IEEE ISIE 2006, July 9-12, 2006, Montreal, Quebec, Canada Modeling and Simulation of a Multivariable Process Control E. Cornieles1, M. Saad1, G. Gauthier2, Hamadou Saliah-Hassane3 The remainder of this paper is organized as follows. The next section gives a description of the workbench. The system identification and modeling are given in section 3. The controller tuning techniques are explained in section 4. Section 5 presents some real time results. Finally a conclusion is given in section 6 Abstract -- This paper presents a comparative survey of different multivariable techniques applied to process control. The modeling of the physical system and real time simulations are also presented using different PID structures and applied for the regulation of level and the temperature of a water reservoir control process. The structure of the multivariable control system has been implanted using LabView software. This structure uses two control loops, the first for the level regulation and the second for the regulation of temperature. Five different PID controllers are included in this paper (Ziegler-Nichols, ITAE, IMC, poles placement and dual loop) and real time results are presented. II. WORKBENCH DESCRIPTION The process used in this paper is shown in Figure 1. The reservoir has a capacity of 0.27 m3 and its section is constant, 0.38 m2. This reservoir has 2 input valves, one for the cold water and the other for the hot water. The flows of these 2 valves are controled to achieve the regulation of level and temperature. The exit flow is fixed manually. A thermocouple sensor is used to measure the temperature and the level is measured using a pressure sensor. Keywords -- Modeling, Simulation, Real time, PID, multivariable control. I. INTRODUCTION In the last decades, digital control was widely applied to get better performances that guarantee the quality, the maintenance and the stability of the process. The utilization of a PID controller is very popular and a lot of works can be found in the literature to show the best regulation strategy. Ziegler-Nichols [1] used the open loop time response to get the controller's gains. Cohen Coon [2] and Ogunnaike and Seborg [8] proposed also techniques while using the open loop time response of the process. Since the reservoir capacity is relatively important, the level control is used between 23 and 50 cm to avoid valves saturation. The controller is achieved using a National Instruments data acquisition card (PCIMIO-16E). This card has 2 digital to analog channels and 16 analog to digital channels. LabView software is used to implement the controller, to measure the level and temperature process variables Pvl and Pv2 and to apply the controls ul (cold water) or u2 (hot water). The control system using the two regulation loops is presented in Figure 1. This global representation of the system permits to visualize the different components of the workbench. Garcia et Morari [6] proposed a multivariable control strategy to tune the PID parameters using the internal model control. Bristol [8,9] analyzed the effect of interactions and perturbation of a multivariable system and proposed the use a static decoupling among the process variables (Haggblom [7]). III. SYSTEM IDENTIFICATION AND MODELING This paper proposes a new modeling approach and compares five different controller-tuning techniques [3]. Real time results for all these techniques using the leveltemperature workbench are also reported to compare the effectiveness of each one. The open loop is used to identify the transfer function of the process level and temperature variables. The output is usually measured following the application of a step input. Figure 2 shows the open loop level time response for a 6 volts set point. From this Figure, it is easy to determine the level transfer function given in equation (1). One notes the time delay of 6 sec. in the level output. 'Groupe de Recherche en Electronique de Puissance et Commande Industrielle, Departement de g6nie 6lectrique, Ecole de technologie sup6rieure, Montr6al, Canada, 0.53e 6s 90s+1 2DMpartement de g6nie de la production automatis6e, Ecole de c technologie sup6rieure, Montr6al, Canada, g ahi 3T6l6universit6, Montr6al, Canada, 1 1-4244-0497-5/06/$20.00 2006 IEEE 2700 (1)
Figure 1. Workbench process illustration 10.0_ -The same procedure can be followed to find the 9.0 - --temperature transfer function. From Figure 3 obtained for a 4 80 - F LEF volts set point, the transfer function is given as follows: 6.0-... 4.0: 1. 15e 8 PV. G(s)= (2) > 20 ri7s+1 1.0 0.0 0This relation is similar to the transfer function found in equation (1) with a gain equal to 1.15 and a time constant 0 Nombre de points equal to 7sec. Figure 2. Open loop level time response 2 2701
