Extensions and Modifications of Relay Autotuning - Åbo Akademi

Extensions and Modifications of Relay Autotuning

Mats Friman

Academic Dissertation

Department of Chemical Engineering Åbo Akademi University FIN-20500 Åbo, Finland

Preface This thesis is the result of the work that was carried out in a research project about autotuning in process control, at the Process Control Laboratory, Åbo Akademi University during the period of time stretching from 1992 to 1997. A research project concerning autotuning started in 1990 with two diploma works (Kim Roos and Mats Friman) under the supervision of Professor Kurt Waller. This thesis is the continuation of that work. I am grateful to my supervisor, Professor Kurt Waller, for offering me a position as a graduate student at the laboratory and for arranging financial support. I appreciate the qualified guidance in the form of clear and logical scientific principles as well as the honest and prompt judgement of various thoughts and ideas that I suggested during the work. I would like to thank the entire personnel at the Process Control Laboratory for providing a pleasant working environment. Specially I want to thank Associate Professor Hannu Toivonen for interesting discussions and lectures and for co-ordinating the post-gradual courses, Dr. Tore Gustafsson, Dr. Kurt-Erik Häggblom, Kim Roos, and Kati Sandström for valuable comments and interesting discussions, and Jari Böling, Pekka Lehtiö, Päivi Nurmi, and Stefan Rönnblad for their assistance during the experimental runs on the distillation column. Many thanks also go to Ann-Christin Waller for correcting the language in the manuscripts. Valuable comments on the manuscripts by Professor William Luyben (Lehigh University, Bethlehem, Pennsylvania, USA) and Dr. Steve Walsh (Imperial College, London, U.K) are also appreciated. I would like to thank the various funding organizations that have helped to finance this work, including the Academy of Finland / Graduate School in Chemical Engineering, Nordisk Industrifond, Tekes, Neste OY, and Neste Foundation. Finally, I would like to thank my family and friends for their support. Åbo, July 1997 Mats Friman

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List of Publications This thesis is based on the following four papers: I.

Friman, M.; Waller, K. V. Autotuning of Multiloop Control Systems. Industrial & Engineering Chemistry Research. 1994, 33, 1708-1717.

II.

Friman, M.; Waller, K. V. Closed-Loop Identification by Use of Single-Valued Nonlinearities. Industrial & Engineering Chemistry Research. 1995, 34, 30523058.

III.

Friman, M.; Waller, K. V. A Two-Channel Relay for Autotuning. Accepted for publication by Industrial & Engineering Chemistry Research. 1997.

IV.

Friman, M. Automatic Re-Tuning of PI Controllers in Oscillating Control Loops. Accepted for publication by Industrial & Engineering Chemistry Research. 1997.

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Abstract In this thesis extensions and modifications of Åström-Hägglund autotuning are investigated. A method where relay autotuning is extended to multi-input-multi-output control systems is suggested. The method is based on identification of n×n simple two-parameter transfer functions through n identification experiments. The method is experimentally tested on a water-mixer and a pilot-plant distillation column. Two methods where the relay, used in standard autotuning, is replaced by some other nonlinearity are suggested. In the first method, the relay is replaced by a two-parameter nonlinearity so as to improve the accuracy of the identification. In the second method, the relay is replaced by two relays operating in parallel, one on the process output, and the other on the integral of the process output. With this construction, a point on the Nyquist curve at a userselected angle in the third quadrant is identified, something that has certain advantages with respect to controller tuning. Moreover, a method where the ideas of autotuning are utilized for an oscillating (unstable) PI control loop is suggested. An oscillating control loop provides a useful possibility for process identification and subsequent controller tuning. This method has proven to be useful for retuning of unstable PI control loops and for rapid start-up of feedback-controlled chemical processes.

