International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: editor@ijaiem.org Volume 3, Issue 5, May 2014 ISSN 2319 - 4847 DIRECT SYNTHESIS APPROACH FOR DESIGN OF PID CONTROLLER Ms. Dighe Y.N1, , Prof. Kadu C.B2 and Prof. Parvat B.J3 1 2 M.E Scholar, Department of Instrumentation & Control Engineering, Pravara Rural Engineering College, Loni (M.S), India. Associate Prof and Head, Department Instrumentation & Control Engineering, Pravara Rural Engineering College, Loni (M.S), India. 3 Associate Prof, Department of Instrumentation & Control Engineering, Pravara Rural Engineering College, Loni (M.S), India. Abstract The presence of dead time is never a good thing in a control loop. For any process, as dead time becomes larger, the control challenge becomes greater and tight performance becomes more difficult to achieve. The main objective of this paper is to design robust method to PID controller design for first order unstable time delay process and Second order process by using DS-d approach and Modified IMC approach to compare the results of this two methods. Direct synthesis for disturbance rejection (DSd) is employed and analytical expressions are developed to obtain the parameters of the PID controllers. The DS-d design method has a single design parameter, the desired closed-loop time constant, . The new PID controller is nothing but an ideal PID controller by using DS-d approach for unstable & time delayed system. Although the controller is designed for disturbance rejection, the set point response is satisfactory. Two analytical simulation examples demonstrate that the DS-d design method results in very good control for process models. The analytical simulation shows that the DS-d design method provides better disturbance rejection than the internal model control methods. Keywords: Direct Synthesis (DS-d), PID controller, Disturbance rejection, Internal Model Controller (IMC). 1. INTRODUCTION The dead time is the delay from when a controller output (CO) signal is issued until when the measured process variable (PV) first begins to respond. The presence of dead time, Өp, is never a good thing in a control loop for any process, as Өp becomes larger, the control challenge becomes greater and tight performance becomes more difficult to achieve. The control algorithm for a dead time process is actually very simple. A PID controller does a fine job. You can also use a fancy model predictive or model based, pole cancellation, or Internal Model Control, or Dynamic Matrix controller or Dahlin. They all amount to the same thing of using a model inside the controller. Let’s just call them all Model based controllers. Model based controllers can seek out slightly better response than PID but at the sacrifice of robustness. The robustness penalty using model based control (made to be even the same speed as a PI) is severe the dead time of the process can go up or down and the loop will go unstable. Increasing dead time with any process will always eventually drive you unstable. But decreasing dead time to make you unstable is weirdly counter-intuitive. If the dead time were to go down with a PID controller, the loop would remain stable. So why not keep it simple and just use a PID controller? PID (proportional integral derivative) control is one of the earlier control strategies. Its early implementation was in pneumatic devices, followed by vacuum and solid state analog electronics, before arriving at today’s digital implementation of microprocessors. It has a simple control structure which was understood by plant operators and which they found relatively easy to tune. Since many control systems using PID control have proved satisfactory, it still has a wide range of applications in industrial control. 95% of the controllers used in industry are of PI/PID type.An ideal PID controller is given by 1 G PID ( s ) K c 1 TD s T s I (1) The design methods for PID controllers are typically based on a time-domain or frequency-domain performance criterion. In the direct synthesis (DS) approach, however, the controller design is based on a desired closed-loop transfer function.DS design methods are usually based on specification of the desired closed-loop transfer function for set-point changes. Consequently, the resulting DS-d controllers tend to perform well for set-point changes & the disturbance response might be satisfactory. For example, the IMC-PID controller provides good set-point tracking but very sluggish disturbance responses for processes with a small time-delay/time-constant ratio.However, for many process control applications, disturbance rejection is much more important than set-point tracking. Therefore, controller design that emphasizes disturbance rejection, rather than set-point tracking, is an important design problem. Here DS-d approach is used for unstable and time delayed process.In this project analytical expression for the PID controller is derived for Volume 3, Issue 5, May 2014 Page 161 International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: editor@ijaiem.org Volume 3, Issue 5, May 2014 ISSN 2319 - 4847 common process model through the direct synthesis method for disturbance rejection. The DS-d design method has a single design parameter, the desired closed-loop time constant c . 