7.0-6.0- > 40-t 30 ao 'a 20-1.0 o- PV2 Tuning Approach Table 1. PI Tuning Approach PI Parameters K pi Ziegler- 0.9 ( t)3.33 o Nichols Kr 7C 00 Figure 3. Nombre de points 01 Open loop temperature time response ITAE 0.5 L1. 63 0 6 IC IMC 2.K IV. CONTROLLER TUNING The general controller structure used in this paper is the PID Dual Loop [5] shown in Figure 4. The mathematical representation is given in relation (3). u(s) = K1(ref - Pv - K2SPv + ref - Pv (3) K3 S - A,Pv- A2SPv + K4ref Poles t (P1 + P2) 1 K Kp Placement K X P1 P2 PI Dual Automatic tuning Automatic tuning [5] Loop [5] Where K, is static gain and t time constant and Cx the delay. where K1, K2 and K3 are respectively proportional, derivative and integral gains; K4 is a feedforward gain and finally, A1 and A2 are introduced to approximate second order function. Note that K1 is equal to Kp and K3 is equal to Kp/i. It is easy from this representation to find the classical PID structure by setting AI = A2 = 0 The tuning of the five methods compared in this paper is given in Table 1 for a PI structure. The A1 and A2 dual loop PI parameters are usually fixed as: 2 1 A1 and A 2 where 4 and wn are the W n (W n) damping factor and natural frequency of the system. The multivariable control is therefore based on 2 PID controllers and a static decoupling to minimize the interactions between the process variables. The modeling structure allows to control only the level or the temperature separately or to control both variables in the same time. The diagram bloc of the system is shown in Figure 5. The value of of the static decoupling is used as a weighted constant between the two control variables. In our simulation, is fixed to 2, resulting a 66.66% of control variable 1 and 33,33% of control variable 2. Figure 4. PID Dual Loop Structure V. EXPERIMENTAL RESULTS The control techniques presented in Table 1 have been experimentally verified for the level and the temperature control. The values of P and 32 of Figure 5 allow controlling each loop separately or together. The controller parameters for both loops are given in Tables 2 and 3 for the different techniques. The user interface is implemented using LabView software as shown in Figure 6. The results of all the compared tuning techniques are satisfactory. We only present in the following the 3 2702
multivariable results for the ITAE and PI Dual Loop techniques. Figure 7 shows the level and temperature results using ITAE technique. The control actions are also shown for the cold and hot water valves. We note the faster time response of the level compared to the temperature time response. This last variable acts also as a perturbation signal on the level process variable. The same results are shown in Figure 8 using the PI dual loop tuning approach. We can also see the good transient and static performance of the system. It can be seen the robust performance of this controller for any change of the set point or external perturbations in spite of the high control action. Level: P Figure 5.Multivariable bloc diagram TABLE 2 TUNING PARAMETERS FOR LEVEL CONTROL Parametres du re&gulateur PI Dual Loop Type de re~glage K1 K3 Al A2 K4 Ziegler- Nichols 25.47 1.275 0 0 0 ITAE 13.21 0.1496 0 0 0 IMC 8.49 0.094 0 0 0 Figure 6. Simulation Interface Placement de poles (P1 = P2 15.09 0.4245 0 0 0 = -0.05) PI Dual Loop 28.0 0.001 4.466 15.44 0 4 2703
TABLE 3 TUNING PARAMETERS FOR TEMPERATURE CONTROL Parametres du re&gulateur PI Dual Loop Typegde K1 K3 A1 A2 K4 re~glage Ziegler- 0.6848 0.0257 0 0 0 Nichols ITAE 0.45 0.0542 0 0 0 IMC 0.3043 0.0435 0 0 0 Placement de p-les (P1 = P2 0.6522 0.0951 0 0 0 = -0. 125) PI Dual Loop 0.8 0.033 5.73 16.23 0 6.0 5.0 #/- REF2 (I) - 4.0 0* r 3.0 a) n 2.0 REF1 > 1.0 0.0 U2...~~~~~ U1 15.0 -r U) (- 10.0 0 > 5.0 -._ 0) 0.0 - > -5.0 - -10.0 - Number Figure 7. Number of points of points VI. CONCLUSION This paper has presented the modeling of a multivariable process control and a comparison between different tuning techniques. A general PID structure was implemented for both level and temperature control loops. The optimal tuning parameters showed the good performance of the controllers. However, in the multivariable case, the ITAE and Dual Loop control actions showed better performance and robustness for external perturbations. PV2 Level and temperature results using ITAE technique 1000 1000 5 2704
6.0 REF2 D\ /f 5.0 - v 4.0-0* r 3.0 > 1.0 2.0 REFiPV 0.0 0 Number of points 1000 15.0- >0.0-50 '/1 o-5~~~~~~~~~~~~~~~~~~~~~.. en\ \= A...~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...... -50 Number.. of.points 1000. -20. Figure 8. Level and temperature results using PI dual loop teehnique REFERENCES [1] J.G. Ziegler, and N.B. Niehols, "Optimum Settings for Automatic Controllers" Trans. ASME, Vol.. 64, 1942 [2] G.H. Cohen, and Coon, G. A.,"Theorical Consideration of Retarded Control", Trans. ASME, Vol. 75 pp. 827-834, 1953 [3] B. Cornieles and C. Bougeret "Comparaison experimentale de differentes techniques de reglage du regulateur PID et PID Dual Loope", Rapport officiel R97, EPM, 1997 [4] Camacho, and R. Rojas, "A General Sliding Mode Controller for Nonlinear", Chemical Process:, Transaction of the ASME, Vol. 22, December 2000 [5] R. M. De Santis, "A Novel PID configuration for a Speed and Position Control", Transaction of the ASME, vol.116, pp. 542-549, September 1994 [6] C.E. Garcia, and M. Morar, "Design Procedure for Multivariable Systems", American Chemical Society, 472-484, 1985 [7] K. B. Haggblom, "Experimental Comparaison of Conventional and Nonlinear Model Based Control of a Mixing Tank", American Chemical Society, 1993 [8] B. Ogunnaike, and W.H. Ray, Process Dynamics, Modeling and Control, Oxford University, 1994 [9] D.E. Seborg, T.F. Edgar, and D.A. Mellichamp, Process Dynamics and Control, Wiley Series in Chemical Engineering, 1994. 6 2705