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Introduction Control plays a key role in the operation of chemical plants with respect to economical performance, safety and operability. To realize the role of control at a general level, consider the definition of the concept "chemical process" (Pohjola et al., 1994): "Chemical process is control of (physico-chemical) phenomena for a purpose". This definition clearly shows the necessity of control: without control there would be no functional chemical process industry. An example illustrates the assortment of possible control possibilities involved in the definition above. Say that we have a room and an electric heater, i.e. we have a phenomenon (heat transfer from heater through the room) and a purpose (to make it comfortable for people to stay in the room). If we study this process from a control point of view, we find that some of the control possibilities, ordered according to added complexity, are the following: 1. We can adjust the heating power to be constant. This is easy to implement but it would probably make the indoor temperature too high in summer or too low in winter. 2. We can adjust the heating power according to the time of the year. This would take into account temperature changes between seasons, but it would not take into account unexpected variations in the outdoor temperature. 3. We can adjust the heating power according to the measured outdoor temperature (feedforward control). This control possibility is widely used but it does not take into account all possible disturbances (like changes in the ventilation). 4. We can adjust the heating power according to the measured indoor temperature (feedback control). 5. We can combine possibilities 3 and 4. The present work deals with feedback control of chemical processes, i.e. control possibility 4. The main motivation to use feedback control is that the control purpose usually can be fulfilled even if unmodeled (unknown or unpredictable) disturbances affect the process. However, a feedback connection involves also some disadvantages. In addition to a high degree of complexity, feedback is more difficult to handle than e.g. feed-forward control. This relates to the interaction involved, in the example above a change in the heating power affects (in contrast to feed-forward control) the measured temperature, which in turn affects the heating power, etc. Because of this interaction, there is a risk of the control loop turning unstable. In this work, feedback control is realized through proportional-integral-derivative control (PID control). In the example above, this means that a PID controller would adjust the heating power as a linear combination of the following three components: 1. The difference between room temperature and desired temperature (proportional action), 2. Time integral of the difference between room temperature and desired temperature (integral action), 3. Time derivative of temperature (derivative action). Moreover, PI control, i.e. PID control without derivative action, is studied. The vast majority of controllers in the chemical industry are of the PID type, or a reduced version (e.g. PI or P controllers). Their popularity is easy to understand  they have a simple 5

structure, they are familiar to engineers, and their control capabilities have proven to be adequate for most control loops. In order for the PID controller to fulfil its assignment, the weights of proportional, integral, and derivative action must be individually chosen for each implementation. We say that we tune the controller. In a typical chemical plant there are hundreds of PID feedback loops. They are often poorly tuned because the choice of PID controller weights (hereafter called PID controller parameters) requires professional knowledge by the user. The theory of controller tuning involves sophisticated mathematical manipulations, including complex-valued functions, differential equations, and integral transforms. It is thus not a surprise that the average process engineer repeatedly tunes controllers by trial-and-error methods. Because the PID controller has three tuning parameters, controller tuning by trial and error is a search in the threedimensional space. Evidently, optimal controller parameters are seldom instantly obtained by trial and error. Many modern controllers are equipped with various adaptive techniques such as self-tuning, on-line tuning, and autotuning. These features provide easy-to-use controller tuning and have proven to be well accepted among process engineers. One of the most common approaches to tune a controller automatically is to connect a relay as a feedback controller to the process during tuning. This relay autotuner was introduced in 1984 (Åström and Hägglund, 1984) and today several commercial controllers are equipped with this device. In the present thesis, this particular controller tuning approach, commonly labelled "autotuning", is considered. Autotuning is appealing to process engineers as it provides systematic controller tuning in the easiest possible way, i.e. by pressing a button. The purpose of this work is to suggest extensions and modifications of standard relay autotuning. These extensions and modifications regularly show improvements (in terms of accuracy, speed or robustness) of the autotuning procedure compared to the standard method, albeit at the cost of some added complexity. The contents of the four papers are summarized below.

I. Autotuning of Multiloop Control Systems Multivariable systems are more difficult to tune and control than single-input-single-output (SISO) systems are. A multivariable control system where the control loops are independently tuned according to recommendations given for SISO systems often results in an unstable system. The Åström-Hägglund autotuner is designed for SISO-systems and therefore cannot be directly applied to multi-input-multi-output (MIMO) systems. However, with a few modifications autotuning can be applied also to multivariable systems and in this paper one such method is suggested. The approach here suggested is to employ relay autotuning in the identification of a multivariable model of the process. When an identified process model is available, a wide assortment of model-based controller tuning designs found in the literature can be utilized. From a control point of view, it is often convenient to model chemical processes with a firstorder-plus-dead-time model, ke − Ls / ( Ts + 1) . This model has three parameters: the gain k, the dead-time L and the time constant T. In relay identification where only two parameters of the process are identified (i.e. the ultimate gain and the ultimate frequency), it is not possible to 6

identify a three-parameter model in a reliable way. However, for the purpose of feedback control, accurate estimation of the time constant is often unnecessary. Considering frequencies important to feedback control, it turns out that, if the time constant is large (T>>L), the firstorder-plus-dead-time model is well approximated by an integrator-plus-dead-time model ke − Ls / s . Analogically, if T is small (T