2. LITERATURE SURVEY The design methods for PID controllers are typically based on a time-domain or frequency-domain performance criterion. In the direct synthesis (DS) approach however, the controller design is based on a desired closed-loop transfer function. Then, the controller is calculated analytically so that the closed-loop set-point response matches the desired response. The obvious advantage of the direct synthesis approach is that performance requirements are incorporated directly through specification of the closed-loop transfer function. One way to specify the closed-loop transfer function is to choose the closed-loop poles. Two early and well-known design methods were reported by Ziegler and Nichols (ZN)[2] and Cohen and Coon[3] developed to provide a closed-loop response with a quarter decay ratio . K. J. Astrom, C. C. Hang [4 ] proposed a new Smith Predictor for Controlling a Process with an Integrator and Long Dead time but it is important to exercise some care to avoid internally some unstable modes in the system. M.Morari,E Zafiriou[ 7] proposed a robust process control i.e IMC design but it work only for stable system. H.P. Hung, C.C. Chen [10] proposed a method i.e Control-system synthesis for open-loop unstable process with time delay, the strongly stabilizing conditions for the time delayed unstable process are still unclear in this Literature . D.Chen, D.E. Seborg,[ 13] proposed PI/PID controller design based on direct synthesis and disturbance rejection but it was work only for stable system. Wen Tana, Horacio J. Marquezb, Tongwen Chen[14] proposed IMC design for unstable processes with time delays but response of such process is so sluggish. DS-d design methods are usually based on specification of the desired closed-loop transfer function for set-point changes. Consequently, the resulting DS-d controllers tend to perform well for set-point changes, but disturbance response might be satisfactory. For example, the IMC-PID controller provides good set-point tracking but very sluggish disturbance responses for processes with a small time-delay/time-constant ratio. However, for many process control applications, disturbance rejection is much more important than set-point tracking. Therefore, controller design that emphasizes disturbance rejection is an important design problem that has received renewed interest recently. 3. DIRECT SYNTHESIS APPROACH FOR PID CONTROLLER DESIGN The design methods for PID controllers are typically based on a time-domain or frequency-domain performance criterion. In the direct synthesis (DS) approach, however, the controller design is based on a desired closed-loop transfer function.DS design methods are usually based on specification of the desired closed-loop transfer function for set-point changes. Consequently, the resulting DS-d controllers tend to perform well for set-point changes & the disturbance response might be satisfactory. For example, the IMC-PID controller provides good set-point tracking but very sluggish disturbance responses for processes with a small time-delay/time-constant ratio. However, for many process control applications, disturbance rejection is much more important than set-point tracking. Therefore, controller design that emphasizes disturbance rejection, rather than set-point tracking, is an important design problem. Here DS-d approach is used for unstable and time delayed process. In this paper analytical expressions for the PID controller is derived for common process model through the direct synthesis method for disturbance rejection. The DS-d design method has a single design parameter, the desired closedloop time constant . In the direct synthesis approach, an analytical expression for the feedback controller is derived from a process model and a desired closed-loop response. In most of the DS literature, the desired closed-loop response is expressed as a closed-loop transfer function for set-point changes. Consequently, this popular version of the direct synthesis method will be briefly introduced in the next section. Figure 1 Classical Feedback control system Consider a feedback control system with the standard block diagram in Figure 1 Assume that Gp (s)is a model of the process, measuring element, transmitter, and control valve. The closed-loop transfer function for set-point changes is derived as y r G p ( s )G c ( s ) (2) 1 G p ( s )Gc ( s ) Rearranging gives an expression for the feedback controller Volume 3, Issue 5, May 2014 Page 162 International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: editor@ijaiem.org Volume 3, Issue 5, May 2014 Gc ( s) y r y G p ( s ) 1 r ISSN 2319 - 4847 (3) Let the desired closed-loop transfer function for