RELAY METHOD ON AUTO-TUNING AUTOMATION SOLUTIONS. Marco Gonçalo de Sousa Neves

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1 RELAY METHOD ON AUTO-TUNING AUTOMATION SOLUTIONS Marco Gonçalo de Sosa Neves Universidade Técnica de Lisboa, Institto Sperior Técnico, Lisboa, Portgal. Abstract: The PID controller is in the back-bone of the majority of control systems in indstrial environment. As for its simplicity or experienced efficiency the PID controller came to stay. Therefore, it is jstified to work on improvements to its implementation and efficiency, since any innovation in this widely applied method will have a tremendos impact. By stdying modern methods of self-tning, the Relay method for system identification appears as a way to the improvements. Throghot this work, Relay method and some improvements are presented and implemented in software on a Siemens PLC. As a recent method, Siemens does not have Relay-based algorithms for the calibration of PID controllers in the high range of atomation soltions. This techniqe of atomatic calibration of PID controllers can be efficiently applied to most indstrial control systems, with low interference in the prodction process. This is ato-tning the distance of a btton in the SCADA (Spervisory Control and Data Acqisition) system. Keywords: Ato-tning, Atomation, PID, Relay Method. 1) INTRODUCTION There is an increasing interest of ato-tning soltions, since any innovation in the PID controller design will have a tremendos impact. The goal of this work is to stdy, improve and implement in, a Siemens atomation soltion, modern ato-tning methodology that can be applied to most control loops existing in indstrial environment. It is known that great part of PID controllers PID who play its role in the indstry, make it below of its excellent reglation. These can be optimized by 2 ways, appealing the time consming tests of manal reglation or throgh techniqes of ato-tning. After a brief stdy of some of the techniqes of ato-tning existing, the one that I considered more adeqate to the se in processes of nknown and varied model and whose se does not intervene significantly with the prodctive process is known as Relay Method. In this work, I stdy and implement an atomatic techniqe for calibration of PID controllers that can have application to the majority of the systems of indstrial control; Nowadays atomation is available with many different tools and eqipments that make it possible to attain the high standards of qality and efficiency. Empirical stdies have shown that many of the existing control loops in indstrial processes do not flfil their dties with the desired efficiency, leaving a large potential for improvement. Figre 1 - Potential improvements in control loops Advantages of betting in optimal control: Decrease consmption of electricity; Less eqipment wear field; Increased prodctive capacity; Redction of processing time; Increase the qality of the final prodct; Redce the workload of operators; Increased safety of operation; Redced sensitivity to distrbance; Stops or maintenance work, less freqent; Increased efficiency of prodction; Minimizing the environmental impact, by saving reagents. 1

2 The paper is organized as follows. Section 2 describes the experimental system setp, were the test were made. Section 3 describes the classic Relay method, discssing practical aspects of the implementation, and the improvements that were. Section 4, the experimental reslts of different controllers with the experimental setp are evalated and discssed. The inflence of the parameters in the performance of the projected controllers is also evalated. Finally, in Section 5, we present conclsions and directions for ftre work. 2) EXPERIMENTAL SETUP In order to enable the development and testing of the proposed algorithms was given an experimental platform, enabling the analysis, operation and data recording. To this end, it took 3 key eqipment, and software development. The 3 key eqipment sed were, a ET200S-CPU SIEMENS PLC, the pilot plant of the PCT-9 Armfield and a compter monitoring system. Figre 2 - Experimental setp The objective is to control the water level in the tank. The water is pmped to the tank with a level sensor, by a water pmp and a control valve that will be or control otpt via an analoge 4-20mA signal. The tank has 2 electro-valves throgh which the flow ot of the tank is handled. Operation of the system will be made throgh the said motorized valve. The SCADA system offers an easy control of the system, integrating the possibility of graphical