Full Closed-Loop Tests for the Relay Feedback Autotuning of Stable, Integrating, and Unstable Processes

Abstract

The relay (on–off) controller can stabilize wide ranges of processes including open-loop stable, integrating, and unstable processes, producing sustained oscillations. For improved proportional-integral-derivative controller tunings, methods to find process models with mixed closed-loop tests of relay feedback and proportional-derivative (PD) controllers are proposed. For unknown processes with arbitrary initial states, relay feedback tests are first applied and, after cyclic steady states are obtained, PD controllers or other relay feedback tests with set point changes are followed. This full closed-loop operation is desirable for integrating and unstable processes and will be useful even for stable processes when processes are far from their desirable operating points. Refined methods to find exact frequency responses of processes from initial and final cyclic steady states are derived. Whole relay feedback responses need not be saved. Several integrals at the relay switching times are used without iterative tests or computations.

Computer-Added System Selecting the Sub-Optimal Model of the Control Object

“…We calculate the ultimate gain, taking into account the expression for the describing function of relay with hysteresis (4) where: B -amplitude of the control signal -output from the relay, ε -width of the hysteresis zone of the relay.…”

“…For instance, the relay method developed by Åström and Hägglund [1] focused on determining the limit cycle parameters. Based on further research carried out in this area, new methods of improving the accuracy in determining these parameters [2], [3], [4]. One of the methods recently used more often to improve the quality of the created model is the use of an asymmetric relay [5], [6].…”

A Simple Analytical Method for Estimation of the Five-Parameter Model: Second-Order with Zero Plus Time Delay

“…The most common frequency-domain identification method is a relay feedback identification method [2,8,9]. Several variants of relay identification methods have been proposed in the literature [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. According to [6] and [7], they can be categorized into three main groups: describing function method, curve fitting approach, and frequency response estimation for model fitting.…”

Root Loci Analysis of a Simple Quasi-Polynomial And Its Use For Relay-Based Parameter Identification of a Delayed Infinite-Dimensional Heat-Exchanger Process

“…Nevertheless, the given asymmetry may yield the termination of oscillations, which fails the relay test. Numerous other techniques exist, such as the shifting method 51,73,74 , the use of relay transient 48,54,75 or the computation of weighting moments 47,61 .…”

“…Most of the linear process models used in literature when applying some of the relay-based identification experiments include input-output delays within First-Order plus Dead Time (FOPDT) or Second-Order plus Dead Time SOPDT models, either stable 44,45,46,50,55,63,69,76 or unstable 43,44,51,[77][78][79][80][81] ones. The models are represented simply by a series of a delay-free loworder submodel and the delay element.…”