set-point changes be specified as y / r d , and assume that a process model Gp (s) is available. Replacing the unknown y / r and Gp (s) by y / r and Gp (s), respectively, gives a design equation d for G c ( s ) Gc ( s) y r y ~ G p ( s ) 1 r d (4) Because the characteristics of y / r have a direct impact on the resulting controller, y / r should be chosen so that the d d closed-loop performance is satisfactory and the resulting controller is physically reliable. The DS controller in equation 4 results in the following closed-loop transfer function y r y d y r d y ~ ~ G p (G p G p ) r d y ~ G p G d 1 r d y ~ ~ G p (G p G p ) r d Gp DS DS (5) (6) For the ideal case where the process model is perfect (i.e., G p G p ), the closed-loop transfer functions becomes y r y d DS DS y r d (7) y r d (8) G d 1 3.1 Direct Synthesis Design for Disturbance Rejection The PI/PID settings obtained from the DS and IMC approaches are based on specifying the closed-loop transfer function for set-point changes. For processes with small time-delay/time-constant ratios, these PI/PID controllers provide very sluggish disturbance responses. Therefore, it is worth while to develop a modified direct synthesis approach based on disturbance rejection. The new design method will be denoted by “DS-d”. Consider a control system with the standard block diagram shown in Figure 1. The closed-loop transfer function for disturbances is given by y d Gd ( s ) . (9) 1 G p ( s)Gc ( s ) Rearranging gives an expression for the feedback controller Gc ( s) Gd (s) y G p ( s ) d 1 (10) G p (s) Let the desired closed-loop transfer function for disturbances be specified as y / d , and assume that a process d model Gp (s)and a disturbance model Gd (s) are available. Replacing the unknown, and (s) ,respectively, gives a design equation for G d ( s ) by, and G d Volume 3, Issue 5, May 2014 Page 163 International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: editor@ijaiem.org Volume 3, Issue 5, May 2014 Gc ( s) ~ Gd ( s ) y ~ G p ( s) d d 1 ~ G p ( s) ISSN 2319 - 4847 (11) For the DS-d controller, the closed-loop transfer functions is y d DS d y ~ G p Gd d d (12) y ~ ~ G p G d (G p G p ) d d For the ideal case where the model is perfect (i.e., G p G p and Gd G d ), the closed-loop transfer function y d y r DS d DS d y d d y d d (13) (14) 1 ~ Gd (s) The structure and order of the controller depends on the specification of the desired closed-loop response and process model.. 4. RESULTS AND DISCUSSION We have applied DS-d method for different systems and performance was compared with IMC method 4.1 Example 1 Consider first-order plus time delay system Gp ( s ) Gd ( s ) 1e 0.4 s s 1 Here we consider DS-d and IMC method for design of PID controller Tunning Method K 0.4 1 1 DS-d approach ( c =2) Modified IMC approach ( λ=0.3& α =1.7462) 0.4 1 Gc = 1 2.990 s 2 32.860 s 1.3 24.559 s 12.9348s 7.4074s 5 s s 23.9334 4.1.1 Simulation Result of DS-d approach and IMC approach 1.4 Modified IMC method D S-d method 1.2 Process Output 1 0.8 0.6 0.4 0.2 0 0 5 10 15 20 25 30 35 40 45 Time Figure 2 Unit step response of DS-d approach and IMC approach for FOPDT system Volume 3, Issue 5, May 2014 Page 164 International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: editor@ijaiem.org Volume 3, Issue 5, May 2014 ISSN 2319 - 4847 Table.1 Time Domain Specification for FOPDT system Tunning Methods Tr Ts Tsmax Tsmin Tp Mu DS-d( c =2) 3.83 27.55 0.99 0.67 0.42 0.99 Mp P 13 0 Modified IMC( 0.3& 1.74) 2.33 25.18 1.02 0.51 2.76 1.02 25 0 4.1.2 Robustness analysis - For Robustness analysis we have decreased τ by10% and θ has been increased by 10% then Gp was obtained as below, be Gp 1e 0.44 s 0.9 s 1 4.1.3 Simulationon Results of DS-d method and IMC for Changed FOPDT system 1.5 Modified IMC method DS-d method Process Output 1 0.5 0 0 5 10 15 20 25 Time 30 35 40 45 Figure 3 Unit Step Response of Modified IMC&DS-d method for Changed θ &τ of FOPDT system Table 2.Time Domain Specification for changed & of FOPDT system Tunning Methods Tr Ts Tsmax Tsmin Mp P Tp Mu DS-d( c =2) 2.73 26.21 0.99 0.59 0.68 0 .99 11 0 IMC-Modified ( 0.3& 1.74) 23.10 40.93 1.46 0.53 21.01 1.46 27 0 As we compared DS-d method with Modified IMC method, the robustness of DS-d method is more. 4.2 Example 2 Consider Second order system Gp ( s ) Gd ( s ) s 2 s 1s 5 Here we consider DS-d and IMC method for design of PID controller Tunning Method K 0 0.2 1 Gc DS-d approach ( c =2) Gc 0.66 s 2 1.334 s 2 0.667 s Modified IMC ( 0.5, α = 1.655) 0 0.2 1.655s 1 Gc 1 2 0.025s 0.15 s 4.2.1 Simulation Result of DS-d approach and IMC approach 1.5 Modified IMC method DS-d Method Process Output 1 0.5 0 -0.5 -1 0 5 10 15 20 Time 25 30 35 40 Figure 4 Unit Step Response of DS-d and IMC method for Second order system Volume 3, Issue 5, May 2014 Page 165 International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: editor@ijaiem.org Volume 3, Issue 5, May 2014 ISSN 2319 - 4847 Table.3 Time Domain Specification for Second order system Tunning Methods