Pid controller design for process with time delay

TRUONG NGUYEN LUAN VU VIETNAM NATIONAL UNIVERSITY – HO CHI MINH CITY PRESS PID CONTROLLER DESIGN FOR PROCESS WITH TIME DELAY HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION TRUONG NGUYEN LUAN[.]

TRUONG NGUYEN LUAN VU PID CONTROLLER DESIGN FOR PROCESS WITH TIME DELAY VIETNAM NATIONAL UNIVERSITY – HO CHI MINH CITY PRESS HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION TRUONG NGUYEN LUAN VU PID CONTROLLER DESIGN FOR PROCESS WITH TIME DELAY Vietnam National University Ho Chi Minh City Press - 2018 ABOUT THE AUTHOR Truong Nguyen Luan Vu is currently an Associate Professor of Mechanical Engineering at Ho Chi Minh City University of Technology and Education, Vietnam He received his B.S degree from Ho Chi Minh City University of Technology, Ho Chi Minh City National University in 2000, and his Master and Ph.D degrees from Yeungnam University, Republic of Korea in 2005 and 2009, respectively He has also taught at Yeungnam University for two years in terms of an International Professor His research interests include multivariable control, fractional control, PID control, process control, automatic control, and control hardware CONTENTS OVERVIEW CHAPTER DESIGN OF ADVANCED PID CONTROLLERS FOR TIME-DELAY PROCESSES 13 1.1 INTRODUCTION 13 1.2 GENERALIZED IMC APPROACH FOR PID CONTROLLER DESIGN 14 1.3 DESIGN OF PID CONTROLLER CASCADED WITH A LEAD-LAG FILTER 16 1.4 PROPOSED TUNING RULES FOR TYPICAL TIMEDELAY MODELS 18 1.4.1 First-Order plus Dead Time (FOPDT) Process Model 18 1.4.2 Integrator Plus Time Delay Model 18 1.4.3 First-Order Delayed Unstable Process (FODUP) Model 19 1.4.4 First-Order Delayed Integrating Process (FODIP) Model 21 1.5 Second-Order Delayed Unstable Process (SODUP) Model 21 1.5.1 SODUP Model with One Unstable Pole 21 1.5.2 SODUP Model with Two Unstable Poles 22 1.6 PERFORMANCE AND ROBUSTNESS MEASUREMENTS 22 1.6.1 Integral Absolute Error (IAE) Criteria 22 1.6.2 Overshoot 22 1.6.3 Maximum Sensitivity (Ms) Criterion 22 1.6.4 Total Variation (TV) 23 1.7 SIMULATION STUDY 23 1.8 DISCUSSION 43 1.8.1 Effect Of  On the Tradeoff between Performance and Robustness 43 1.8.2 Effectiveness of the Proposed Method for the Dead-Time Dominant Process 45 1.9 CONCLUSIONS 46 REFERENCES 47 CHAPTER IMC-PID CONTROLLER TUNING FOR PROCESS WITH TIME DELAY 49 2.1 INTRODUCTION 49 2.2 GENERALIZED IMC-PID DESIGN APPROACH 49 2.3 IMC-PID TUNING RULES FOR TYPICAL PROCESS 52 2.3.1 First-order Plus Dead Time (FOPDT) Process Model 52 2.3.2 Integrator Plus Time Delay (IPTD) Model 54 2.3.3 First-order Delay Unstable Process (FODUP) Model 55 2.3.4 First-order Delayed Integrating Process (FODIP) Model 58 2.3.5 Second-order Delayed Unstable Process (SODUP) Model 58 2.3.5.1 SODUP Model with One Unstable Pole 58 2.3.5.2 SODUP Model with Two Unstable Poles 60 2.4 ROBUST ANALYSIS 62 2.5 SIMULATION STUDY 64 2.6 CONCLUSIONS 80 REFERENCES 80 CHAPTER FRACTIONAL-ORDER PROPORTIONALINTEGRAL CONTROLLERS DESIGN FOR TIME-DELAY PROCESSES 83 3.1 INTRODUCTION 83 3.2 PRELIMINARIES 84 3.2.1 Fractional calculus 84 3.2.2 Integer Order Approximation 85 3.2.3 Fractional linear model 85 3.2.4 FOPI controller 86 3.3 ANALYTICAL DESIGN OF GENERALIZED FOPI CONTROLLER TUNING RULES 87 3.4 PERFORMANCE AND ROBUSTNESS MEASUREMENTS 92 3.4.1 Integral Absolute Error (IAE) Criteria 92 3.4.2 Overshoot 92 3.4.3 Total variation (TV) 92 3.4.4 Resonant peak (Mp) criterion 92 3.5 SIMULATION STUDY 93 3.6 DISCUSSION 103 3.6.1 Effect of Mp Values on the Tuning Parameters and the Closed-Loop Performance 105 3.6.2 Fractional order (λ) guideline for the proposed FOPI parameter tuning 105 3.7 CONCLUSIONS 108 REFERENCES 108 CHAPTER SMITH PREDICTOR BASED FRACTIONALORDER PI CONTROL FOR TIME-DELAY PROCESSES 111 4.1 INTRODUCTION 111 4.2 THEORY DEVELOPMENT 112 4.2.1 Fractional Calculus 112 4.2.2 Design of FOPI Controller in Frequency Domain 114 4.2.3 SP-FOPI Controller Design Procedure 115 4.3 SELECTION OF TUNING PARAMETERS 119 4.4 SIMULATION STUDY 120 4.5 CONCLUSIONS 134 REFERENCES 134 CHAPTER FRACTIONAL-ORDER PI CONTROLLER TUNING RULES FOR CASCADE CONTROL SYSTEM 137 5.1 INTRODUCTION 137 5.2 PRELIMINARIES 138 5.2.1 Fractional Linear Model 139 5.2.2 Design of FOPI Controller in Frequency Domain 139 5.3 ANALYTICAL TUNING RULES OF FOPI CONTROLLERS FOR CASCADE CONTROL SYSTEM 140 5.3.1 FOPI Controller Design Procedure for General Process Models 140 5.3.2 Design of Secondary Controller 140 5.3.3 Design of Primary Controller 142 5.4 SIMULATION STUDY 144 5.5 CONCLUSIONS 146 REFERENCES 146 APPENDIX USE OF MATLAB IN PID CONTROL 148 REFERENCES 151 OVERVIEW The IMC structure, a control structure incorporating the internal model of plant control, has been widely utilized in the design of PID-type controllers, usually denoted IMC-PID controllers, because of its simplicity, flexibility, and apprehensibility The most important advantage of IMC-PID tuning rules is that the tradeoff between closedloop performance and robustness