OPTIMIZATION OF PID PARAMETERS FOR HYDRAULIC POSITIONING SYSTEM UTILIZING VARIABLE WEIGHT GREY-TAGUCHI AND PARTICLE SWARM OPTIMIZATION
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1 OPTIMIZATION OF PID PARAMETERS FOR HYDRAULIC POSITIONING SYSTEM UTILIZING VARIABLE WEIGHT GREY-TAGUCHI AND PARTICLE SWARM OPTIMIZATION NUR IFFAH BINTI MOHAMED AZMI Thesis submitted in fulfilment of the requirements For the award of the degree of Master of Engineering in Manufacturing Faculty of Manufacturing Engineering UNIVERSITI MALAYSIA PAHANG 2014
2 vi ABSTRACT Controller that uses PID parameters requires a good tuning method in order to improve the control system performance. Especially on hydraulic positioning system that is highly nonlinear and difficult to be controlled whereby PID parameters needs to be tuned to obtain optimum performance criteria. Tuning PID control method is divided into two namely the classical methods and the methods of artificial intelligence. Particle swarm optimization algorithm (PSO) is one of the artificial intelligence methods. Previously, researchers had integrated PSO algorithms in the PID parameter tuning process. This research aims to improve the PSO-PID tuning algorithms by integrating the tuning process with the Variable Weight Grey-Taguchi Design of Experiment (DOE) method. This is done by conducting the DOE on the two PSO optimizing parameters: the limit of change in particle velocity and the weight distribution factor. Computer simulations and physical experiments were conducted by using the proposed PSO-PID with the Variable Weight Grey-Taguchi DOE and the classical Ziegler- Nichols methods. They are implemented on the hydraulic positioning system. Simulation results show that the proposed PSO-PID with the Variable Weight Grey- Taguchi DOE has reduced the rise time by 48.13% and settling time by 48.57% compared to the Ziegler-Nichols method. Physical experiment results also show that the proposed PSO-PID with the Variable Weight Grey-Taguchi DOE tuning responds better than Ziegler-Nichols tuning. In conclusion, this research has improved the PSO-PID parameter by applying the PSO-PID algorithm together with the Variable Weight Grey- Taguchi DOE method as a good tuning method in the hydraulic positioning system.
3 vii ABSTRAK Pengawal yang menggunakan parameter PID memerlukan kaedah penalaan yang baik untuk meningkatkan prestasi sistem kawalan. Terutamanya pada sistem kedudukan hidraulik yang tidak linear dan sukar untuk dikawal, di mana parameter PID perlu ditala untuk mendapatkan kriteria prestasi optimum. Kaedah penalaan kawalan PID dibahagikan kepada dua kaedah iaitu kaedah klasik dan kaedah kecerdasan buatan. Algoritma Pengoptimuman Kawanan Partikel (PSO) adalah salah satu kaedah kecerdasan buatan. Sebelum ini, penyelidik telah menyatupadukan algoritma PSO dengan parameter PID untuk tujuan proses penalaan. Kajian ini bertujuan untuk meningkatkan algoritma penalaan PSO-PID dengan mengintegrasikan proses penalaan dengan kaedah Rekabentuk Experimen (DOE) Pembolehubah Berat Grey-Taguchi. Ini dilakukan dengan melaksanakan DOE pada dua PSO optimum parameter: iaitu had halaju partikel dan faktor pengagihan berat. Simulasi komputer dan eksperimen fizikal telah dijalankan dengan menggunakan cadangan PSO-PID bersama DOE Pembolehubah Berat Grey-Taguchi dan kaedah klasik Ziegler-Nichols. Ia dilaksanakan pada sistem kedudukan hidraulik. Keputusan simulasi menunjukkan bahawa PSO-PID yang dicadangkan dengan DOE Pembolehubah Berat Grey-Taguchi telah mengurangkan masa naik sebanyak 48.13% dan 48.57% oleh masa penetapan berbanding dengan kaedah Ziegler-Nichols. Tambahan pula, ralat keadaan mantap juga diminimumkan. Keputusan eksperimen fizikal juga menunjukkan bahawa algoritma penalaan PSO-PID yang dicadangkan dengan DOE Pembolehubah Berat Grey-Taguchi bertindak balas dengan lebih baik daripada algoritma penalaan Ziegler-Nichols. Kesimpulannya, kajian ini telah menambah baik pengoptimuman parameter PSO-PID dengan menggunakan algoritma PSO-PID bersama kaedah DOE Pembolehubah Berat Grey-Taguchi sebagai kaedah penalaan yang baik dalam sistem kedudukan hidraulik.