analyses. The ato-tning methodology is parameterized and activated directly in the SCADA system. Figre 3 - SCADA system image 3) PID CONTROLLER As was already told this paper is dedicated to modern ato-tning soltions that can be sed in the design of a PID controller. Becase this is a well stdied sbject I will jst represent the discrete PID formla sed in the PLC. n kpt kptd ( n) = kpe( n) + e( k) ( y( n) y( n 1)) T + T i k = 0 4) TUNING METHODOLOGIES a) Conventional Tning Methods Ziegler and Nichols proposed in 1942 two different tning strategies for PID controllers. These have been sccessfl contribtions that proportionate acceptable control performance in many systems. However these methods have week points that led them not to be widely sed. Becase its implementation is qite npredictable many times casing nintended distrbance in the prodction process. b) Tning with Relay Method The relay method presented as an alternative to the conventional method of Ziegler-Nichols for closed loop, in the identification of model systems by Astrom and Hagglnd [8] in 1994, seems to be the soltions. It has the advantage to generate and maintain a controlled oscillation (the magnitde of the oscillation can be defined). The sccess of this method is de to the simplicity of the mechanisms of identification and calibration, and also its applicability in slow or highly nonlinear systems. Relay method is very efficient in determining the critical gain K and critical freqency ω. Advantages of the Relay method: Reqires little mathematical processing; Identify the characteristics of the model arond its, critical freqency (where phase margin is π ); Fits varios indstrial processes; Application does not reqire knowledge of the mathematical model of the system; Calibration possible in prodction, becase the distrbance is limited by its parameters; Low sensitivity to distrbances; For processes with a very high time constant, it is more efficient in terms of time than conventional methods of step or plse; Avoids the tedios, procedre of trial and error in determining the critical gain. 2

3 The relay proposed by Astrom and Hagglnd was an Ideal Relay. Figre 4 - Ideal Relay Their procedre determines the gain introdces capable of introdcing a delay of half cycle when operating in feedback. This is the critical gain, which is related to the point where the Nyqist crve first crosses the real axis. Part of the sccess of this method of identification comes from the fact that this can be taken directly from the experimental reslts, since very rarely the model of the system is know. Figre 5 - Example of relay implementation The procedre is relatively simple and efficient. Involves, physically moving the maniplated variable from the process. Considering a system of positive static gain. When increasing the inpt (action), the otpt of the system tends to increase. When the PV (process vale) passages of the SP (setpoint), the inpt is moved in the opposite direction. As a reslt we have an oscillation of the system, were the amplitde can be adjsted. The relay was integrated in a PID controller, reslting in a similar model to the one in figre 6. When the operator activates the ato-tning, the PID is deactivated and the control passes on to the relay, after determining the parameters, the PID controller is activated with the calclated gains. Figre 6 - Controller with integrated relay The classic Ideal Relay proposed by Astrom and Hagglnd, was improved mainly in two aspects: Less sensitivity to the presence of noise, with the introdction of hysteresis. Atomatic adjst of the Ot _ Bias (mid vale sed as otpt of the Relay) necessary to easily obtain a symmetric oscillation of PV arond SP. Figre 7 - Relay with hysteresis Withot the addiction of hysteresis, the calibration of the controller is easily affected by the presence of noise or distrbances in PV. In an experiment sing relay with hysteresis the critical gain can be easily obtained from the eqation: 4 K = 2 2 a π ε Where represents the amplitde of actation sed in the relay, ε represents the hysteresis and a is the amplitde of the reslting oscillation. As for the critical period, P, it can be obtained directly from the oscillation, like demonstrated in figre 5. Having K and P we can calclate de PID gains sing the table for the closed-loop method of Ziegler- Nichols: P Kp Ti Td 0,5K PI 0, 4K PID 0,6K 0,8P 0,5P 0,125P Table 1 - Ziegler-Nichols table for the closed-loop method The atomatic adjst of Ot _ Bias brings s to the sitation were the pper and lower actation vales of the relay prodce similar effect on the process, reslting in a better approximation of the mathematical model sed. Within each complete period of PV, Ot _ Bias is corrected if the difference between the positive and negative periods is more than 10% of the oscillation period: TUP T DOWN Ot _ Bias = Ot _ Bias ( TUP + TDOWN ) It is now possible to calibrate a PID controller, by pressing a btton in the SCADA system, after defining hysteresis and the magnitde of actation of the relay. 3

