Abstract :
Handling delays in control systems is difficult and is of long-standing interest. It is well known that, given a finite-dimensional linear time-invariant (FDLTI) plant and controller forming a strictly proper stable feedback connection, closed-loop stability will be maintained under a small delay in the feedback loop, although most closed loop systems become unstable for large delays. One previously unsolved fundamental problem in this context is whether, for a given FDLTI plant, an arbitrarily large delay margin can be achieved using LTI control. Here, we adopt a frequency domain approach and demonstrate that, for a strictly proper real rational plant, there is a uniform upper bound on the delay that can be tolerated when using an LTI controller, if and only if the plant has at least one closed right half plane pole not at the origin. We also give several explicit upper bounds on the achievable delay margin, and, in some special cases, demonstrate that these bounds are tight.
Keywords :
closed loop systems; delays; feedback; frequency-domain analysis; linear systems; multidimensional systems; stability; LTI control; closed loop system; closed-loop stability; control systems; delay handling; delay margin; feedback loop delay; feedback stability; finite-dimensional linear time-invariant controller; frequency domain approach; plant stability; time delay; Control system synthesis; Control systems; Councils; Delay effects; Feedback control; Feedback loop; Frequency domain analysis; Process control; Robust control; Upper bound; Delay margin; frequency domain; linear systems; time delay;