4 viii TABLE OF CONTENTS SUPERVISOR S DECLARATION STUDENT S DECLARATION ACKNOWLEDGEMENTS ABSTRACT ABSTRAK TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS LIST OF ABBREVIATIONS Page ii iii iv vi vii viii xi xiii xv xvii CHAPTER 1 INTRODUCTION 1.1 Research Background Research Problem Statement Research Objective Research Scope Research Approach Thesis Organization 4 CHAPTER 2 PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROLLER AND PARTICLE SWARM OPTIMIZATION REVIEW 2.1 Introduction Hydraulic System Servo Control of Hydraulic System Classical Feedback Control Proportional (P) Controller Proportional-Integral (PI) Controller Proportional-Derivative (PD) Controller Proportional-Integral-Derivative (PID) Controller PID Controller Tuning Method 22
5 ix PID Controller Tuning Rules Tuning Rules Based on Minimizing Performance Criteria Techniques of Optimizing PID Controller Parameters Parameters Optimization Techniques Conventional PID Controller Tuning Approach Alternative PID Controller Tuning Approach Swarm Intelligence Particle Swarm Optimization (PSO) PSO Algorithm Parameters of PSO Algorithm Parameters and Tuning of Parameters in PSO Variable Weight Grey-Taguchi Method Summary 48 CHAPTER 3 THE PROPOSED PSO-PID AND THE VARIABLE WEIGHT GREY-TAGUCHI TUNING ALGORITHM 3.1 Introduction PSO-PID Tuning Algorithm Developed by Gaing (2004) The Proposed PSO-PID Tuning Algorithm with the Variable Weight Grey-Taguchi Method The Objectives and Phyisical Experiments Setup Computer Simulation and Physical Experiments on the Hydraulic Positioning System Parameters Optimization of PID Controller Ziegler Nichols (Reaction-Curve) Method Summary 73 CHAPTER 4 RESULTS AND DISCUSSION 4.1 Introduction Modelling Process PID Parameter Optimization Process Data Analysis Comparison of Performance Response 99
6 x 4.4 Summary 104 CHAPTER 5 CONCLUSSION 5.1 Introduction Research Summary and Conclusions Recommendations for Future Works 106 REFERENCE 107 APPENDIX A PSO Algorithm MATLAB Program 114 B Variable Weight Grey Taguchi Method Program 118
7 xi LIST OF TABLES Table No. Title Page 2.1 Characteristics difference between servo valve and proportional valve PID parameter values based on Ziegler-Nichols reaction-curve method L 27 Orthogonal Array (OA) for four-factor and three-level Control and response factors on L Control electronics specifications Electrical specifications Speed for each input PSO parameters and their respective levels PSO parameters respective levels selection using standard L 27 orthogonal Performance response from PSO algorithm based on OA structures for 1 st set Performance response from PSO algorithm based on OA structures for 2 nd set data The normalized value, Grey relational coefficients (GRC) and Grey relational grade (GRG) for 10%, 1% and 0.1% of the variable dynamic range on each dimension using Variable Weight Grey-Taguchi Algorithm PSO parameters from trial with highest GRG Performance characteristics from trail with highest GRG The average values of GRG for PSO parameters and their respective levels PSO parameters from optimum PSO parameters Performance characteristics from optimum PSO parameters The normalized value, Grey relational coefficients (GRC) and Grey relational grade (GRG) for 20%, 2% and 0.2% of the variable dynamic range on each dimension using Variable Weight Grey-Taguchi Algorithm PSO parameters from trial with highest GRG 97
8 xii 4.14 Performance characteristics from trail with highest GRG The average values of GRG for PSO parameters and their respective levels PSO parameters from optimum PSO parameters Performance characteristics of the optimum PSO parameters Comparison of performance response between 1 st data set and 2 nd set data PID Parameters values Comparison efficiency performance response of step response Performance response for different set point of step response 104
9 xiii LIST OF FIGURES Figure No. Title Page 2.1 Proportional valve Proportional solenoid Basic proportional valve configuration Hydraulic circuit diagram of a hydraulic system using proportional valves Components in an electro-hydraulic servomechanism P controller block diagram PI controller block diagram Proportional-derivative (PD) controller block diagram Basic PID controller block diagram Second-order step response plot together with the control performance criteria The reaction-curve method for a block diagram of test setup Step response of the second-order system process Artificial intelligence paradigms A scheme of PSO algorithm Social Network Topology PSO PSO-PID tuning algorithm flowchart The proposed PSO-PID tuning algorithm flow chart National instruments platform (NI ELVIS II) Experiment Block Diagram Front panel of LabVIEW Physical experiment setup of hydraulic positioning control Amplifier circuit 70