4 5) EXPERIMENTAL RESULTS In this section are presented and discsses the reslts obtained in experiments performed with different tning methodologies. It is also stdied the effect of parameter variation in the relay. a) Ziegler-Nichols open-loop tning method Figre 10 - Closed-loop Ziegler-Nichols tning Figre 8 - Reaction crve of open-loop Ziegler-Nichols tning 1 This method presents some difficlties in implementation. The experience takes a long time (20 mintes) in this system, and mst be initiated at a stable PV. Another difficlty of this method is the amplitde of the step that has to be different depending on the systems characteristics. The estimation by this method cased a change in PV, abot 30%, which makes the se of this method, dring the prodction process impractical for many systems. Figre 11 - Performance test to ZN closed-loop tned PID The closed-loop method of Ziegler-Nichols gives s a very slow response and an oscillatory behavior. This behavior can scceed of the test characteristics itself and leads to higher wear of the actator. c) Ideal Relay Figre 9 - Performance test to ZN open-loop tned PID The controller reveals some overshoot and good steady-state follow-p. The controller responds qickly and smoothly. On the way down to the setpoint of 50% the driver revealed a large deviation de to a blockage of the valve and not the control methodology. b) Ziegler-Nichols closed-loop tning method This experiment also took 20m. It s an iterative method that can become dangeros becase of the ncontrolled oscillation that it generates. Figre 12 - Test to the PID tned sing Ideal Relay As can be seen from the above figre, it is not advisable to estimate the PID sing an ideal Relay becase it is very sensitive to distrbances or noise in the process variable. Any passage of PV from SP will case an nwanted change in the maniplated variable. 1 Legend: Spa Setpoint ato; Spm Setpoint manal; Act Actal vale (PV); Ot Control otpt (MV). 4

5 d) Relay with 2% hysteresis Figre 13 - Test to the PID tned sing Relay (2% hysteresis) The estimation of parameters with 2% hysteresis represents a significant improvement over the ideal relay. The identification takes abot 4 mintes bt in trn the response is mch smoother. At this stage, withot introdcing external distrbances in the system, the PID controller reveals good performance despite being slightly slower than the ideal relay is qite smooth. Figre 15 - Test to the PID tned sing (15% amplitde) The decrease to 15% makes the estimation slower. The decrease reslting in the proportional gain shold make it smoother before distrbance. The controller has been improved by the decrease in the amplitde of the Relay. g) Inflence of distrbance in Relay method e) Atomatic adjst of Ot _ Bias in Relay Figre 14 - Test to PID tned sing Relay withot Bias ato-adjst As shown by the figre, higher level is reached mch faster than the lower one, sggesting a system nbalanced between the two levels of MV (maniplated variable). This leads to a less accrate estimation of the vales determined dring the identification system. As a reslt the controller withot the atomatic adjst, seems to be very slow. A very high vale of time integral is the sorce of great difficlty on eliminating the stationary error. It ths appears that the atomatic adjstment is an important factor in the estimation of the controller, greatly benefit from the atomatic adjstment of Ot _ Bias. f) Inflence of the amplitde of the Relay In this experiment we test the inflence of the amplitde of the maniplated variable (MV) between it s high and low level of the Relay. In previos experiments, the vale was fixed at 25%. Figre 16 - Calibration and test of PID with distrbance In order to predict the behavior estimated controllers, in less favorable conditions, it is manally introdced in the experiment a distrbance of abot 2% in level of water in the tank. The distrbances are present since the beginning of the experiment. As shown by the previos figre, the controller reacts to distrbances withot mch variation in the range of action. It has been obtained by the method Relay, a controller very efficient and with good behavior in the presence of distrbances. Parâmetro Valor (%) PV 2 Ot 15 Ot _ Bias 38,1 Table 2 - Relay parameters in the presence of distrbance Kp Ti Td PID 10, Table 3 - Estimated PID controller gains 5

