Autotuning for model‐based PID controllers

Abstract

The autotuning test of h r o m and Hagglund (1984) is conducted by using a relay in the feedback loop to produce periodic cycles so that the ultimate gain and ultimate frequency of the proocess can be derived. In the autotuning (AT) procedure of Astrom and Hagglund, such ultimate data are used to find the PID controller settings based on Z-N rules (Ziegler and Nichols, 1942). Although it was found that such data are always accompanied with errors (sometimes as high as 20%), the effect of such errors to the performance of PID loops would be immaterial.However, as the Z-N method is aimed at one-quarter decay ratio, the resulting control loop usually has excessive oscillations that lead to poor performance. To achieve better performance, many other tuning methods which use modelbased designs such as IMC (Rivera et al., 1986) or integral performance criteria such as ISE, IAE, ITAE, etc. (Lopez et al., 1967) have to be considered. However, to apply these tuning rules, there needs to be a proper parametric model such as the FOPDT. This brought forth quite a few studies (Luyben et al., 1991;Li et al., 1991) that aim at identifying such models by using the AT test. But, to apply such models derived from the conventional AT test, one should consider the following facts: if the process is truly of FOPDT, the frequency data will be accompanied with errors which would lead to an erroneous ratio of e/r; on the other hand, if the process is of higher order, the FOPDT model derived from the AT test would have a lower value of O/r than other parametric fitted models. Since O/T ratio of a FOPDT model is essential for tuning a model-based PID controller, the controller thus obtained would be tightly tuned and the control system would be apt to have more oscillatory responses when subjected to modeling errors. It has been noticed (Smith, 1972) that a FOPDT model that has a better fit to the step response of the true process would have a larger value of e/r that would lead to a more robust tuning and a minimal ITAE design. It is thus the purpose of this article to propose an autotuning method using a proposed attotuning test. The proposed AT test is similar to the one of Astrom and Hagglund except the output is tailed-off at the end. The amplitude and the period of the constant cycles together with input and output moments in one run are used to compute the parameters of the ~~ Correspondence concerning this note should be addressed to H.-P. Huang. AIChE JournalSeptember 1996FOPDT model. The resulting FOPDT model is then used to determine a model-based PID controller. When applying this proposed method to a true FOPDT process, the resulting FOPDT model for autotuning would have perfect match. On the other hand, as an approximation to higher-order processes, the derived FOPDT model for autotuning would emphasize having a good fit to the step response of the true process. Such an FOPDT model usually has a close ultimate frequency but a smaller ultimate gain compared with those from the conventional AT test. A smaller ultimate gain ...

A Methodology for Autotuning of Multivariable Systems

“…) (8) Example TY: G p3 (s) ) ( -0.1153(10s + 1)e -0.1s (4s + 1) 3 0.2429e -2s (33s + 1) 2 -0.087e -12.6s (43s + 1)(22s + 1) 0.2429e -0.17s (44s + 1)(20s + 1) ) (9) Example OR: G p4 (s) ) ( 0.66e -2.6s 6.7s + 1 -0.61e -3.5s 8.64s + 1 -0.0049e -s 9.06s + 1 1.11e -6.5s 3.25s + 1 -2.36e -3s 5s + 1 -0.01e -1.2s 7.09s + 1 -34.68e -9.2s 8.15s + 1 46.2e -9.4s 10.9s + 1 0.87(11.61s + 1)e -s (3.89s + 1)(18.8s + 1) ) (10) Example T4: G p5 (s) ) ( -2.986e -0.71s 66.67s + 1 -5.24e -60s 400s + 1 -5.984e -2.24s 14.29s + 1 0.0204e -0.59s (7.14s + 1) 2 -0.33e -0.68s (2.38s + 1) 2 2.38e -0.42s (1.43s + 1) 2 0.374e -7.75s 22.22s + 1 -11.3e -3.79s (21.74s + 1) 2 -9.811e -1.59s 11.36s + 1 ) (11) Example NI: G p6 (s) ) 1 (s + 1)(2s + 1) 2 (0.5s + 1) ( 0.5 -0.6 0.1 0.2 0.8 0.3 -1.0 0.1 1.0 ) (12) Example DL: G p7 (s) ) ( -9.811e - 5.11e -11s (13.3s + 1) 2 4.61e -1.02s 18.5s + 1 -5.48e -0.5s 15s + 1 -11.18e -2.6s (43s + 1)(6.5s + 1) 14.04e -0.02s (45s + 1)(10s + 1) -0.1e -0.05s (31.6s + 1)(5s + 1) 4.49e -0.6s (48s + 1)(6.3s + 1) ) (14) The performance of the controllers tuned by ATLS and the ATV+ method for the three TITO examples was studied for a step change in the set point of each loop. A unit step change was first applied to the set point of the first loop, and the process responses were recorded; then another step change was applied to the second loop.…”

“…These data were combined with the ATV method to obtain better process models. Other procedures by Sung et al, 9 Huang et al, 10 Wang et al, 11 and Sung et al 12 incorporated relay tests to identify parametric models. Model-based controller tuning techniques may then be used.…”

Combined PID and adaptive nonlinear control for servo mechanical systems

“…Over the years, many techniques have been suggested for tuning of the PID parameters, such as the refined Ziegler-Nichols method [1], the gain-phase margin method [2], an optimization method [3], and one based on the Internal Model Control [4]. Among them, the model-based tuning methods appear to be very encouraging [5]. However, the limitations of PID control rapidly become evident when applied to more complicated systems such as those with a time-delay, poorly damped, nonlinear and time-varying dynamics.…”

Effective Decentralized Tito Process Identification From Closed-Loop Step Responses

“…A majority of the existing techniques for closed-loop process identification are performed in the frequency domain, while the frequency range of interest for such applications usually ranges from zero up to the process critical frequency [13,14]. In practical process control, the closed-loop relay feedback test provides several interesting advantages [15][16][17][18], such as robustness, effectiveness in dealing with strong nonlinear systems, and the ease of combining it with auto-tuning control methods [19,20]. Despite these advan- Wen-Jian Cai and Qiang Xiong are with School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798. tages, however, it is time consuming for the closed-loop relay feedback test to achieve stable oscillation, which is necessary to obtain correct results.…”