10 xiv 3.8 Process flow for overall optimization procedure Ziegler-Nichols open loop method: The equivalent dead-time L and rate R read off from the process step response Block diagram of open-loop system Comparison of time response with different input voltage Graph speed vs input voltage Simulation results of open-loop system model; (a) 4V input (b) 5V input (c) 6V input (d) 7V input (e) 8V input and (f) 9V input Closed-loop MATLAB Simulink model Comparison simulation and experiment results of closed-loop system model Graph of GRG from Variable Weight Grey-Taguchi algorithm Graph of average GRG by Variable Weight Grey-Taguchi for 1 st data set Graph of GRG from Variable Weight Grey-Taguchi algorithm Graph of average GRG by Variable Weight Grey-Taguchi for 2 nd data set Step response of the hydraulic positioning system Step response of the physical experiment for the hydraulic positioning system PID position control 10 cm set point Step response of the physical experiment for the hydraulic positioning system PID position control 9 cm set point Step response of the physical experiment for the hydraulic positioning system PID position control 8 cm set point Step response of the physical experiment for the hydraulic positioning system PID position control 7 cm set point 103
11 xv LIST OF SYMBOLS x Square of mean Weight distribution factor CV Percent step change of control variable PV Change in the process variable c Damping ratio S/N value Distinguishing coefficient 2 Variance Inertia weight factor d Damped natural frequency max Maximum inertia weight min Minimum inertia weight n Natural frequency c final C s e The steady-state condition Transfer function of the controller Error Ess E s e t iter Steady-state error Laplace transform of the error signal Error signal at time t Current number of iterations
12 xvi iter max Maximum number of iterations K [ K p, Ki, K d ] K d Derivative gain constant K i Integral gain constant K p L Proportional gain constant Lag time M p n N Maximum overshoot Number of particles in a group Slope of the system response curve N f Number of factor r t Desired output signal s t T p Laplace domain Time Peak time T r Rise time T s U s Settling time Laplace transform of the corresponding control input u t Control signal at time t V max W y t K Limit of change in particle velocity Performance criterion Measured output signal
13 xvii LIST OF ABBREVIATIONS ACO AI AVR CLF DC DOE DOF GA GASA GRA GRC GRG IAE IMC ISE ITAE LQR MSE OA P PD PI PID Ant Colony Optimization Artificial Intelligence Automatic Voltage Regulator Control Lyapunov Function Direct Current Design of Experiment Degree of Freedom Genetic Algorithm Genetic Algorithm Simulated Annealing Grey Relational Analysis Grey Relational Coefficient Grey Relational Grade Integral of Absolute Error Internal Model Control Integral Square Error Integral Time of Absolute Error Linear Quadratic Regulator Mean Square Error Orthogonal Array Proportional Proportional-Derivative Proportional-Integral Proportional-Integral-Derivative
14 xviii PSO SI Particle Swarm Optimization Swarm Intelligence
15 CHAPTER 1 INTRODUCTION 1.1 RESEARCH BACKGROUND Hydraulic positioning system has been used in modern industrial applications. This is due to the capabilities of the larger driving force and high power-weight ratio. Hydraulic positioning system is generally categorized in the stabilization and tracking control. This system will always be the driving force to reduce energy consumption and to improve the efficiency and accuracy of the motion control. As the hydraulic positioning system is widely applied to high-tech achievements, then it is becoming more and more complex with existing feedback and controller. However, the nonlinearity of the system causes the difficulty for accurate control. Recently, researchers have focused on dynamic characteristics of a hydraulic positioning system for the controlling purpose. Some of them designed and implemented a suitable controller proper operation with nonlinear and dynamics system (Maneetham and Afzulpurkar, 2010). Hydraulic positioning system uses proportional-integral-derivative controllers (PID). This controller is the most famous controller among industrial player because of the simplicity of PID structure and easy to implement in various industrial applications. However, PID controller has some issues that limit their application. The main issue is the difficulty to tune the PID controller. This is significant when the controlled system is highly dynamic. It will be hard for the system to achieve the desired performance when the system is nonlinear and time-varying.