can be directly obtained using a single parameter related to the closed-loop time constant IMC-PID tuning rules can provide good set-point tracking, but have been lacking regarding disturbance rejection, which can become severe for processes with a small time-delay/time constant ratio Disturbance rejection is more important than set-point tracking in many process control applications, and thus is an important research topic A 2DOF control scheme can be used to improve disturbance performance for various time-delay processes The controller’s performance can be significantly enhanced using a PID controller cascaded with a conventional filter, something easily implementable in modern control hardware Consequently, several controller tuning rules have been reported despite PID controllers cascading with conventional filters being often more complicated than a conventional PID controller for processes with time delay However, this difficulty can be overcome by using appropriate low-order Padé approximations of the time delay term in the process model Therefore, the PID-type controller can be indirectly obtained by considering the Padé approximations Accordingly, first-order Padé approximations have been used by a number of authors This expansion does introduce some modeling errors, though within acceptable limits To reduce this problem, a higher order Padé approximation has been used Alternatively, a Taylor expansion can be directly applied to transform an ideal feedback controller into a standard PID-type controller The performance of the resulting IMC-PID controller is largely dependent on how closely the PID controller approximates an ideal controller equivalent to the IMC controller It also depends on the structure of the IMC filter Many methods for approximating an ideal controller to a PID controller have been discussed, but most are case dependent Few unified approaches to PID controller design that can be employed for all typical time-delay processes have been fully achieved PID filter controllers closely approximating ideal feedback controllers are also obtained by using directly high order Padé approximations, since those of previous works are only indirectly used Padé approximations in terms of the time delay part The study is focused on the design of PID controllers cascaded with a lead-lag filters to fulfill various control purposes; tuning rules should be simple, of analytical form, model-based, and easy to implement in practice with excellent performance for both regulatory and servo problems Recently, fractional-order dynamic systems are useful in representing various stable physical phenomena with anomalous decay because they can provide increased flexibility with less computational cost, allowing precise simulation and implementation Fractional calculus (i.e fractional integro-differential operators) is a generalization of integration and differentiation to non-integer orders It is obtained from ordinary calculus by extending ordinary differential equations (ODE) to fractional-order differential equations (FODE) Similarly, a fractionalorder proportional-integral-derivative (FOPID) controller is a generalization of a standard (integer) PID controller; its output is a linear combination of the input and the fractional integral or derivative of the input [2] It affords more flexibility in PID controller design due to its five controller parameters (instead of the standard three): proportional gain, integral gain, derivative gain, integral order, and derivative order However, the tuning rules of fractional-order PID (FOPID) controllers are much more complex than those of standard (integer) PID controllers with only three parameters The two extra parameters (λ and µ) give this 10 type of controller improved flexibility over integer PID controllers, giving it much industrial applicability Tuning methods of PIλDμ controllers can be generally classified as either analytic or heuristic Most analytic methods are tuned by considering the nonlinear objective function, which is depended on user-imposed specifications In this book, several case studies are reported to demonstrate the simplicity and effectiveness of the proposed method compared with several other prominent design methods The simulation results confirm that the proposed method can afford robust PID filter controllers for both disturbance rejection and set-point tracking 11 ... CHAPTER DESIGN OF ADVANCED PID CONTROLLERS FOR TIME- DELAY PROCESSES 13 1.1 INTRODUCTION 13 1.2 GENERALIZED IMC APPROACH FOR PID CONTROLLER DESIGN 14 1.3 DESIGN OF PID CONTROLLER. .. CHAPTER IMC -PID CONTROLLER TUNING FOR PROCESS WITH TIME DELAY 49 2.1 INTRODUCTION 49 2.2 GENERALIZED IMC -PID DESIGN APPROACH 49 2.3 IMC -PID TUNING RULES FOR TYPICAL PROCESS ... tracking 11 Chapter DESIGN OF ADVANCED PID CONTROLLERS FOR TIME- DELAY PROCESSES 1.1 INTRODUCTION The design of proportional-integral-derivative (PID) controllers cascaded with first-order lead-lag