Hybrid controller to Oscillation Compensator for Pneumatic Stiction Valve

Original Paper Hybrid controller to Oscillation Compensator for Pneumatic Stiction Valve Paper ID: IJIFR/ V2/ E1/ 011 Pg. No: 10-20 Research Area: Process Control Key Words: Stiction, Oscillation, Control Valve, Sliding Mode, PID Omer Mahagoub Ahmed Mahmoud Elagemi Assistant Professor, Department of Control Engineering International University of Africa Madani St, Khartoum 12223, Sudan Abstract Oscillations in process control loops significantly affects the performance of the controller and lead to devastate of energy, a raise of process variability, and a severe deprivation of product quality. Such oscillations are either the result of badly tuned controller or produced by the undesirable presence of a nonlinear element. Valve stiction due to wear and tear or due to mishandling of the actuator is an example of malfunction control loop component that leads to such situation. Stiction problem is by far the most frequent anomaly in process and control. In this paper, I propose a new method to compensate for valve stiction, reduce the variability of the process, and increase the life cycle of the valve. Therefore, a new approach based on sliding mode control with PID is applied to compensate for an unknown valve stiction degree. The performance of the new approach is presented through various simulation results which demonstrate the strength of the approach when compared to recent published methods. 1 Introduction One third of the poor design in industrial application is initiated by the presence of non-linearity in control valve such as static friction. [1] This nonlinearities will effect to the oscillation problem producing the limit cycle which leads the increase of variability in the process. Oscillation problems also can be generated by the presence of dead band and backlash. The corresponding input-output characteristic can be altered by the presence of nonlinearities factor in fig 1. Dead band and stick band as static part are described by S and J expresses the slip jump. Many researches have discussed and studied the problem by identifying the stiction as black box [2], control design using compensator, [3-6], detection and quantification of the stiction presence investigated in control system by identifying some variable such controller output (OP) and controlled variable (PV) [7-9] while the identification of backlash is also presented in Tore [10]. This proposed controller design will employ the stiction valve model as Karnopp model [11] which is evaluated in Garcia [12]. The evaluation of valve actuator problem in order to deal with the presence of hard nonlinearities, the maintenance is performed, once the stiction is detected commonly every 6 months and 3 years. The control method to compensate the presence of oscillation is developed to get a desirable output performance by removing oscillation without regular maintenances. Our main purpose for this paper is designing PID-sliding mode controller to compensate the oscillation problem www.ijifr.com Copyright IJIFR 2014. All Rights Reserved IMPACT FACTOR = 3.059(SJIF) 10

due to the stiction. Once the oscillation is detected and PID controller suffers the increasing error, sliding mode controller will augment the PID controller to compensate the oscillation and eliminate the error. This process reveals a better performance than the previous control method has been proposed. The analysis to be performed is considering the pure control process without time delay and with a time delay. The organization of this report is composed as follows. Section I will elaborate the brief nonlinear problem presence in pneumatic valve and literature review. In section II, model of the section is presented. In section III, the controller design is constructed using sliding mode and PID. The sliding mode controller will assist PID to reach and follow the references. The simulation result for the system performance of PID Sliding Mode with time delay and without time delay is presented in section IV. In chapter V, the papers will summary the outcomes. II. Stiction Model Of Pneumatic Valve In pneumatic valve stiction the relation between Input outputs can be seen in figure 1. In Garcia, eight proposed model is developed. One of the models, Karnopp model will be used in this paper can describe the control valve dynamic as stick-slip. The parameter used in this paper also was employed in Karnopp model (using S as the static part and J as slip jump). Newton law will give m, x, describes as the mass of the valve, and the steam position respectively. Figure 1: Corresponding pressure and valve relation for pneumatic control valves. 11

Figure 2. Proposed control design block for stiction valve in process without delay transport When valve stem is in point A, B and C, the stem valve is getting stuck and it has the initial velocity and acceleration as zero. The Eq. (1) becomes: F Pressure = F Spring + F Friction When valve in point A the corresponding equation for describing it will be: When valve stem in point B and C, the equation can be derived as Eq. (7) and (8). When v has some values that more than 0. The model will be The total equation and dynamic of the system after integrating the process component can be seen in Eq. (14). The total model design and nonlinearity performed in this paper is shown in the equation 15,while the block diagram for controller design is described n figure 2 and figure 8 for system with time delay and without time delay. 12