16 2 Recently, particle swarm optimization (PSO) has been implemented in various applications. PSO algorithm is a new evolutionary computational technique. This algorithm is designed to solve optimization problems and easy to be implemented (Allaoua et al., 2009). PSO algorithm is used to determine the optimal PID controller parameters. The goal of this study is to implement PSO-PID tuning algorithm together with the Variable Weight Grey-Taguchi Design of Experiment (DOE) so that an optimal performance of hydraulic positioning system is achieved. 1.2 RESEARCH PROBLEM STATEMENT The hydraulic positioning system is a complex system because their system dynamic is highly nonlinear. This brings difficulty to control the system that requires conflicting performance criteria. For example, the system response (the rise time) is required to be fast but if the response is too fast, the response may overshoot. Conversely, if the response is not allowed to overshoot, then the response cannot be too fast. These are conflicting performance criteria. The standard PID controller is commonly used in many applications. To achieve the conflicting criteria (the optimum response), proper tuning is required to determine the right values of the PID parameters. The oldest and the standard tuning method is proposed by Ziegler-Nichols (Patki et al., 2013). In the last decade, intelligent techniques are applied in many optimization problems. One of the techniques is PSO technique. When using the PSO technique, a performance function is created based on the conflicting criteria. Then, the controlling factors, which are the parameters to be optimized, are represented as particles. The advantage of PSO technique is the sharing and cooperating of controlling factors between the particles. Gaing (2004) has proposed the PSO-PID tuning algorithm to optimize the PID parameters in an automatic voltage regulator system (AVR). He found that the tuning algorithm is a better approach in determining the optimum parameters compared to the GA algorithm. However, the PSO-PID tuning algorithm proposed by his can still be
17 3 improved because two of the important parameters in the algorithm are not properly studied. The parameters are the limit of change in particle velocity and the weight distribution factor between the particles. Both parameters are studied using the Variable Weight Grey-Taguchi DOE method in order to obtain better system performance. 1.3 RESEARCH OBJECTIVE The objectives of the research are: (i) To identify and obtain the mathematical transfer function of the hydraulic positioning system. (ii) To simulate the performance of the PSO-PID tuning algorithm of hydraulic positioning system. (iii) To modify and simulate the performance of PSO-PID tuning of hydraulic positioning system by using Variable Weight Grey-Taguchi with DOE method. (iv) To experimentally verify the proposed PSO-PID tuning algorithm of hydraulic positioning system. 1.4 RESEARCH SCOPE Below are the research scopes: (i) This research is limited only in position control of hydraulic positioning system. (ii) This research uses MATLAB and Simulink to model hydraulic positioning system using mathematical transfer function and to simulate the system performance. (iii) This research only focuses on the hydraulic positioning system by using PID controller. System performance uses terminal step response as an observation platform.
