Synthesis and design of PID controllers
Abstract
controllers for discrete-time systems and time-delayed systems. By using bilinear
transformation and orthogonal transformation, earlier research results obtained in
the continuous-time case are extended to discrete-time situation. The complete set of
stabilizing PID controllers for the discrete-time systems is thus obtained. Moreover,
this set remains to be a union of convex sets when one particular parameter is fixed.
Thus a method to design robust and non-fragile digital PID controllers is proposed
by following a similar design procedure for the continuous-time systems. In order to
find the stabilizing controller set for systems with time-delays, the relationship between
the Nyquist Criterion and Pontryagins theory is investigated. The conditions
under which one can correctly apply the Nyquist Criterion to time-delayed systems
are derived. Then, the complete set of stabilizing PID controllers for arbitrary order
LTI systems with time-delay up to a given value is obtained. Furthermore, the stability
issue of a system with fixed-delay is also studied and a formula which provides
complete knowledge of the distribution of the closed-loop poles is presented. Based
on this formula, stabilizing P and PI controller sets for the system with fixed-delay
can be computed.
Citation
Xu, Hao (2004). Synthesis and design of PID controllers. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /1480.