3 Controller Design The PID control designs are able to generate good performance for the steady state responses in the absence of Karnopp valve for stem can be presented as Eq. (5). The constant values used to simulate the system are mentioned in Garcia 2008. Viscous friction coefficient (Fv) and mass (m) are 612 Ns/m and m=1.36 kg. As the big comparison between two values, the system can be approximated as first order with time constant τv=fv/km. The system design for this problem will be connected to the process model representing the chemical reaction or dynamic flow of the fluid. The model is described by the first order system in Eq. (10). The system will be connected to the dynamic of valve system coming from the stiction. The first and second derivation of the stiction position to the output system can be derived the following in Eq. (11) and Eq. (12).However, the stiction emerging in the valve will affect to the limit cycle behavior and create oscillation in the final steady state responses. The undesirable oscillation will become the problems, therefore the additional controller which has a good response to control the nonlinear behavior to eliminate oscillation and have robustness are required. In this case, the sliding mode controller suffices the requirement and employees to improve the performance and the robustness due to the disturbance and noise [13-15]. The sliding mode design consists of building the sliding surface and forcing the system to follow the sliding surface called as sliding condition. The equation governs to generate sliding surface can be seen in equation: Figure 3: Proposed control design block for stiction valve in process with delay transport 13

The general design for PID control utilizing sliding mode control for stiction valve compensation in the process system can be seen clearly in figure 2. The simulation for system design in the system will combine the conventional method employing PID control and the sliding mode control which directives. The selection coefficient of λ and K slide will have a great effect to the time required by the system to follow the trajectory while it also initiates the chattering effect as the selection of higher K slide.the chattering effect can be seen in figure 4. Figure 4. Chattering effect of Sliding Mode [14]. 4. Simulation Results I simulated my proposed control for stiction without consider the time delay and with time delay. The input system employed as reference is sinusoidal waves. In this paper, I applied the PID during 0s up to 10s and SMC during 10s up to 15s. In figure 5, I can see the PID and SMC performance to control the valve for process without time delay and without time delay. I also investigate the time delay Effect to valve system and what the optimum time delay for our SMC. A. PID and SMC without Time Delay Process The following table is the coefficient of our controller without time delay. The variation of coefficient friction for small, medium and big coefficient for the design of vendor, nominal and rough. The value of corresponding design of those friction can be seen completely in Garcia[12]. Table 1. Controller Coefficient without time delay The following figure illustrates our proposed control without time delay with sinusoidal input reference where I applied PID during 0s up to 10s and SMC during 10s up to 15s. I can see that SMC improve the PID performance to control the valve. 14

Figure. 5. Response system for tracking 3 difference values of friction using PID and SMC with sinusoidal input reference Figure 6 shows PID performance in detail and figure 7shows the SMC performance. Red, blue black and green are described each performance of vendor, nominal and rough nonlinear system respectively. The figure shows that the less friction is applied the smaller error of the steady state Performance will be. In figure 7, when the friction of model employed increase, the system will have more chattering. Therefore, the system coefficient This result employs similar coefficient value for λ and K slide for vendor, nominal and rough. Figure 6: Response system for tracking 3 different values of friction using PID with sinusoidal input reference 15

Figure. 7. Response system for tracking 3 different values of friction using SMC with sinusoidal input reference The following figure 8 and 9describe the performance of system using the step references. Figure. 8. Response system for tracking 3 different values of friction using PID and SMC with sinusoidal input reference Figure 9 shows the PID performance to follow the step input reference during 0s up to 10s and figure 10 illustrates the improvement our controller using SMC during 10s up to 15s. When the friction increases, the system will have a bigger overshoot than the smaller frictions. The oscillation will increase when the value of friction is increased and it becomes more dominances to the linear parts. 16

Figure 9: Response system for tracking 3 different values of friction using PID with step input reference The figure 10 for vendor will generate oscillation but it still produces the higher error. For rough design, the error steady state will have smaller error but it produces higher chattering. B. PID and SMC With Time Delay Process The following table is the coefficient of our controller with time delay. The variation of coefficient friction from vendor, nominal and rough. The value of corresponding design of those friction can be found in Garcia[12]. Table 2 provides understanding the influence of friction and selection of coefficient of controller to the error value. Due to the presence of time delay, the increase of friction will diminish the error magnitude with the similar gain and coefficient controller. On the other hand, the increase of coefficient will elevate the error value when applying the similar friction of valve for vendor design. Finally, maximum resistance of time delay can be achieved by selecting carefully the coefficient of controller which is K smc equal to 20 and time delay maximum is 0.01 for vendor design. The figure 11 illustrates the SMC performance with time delay and varying K smc. The PID is applied for 0-10 s to 17

control the valve with time delay and PID-SMC will continue from 10 to 15s. PID-SMC worked successfully when the coefficient of Ksmc is properly selected. When the coefficient of control decreased the system can adapt nd follow the references since they do not generate a great correction due to the errorness however, the higher significant correction will lead the poor performance for tracking reference in the system with time delay. Therefore, in the red line which have the smaller coefficient, the system can follow the reference while the higher coefficient in the blue line will fail to follow the references. Figure 11. Response system for tracking reference using SMC with varying Ksmc and time delay Figure 12. Response system for tracking 3 different values of friction using PID and SMC with step input reference and time delay 18

