Pid Controller Synthesis for a Class of Unstable Mimo Plants With I/O Delays

Abstract

Conditions are presented for closed-loop stabilizability of linear time-invariant (LTI) multi-input, multi-output (MIMO) plants with I/O delays (time delays in the input and/or output channels) using PID (Proportional + Integral + Derivative) controllers. We show that systems with at most two unstable poles can be stabilized by PID controllers provided a small gain condition is satisfied. For systems with only one unstable pole, this condition is equivalent to having sufficiently small delay-unstable pole product. Our method of synthesis of such controllers identify some free parameters that can be used to satisfy further design criteria than stability. ᭧

PID controller design for fractional-order systems with time delays

“…rather than (15), and then applying the small gain theorem, as was done in [28], does not work in the case of fractional systems. So, we have to compute R α (γ ) as a function of γ for the specific α value appearing in the plant transfer function.…”

“…As in [28], the design will be done in two steps: first, PD controllers will be investigated, and then the integral action will be added.…”

Integral Action Controllers for Systems with Time Delays

“…In this section we discuss the design of C1 for the largest allowable range of ρ, (9), for a class of single input single output (SISO) plants with time delays. In this case, from (9) we see that C1 should be designed to minimize…”

“…EEEAG-105E156). Cpi, is a stabilizing controller for the new plant P (I + C1P ) −1 , then the parallel connection of the controller, Cpi + C1, is a stabilizing controller for the original plant P , see [9,14,16]. One can study the problem choosing the best C1 so that the allowable range of ki is maximum.…”

Stable ${{\mathcal H}^\infty}$ Controller Design for Systems with Time Delays

“…[13] and its references. An alternative approach for SS0PD would be to use the results of [7,11], where a simple but conservative design method is proposed for proportional plus derivative (PD) controller synthesis for systems with time delays.…”