢+a 1z +a 0 ² The image of P(z) evaluated …

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