The following figure shows the SMC performance in detail to improve the controller performance during 10s up to 15s.When the smaller is decreasing, the system will perform better and follow correctly to the references. It can be seen clearly in figure 12 that the vendor and nominal design will have less overshoot and final error than the rough friction design. Figure 13. Improvement controller using SMC for tracking 3 different values of friction with step input reference and time delay By adjusting the coefficient of Ksmc (coefficient of sliding mode), I can obtain the maximum of time delay that can be handled by the system. The time delay maximum in our simulation 0.01 with coefficient as 20 for vendor friction design. The simulation result for the maximum tolerance of time delay that can be applied in this system is presented in figure 14. Figure 14. The response system for tracking 3 different values of friction with maximum time delay 19

5 Conclusion This paper for the design sliding mode and PID will be simulated for the process system with time delay and without time delay. The selection of controller coefficient such Kslide and λ are required adjusting.the higher value of coefficient will follow the reference faster but it will have the higher chattering. The higher coefficient friction of nonlinear will produce the higher oscillation and errors of the response when following the references. The time delay analysis in part II will approach the real system. The adjustment of controller coefficient will impact to the maximum sensitivity of the controller to compensate the delay system. In our system, the maximum time delay response that can be compensated by the sliding mode and PID controller. I simulated PID as common controller in the industry from 0 to 10.s and I improved the controller using SMC from 10 to 15. I can see from the figures I show that the performance of SMC can assist the PID. I also applied time delay to test PID and SMC performance and I find the maximum delay effect can be coped up by the controller. SMC is able to reach the desired trajectory with time delay and without time delay and have improved the error from PID controller. 6 References [1] Sivagamasundari, S., & Sivakumar, D. (2013). A New Methodology to Compensate Stiction in Pneumatic Control Valves, (6), 480 484. [2] Zabiri, H., & Mazuki, N. (2010). A Black-Box Approach in Modeling Valve Stiction, 9 16. [3] Ha, T. (2002). A friction compensator for pneumatic control valves, 12,897 904. [4] Karthiga D., K. S. (2008). A new stiction compensation method in pneumatic control valves. International Journal of Electronics and Computer Science Engineering. [5] Srinivasan, R., & Rengaswamy, R. (2008). Approaches for efficient stiction compensation in process control valves. Computers and Chemical Engineering, 32(1 2), 218 229. [6] De Souza L. Cuadros, M. A., Munaro, C. J., & Munareto, S. (2012). Improved stiction compensation in pneumatic control valves. Computers & Chemical Engineering, 38, 106 114. doi:10.1016/j.compchemeng.2011.09.006. [7] Choudhury, M. A. A. S., Shah, S. L., Thornhill, N. F., & Shook, D. S. (2006). Automatic detection and quantification of stiction in control valves. Control Engineering Practice, 14(12), 1395 1412. [8] Rossi, M.; Scali, C. Automatic Detection of Stiction in Actuators: A Technique to Reduce the Number of Uncertain Cases. In Proceedings ofthe SeVenth IFAC-DYCOPS Symposium, Cambridge, MA, July 5-7, 2004;Paper 157. (CD-ROM.). [9] M. A. A. Shoukat Choudhury, Mridul Jain and Sirish L. Shah, Detection and Quantification of Valve Stiction, Proceedings of the 2006 American Control Conference. [10] Hägglund, T. (2007). Automatic on-line estimation of backlash in control loops. Journal of Process Control, 17(6), 489 499. doi:10.1016/j.jprocont.2007.01.002 [11] R.A. Romano, C. Garcia, Karnopp friction model identification for a real control [12] Garcia, C. (2008). Comparison of friction models applied to a control valve. Control Engineering Practice, 16(10), 1231 1243. doi:10.1016/j.conengprac.2008.01.010 [13] H K. Khalil, Nonlinear Systems, Prentice-Hall, 2002 [14] J.J. E Slotine, and Weiping Li, Applied Nonlinear Control, Prentice- Hall, 1991 [15] Horacio. J Marquez, Nonlinear Control Design Systems Analysis and Design, John Wiley and Sons, 2003. [16] C Edwards, and S Spurgeon, Sliding Mode Control: Theory And Applications, Taylor and Francis, 1998. [17] Maolin Jin, Sang Hoon Kang, and Pyung Hun Chang, Robust Compliant Motion Control of Robot With Nonlinear Friction Using Time-Delay Estimation, IEEE Transactions on Industrial Electronics Vol 55, No. 1, January 2008. [18] Shoukat Choudhury, M. a. a., Thornhill, N. F., & Shah, S. L. (2005). Modelling valve stiction. Control Engineering Practice, 13(5), 641 658. doi:10.1016/j.conengprac.2004.05.005 20