Polynomial Design of Low-Order Controllers for SISO DAE Systems

Abstract—We apply polynomial approach to the design of optimal low-order controllers for linear stationary SISO systems described by differential and algebraic equations. The method of critical root diagrams and root polynomials is used to design such controllers in classical control systems. An unstable control plant is given by an improper transfer fraction with a sextic numerator and a quartic denominator. For it, stabilizing PI${}_{3}$ controllers are tuned; the optimal controller according to the relative stability is chosen among them. Calculation of the impulse response confirms its astatism and lack of impulse. The method is the same as for classical control systems, however, the resulting polynomial systems of equations turn out to be higher in degree and more difficult to solve numerically.