Synthesis Of Proportional-integral-derivative Controllers Research Articles

An Approach to Synthesis of Multivariable PID Controllers for a Class of Nonlinear Systems and Its Application

AbstractThis paper considers a synthesis of multivariable proportional-integral-derivative (PID) controllers for a class of nonlinear systems. First, mathematical models of plant with a class of nonlinearities and PID controller with saturation nonlinearity are given. Then, the closed-loop system is described by a descriptor form. Secondly, an analysis condition for descriptor systems with sector-bounded nonlinearity is introduced. Based upon the condition and a representation for the nonlinearities in the control system, the synthesis problem is formulated as a bilinear matrix inequality one. The matrix inequality problem is solved by an iterative linear matrix inequality algorithm to synthesize a PID controller so as to minimize the L2-gain and expand the region of sector. Finally, to verify the effectiveness, the synthesis method is applied to the synthesis of PID controller for a ball-on-wheel system with input saturation.

Synthesis of PID controllers for integral processes with time delay

AbstractThis article deals with the problem of determination of the stabilizing parameter sets of Proportional‐Integral‐Derivative (PID) controllers for first‐order and second‐order integral processes with time‐delay. First, the admissible stabilizing range of proportional‐gain is determined analytically in terms of a version of the Hermite–Biehler Theorem applicable to quasi‐polynomials. Then, based on a graphical stability condition developed in parameter space, the complete stabilizing regions in an integral‐derivative plane are drawn and identified graphically, not calculated mathematically, by sweeping over the admissible range of proportional‐gain. An actual algorithm for finding the stabilizing parameter sets of PID controllers is also proposed. Simulations show that the stabilizing regions in integral‐derivative space are either triangles or quadrilaterals. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Reliable decentralized PID controller synthesis for two-channel MIMO processes

Reliable stabilization and regulation of two-channel decentralized multi-input multi-output (MIMO) control systems is considered. The system has integral-action due to using proportional + integral + derivative (PID) controllers. Closed-loop stability and asymptotic tracking of step-input references are achieved at each output channel when all controllers are operational. Stability is maintained when one of the controllers fails completely and is set to zero. Controller synthesis procedures are proposed for stable MIMO plants and for several unstable MIMO plant classes that admit PID controllers. These synthesis procedures are applied to various examples of process systems to illustrate the design methodology.

PID controller synthesis for a class of unstable MIMO plants with I/O delays

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.

Comments on "New results on the synthesis of PID controllers"

Silva, Datta, and Bhattacharyya (in the above paper) have studied the feedback control system, provided with a proportional-integral-derivative (PID) controller and relative to a first-order plant with a time delay, and have determined the range of the PID controller parameters suitable for the stability by means of a version of the Hermite-Biehler theorem. The purpose of this note is to find the same results in a simpler way by means of the classical Nyquist's stability criterion.

New results on the synthesis of PID controllers

This paper considers the problem of stabilizing a first-order plant with dead time using a proportional-integral-derivative (PID) controller. Using a version of the Hermite-Biehler theorem that is applicable to quasi-polynomials, the complete set of stabilizing PID parameters is determined for both open-loop stable and unstable plants. The range of admissible proportional gains is first determined in closed form. For each proportional gain in this range, the stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid, a triangle or a quadrilateral. For the case of an open-loop unstable plant, a necessary and sufficient condition on the time delay is determined for the existence of stabilizing PID controllers.