Tr Ts Tsmax Tsmin Mp P Tp Mu DS-d( c =2) 1.51 6.90 1.00 0.83 0 1 1 0 Modified IMC (λ=0.5,α=1.65) 0.76 2.86 1.05 1.00 5.12 1.05 2 0 4.2.2 Robustness analysis - For Robustness analysis we have decreased τ1 by10% and τ2 has been increased by 10% then Gp was obtained as follows, Gp ( s ) s 2 1.1s 10.18s 1 4.2.3 Simulation Result of DS-d and IMC for changed Second order system 1.5 Modified IMC method DS-d Method Process Output 1 0.5 0 -0.5 -1 0 5 10 15 20 Time 25 30 35 40 Figure 5 Unit step Response of DS-d and Modified IMC for Second order system Table 4 Time Domain Specification of Modified IMC and DS-d for changed Second order system Tunning Methods Tr Ts Tsmax Tsmin Mp P Tp Mu DS-d( c =2) 0.86 5.73 1.00 0.80 0 1.46 1 146.3 Modified IMC ((λ=0.5,α=1.65) 0.79 1.97 1.01 1.00 1.12 1.01 4 0 As we compared Modified IMC method with DS-d method the robustness of DS-d method is more. 5. CONCLUSION The main objective of this study is to design robust PID controller for first order unstable time delay process and second order process by using IMC Modified and DS-d approach. In the DS-d design method, the closed-loop time constant c is the only design parameter, all other parameters are calculated analytically using it. Thus, the DS-d design procedure is simple and easy to implement. Although the PID controllers are designed for disturbance rejection, the set-point responses are usually satisfactory.Two simulation examples have been used to compare alternative design methods. The simulation results demonstrate that the DS-d method provides better disturbance rejection than Modified IMC method and provide satisfactory response to set point. The DS-d method furnishes a convenient and flexible design method that provides good performance in terms of disturbance rejection and set-point tracking. The performance of the controller can be further improved by modifying filter parameter. References [1] Miroslav R. Mataušek*, Tomislav B.Šekara, “PID controller frequency domain tuning for stable, integrating and unstable processes, including dead-time”, Journal of Process Control, 2010,PP. 1188-1199 [2] Ziegler J. G, Nichols N. B, “Optimum Settings for Automatic Controllers”. Trans. ASME, 1942, 64, 759. Volume 3, Issue 5, May 2014 Page 166 International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: editor@ijaiem.org Volume 3, Issue 5, May 2014 ISSN 2319 - 4847 [3] Cohen G. H, Coon G. A, “Theoretical Consideration of Retarded Control”. Trans. ASME, 1953, 75, 827. [4] K.J.Astrom,C.C Chen, “A new smith predictor for controlling a process with an integrator and long dead-time” IEEE transactions on automatic control, vol. 39, no. 2. february 1994 343-345. [5] Åström K. J, Hägglund T, “PID Controllers: Theory, Design, and Tuning”, 2nd ed, Instrument Society of America: Research Triangle Park, NC, 1995. [6] Dahlin E. B, “ Designing and Tuning Digital Controllers”, Instrum. Control Sys, 1968, 42 (6), 77. [7] M. Morari, E. Zafiriou, “Robust Process Control”, Prentice Hall,Englewood Cliffs, NJ, 1989. [8] ChienI.L,P.S.Fruehauf, “Consider IMC Tunning to improve controller performance.”chem.Eng.Prog.,86(10),3341(1990) [9] Y. Lee, J. Lee, S. Park,“PID controller tuning for integrating and unstable processes with time delay”, Chemical Engineering Science,55, (2000), 3481–3493. [10] H.P. Hung, C.C. Chen,“Control-system synthesis for open-loop unstable process with time-delay”, IEE Proc. Part D 144, (4), (1997),334–346. [11] A.M.D. Poar, M. O. Malley,“Controllers of Ziegler-Nichols type for unstable processes”, Int. J. Control, 49, (1989), 1273–1284. [12] B.Wayne Bequette, “Process Control –Modelling, Design And Simulation”, Eastern Economy Edition, PP. 245290. [13] D. Chen, D. E. Seborg, “PI/PID controller design based on direct synthesis and disturbance rejection”, Ind. Eng. Chem, vol. 41,2002, PP. 4807-4822. [14] Wen Tan ,Horacio J.Marquez,Tongwen chen, “IMC design for unstable processes with time delays”Journal of process control ,13,(2003),203-213 [15] Luyben M .L., W.L.Luyben, “Essentials of process control “, McGraw-Hill, New York (1997) AUTHOR Ms. Yogita Dighe receieved the B.E degree in Instrumentation Engineering from Pravara Rural Engineering College, Loni (M.S), India, in the year 2003. Presently she is working as a Lecturer in Amrutvahini Polytechnic, Sangamner. She is currently a M.E scholar in Department of Instrumentation Engineering, Loni (M.S), University of Pune, Pune, India. Mr. Chandrakant B. Kadu is working as an Associate Prof. & HEAD, Instrumentation & Control Engineering, Pravara Rural Engineering College, Loni (M.S), University of Pune, Pune, India. He is a Member of Board of Studies Instrumentation, University of Pune, Pune .He is also Govering Council Member of Instrumentation Society of India (ISOI) Bangalore. He has published more than 15 National &International paper in the field of Process Control. Presently pursuing Ph.D from College of Engineering Pune (COEP), University of Pune, Pune. Volume 3, Issue 5, May 2014 Page 167