6 6) CONCLUSIONS AND FUTURE WORK This work s main goal was to improve the modern method of self-tning a system of Siemens atomation. In ftre work, it wold be important to observer and conseqently to a better overall performance. In order to estimate gain and critical period more precise, the variation can be simltaneosly implemented in the iterative process of variation. Ths, in addition to vary the focal point of action that balances the excitement, the amplitde of action wold also be adjsted to adapt to the needs of the system. In order to complement the method of self-tning presented, it is expected that it can stretch to the development of a monitoring system of higher edcation that is continosly monitoring and recording the efficiency with which the PID controllers are performing their dties. In this work, we developed a methodology for atotning which shows that the method Relay is able to be sccessflly applied to the majority of PID control systems. In search of a more efficient control several factors that may contribte to their performance. Yo can not jst concentrate on getting the best parameters for the PID and ignore the existence of imperfect actators or sensors as well as freqent distrbances. The method Relay easier to tackle the calibration of PID controllers, it allows a rapid avoiding the need for a thorogh knowledge of control. Despite the good performance of the PID controller estimated by the response crve of Ziegler-Nichols, it is considered that the method overcomes the relay becase of its simplicity, fewer restrictions and less interference in the prodction process. Analysis of the introdction of hysteresis in the relay method, it is conclded that this clearly improves the estimation, redcing their sensitivity to noise and distrbance. Drivers estimated to have an ideal Relay oscillatory behavior even in a stable condition. It was also conclded that the vale shold be the least able to easily generate a sstained oscillation, for a vale too high increases the proportional gain of PID and respectively, their sensitivity to distrbance. The atomatic convergence enabled improvements to the method of classical Relay, greatly facilitating its implementation and improving the estimation of parameters. Method Relay appears to be capable of scaling PID controllers with good rejection of distrbances. Once the distrbance decreases, the PID back to respond gently normal. The controllers obtained were able to provide rapid and smooth as needed. This is a method that easily estimated controllers largely identical to the same parameters. Method Relay proved a sccessfl option to achieve the targets proposed, inclding to implement a ACKNOWLEDGMENTS I wold like to thank to all personal, from work or academic environment that encoraged this work. The development proved to be a great challenge that I m glad for the accomplishment. REFERENCES [1] Y, Cheng-Ching. Atotning of PID Controllers: A Relay Feedback Approach, 2ªEd. Springer. London, 2006; [2] Astrom, Karl J. and Hagglnd, Tore. Advanced PID Control. ISA, 2005; [3] Dillenbrg, Marcos R. e Ferraz, G. M. Implementação de Controle PID Ato-Adaptativo tilizando o mínimo de recrsos em microcontroladores de baixo csto. 4º Congresso Inst. de Atomação, Sistemas e Instrmentação. São Palo, 2004; [4] Leva, A., Cox, C. and Rano, A. Hands-on PID atotning: a gide to better tilisation, IFAC Professional Brief, 2003; [5] M. Grégroire, A. Desbiens, and É. Richard. Development of an Ato-tning PID and Applications to the Plp and Paper Indstry. In Third International Conference on Indstrial Atomation, pages , Montréal, Canada, 1999; [6] Flores T., Antonio. Relay Feedback Ato Tning of PID Controllers, Universidad Iberoamericana, Mexico, 2007; [7] Franklin, Gene F., Powell, J. David e Emami- Naeini, Abbas. Feedback Control of Dynamic Systems, 4ªEd, Prentice Hall, 2002; [8] Astrom K.J. & Haglnd T. H. New Tning Methods for PID controllers, Proc. 3ª Eropean Control Conference, p , 1995; [9] K. J. Astrom & T. Hagglnd, PID Controllers: Theory, Design, and Tning. International Society for Measrement and Con. 1995; [10] Ziegler, J.G. e Nichols, N.B. Optimm Settings for Atomatic Controllers. Trans. ASME, pp , 1942; [11] Lyben, WL. Getting more information from relay feedback tests. Ind. Chem. Res.,