18 4 (iv) This physical experiment is designed and conducted to validate the performance of position control only. Speed control is not part of this research. (v) This physical experiment use closed-loop experimental data from the results of the proposed PSO-PID tuning parameters and compare the performance with the Ziegler-Nichols tuning method. 1.5 RESEARCH APPROACH Firstly, reviews of hydraulic positioning system were carried out. This review was done on the design and application of a controller system, the principles of PID controller, the tuning method of the PID parameters, the principles of PSO algorithm and the previous research on the optimization of PID controller as well as their limitations and improvements. Secondly, modelling of the hydraulic positioning system was carried out in order to obtain the mathematical transfer function of the system. Then, the transfer function was simulated to confirm with the experimental data. Next, optimization process was applied to the transfer function using the PSO-PID tuning algorithm in order to obtain the optimum values of PID parameters. The Variable Weight Grey-Taguchi is then implemented in order to determine the suitable PSO parameters. The simulation processes were performed using MATLAB and Simulink. Both the proposed and Ziegler-Nichols tuning algorithm were implemented on the hydraulic positioning system and the optimum parameters were identified. Lastly, physical experiment is conducted to validate the simulation results. The validation process analyses the system performance using transient response and steady-state response. 1.6 THESIS ORGANIZATION The thesis is structured as follows: Chapter 2: Literature Review of Proportional-Integral-Derivative Controller and Particle Swarm Optimization discussing on hydraulic positioning
19 5 system, PID controller and PSO algorithm in the perspective of the background knowledge and research literature. Chapter 3: The Proposed PSO-PID and the Variable Weight Grey- Taguchi Tuning Algorithm this chapter presents in detail of PSO-PID controller by Gaing (2004) algorithm. Then, the proposed PSO-PID tuning algorithm is based on the implementation of Gaing (2004) algorithm as well as the Variable Weight Grey- Taguchi DOE method is presented. Chapter 4: Results and Discussion this chapter presents the process and result of simulations and physical experiments using a classical PID controller and PSO-PID controller. Using the results obtained from experiment, comparison is made between the Ziegler-Nichols and the proposed PSO-PID based on the step responses of the hydraulic-position system. Finally, in Chapter 5: Conclusion this chapter presents the conclusions of the research and recommendations for future research work.
20 CHAPTER 2 PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROLLER AND PARTICLE SWARM OPTIMIZATION REVIEW 2.1 INTRODUCTION This chapter presents reviews of hydraulic positioning system specifically the mathematical modelling and parameter optimization of the PID controller and its tuning method. This review begins with the introduction of the hydraulic positioning system, concentrating on proportional valve and servo control unit. Later, this review continues with the description of the servo controller and the use of the PID controller followed by a brief description of the controller structure. Furthermore, the review discusses the PID parameter tuning methods that lead to the artificial intelligence techniques. Then, the review includes a brief discussion on swarm intelligence whereby the PSO is one of the method lies within the techniques. Lastly, the review presents recent studies on PID tuning methods using the PSO algorithm. 2.2 HYDRAULIC SYSTEM The industrial revolution was the transition from an old water clock mechanism to a new manufacturing process using fluid power technology (Maskrey and Thayer, 1978). During that time, the inventions like hydraulic accumulators, control valves and actuators were essential components of all hydraulic systems. The technology drove major developments of the second half of the 20 th century (Maskrey and Thayer, 1978).
21 7 Initially, hydraulic flow control device used open loop control technique. Then, a few years after the World War II, development of servo-control technique known as closed-loop control had increased. Historically, Maskrey and Thayer (1978) assist in the research and development of hydraulic servo-technique. Nowadays, hydraulic system is one of the important and widely used in the manufacturing industry (Jelali and Kroll, 2002). In the manufacturing industry, machine applications such as punching, pressing, mobile lifting, digging and material handling use hydraulic system because of the large force requirement. Another characteristic of the hydraulic system is stiff response (Jelali and Kroll, 2002). Because of this characteristic, rolling mill, machine tool drives and flight simulator use hydraulic system. The accurate control of response is necessary to the system so that the systems can be used in the control surface of aircraft, machine tool slides and industrial robots (Merritt, 1967). The hydraulic system has many advantages. Merritt (1967) and Bauer (1998) stated that hydraulic system produces larger force and have a good stiffness characteristic. The system can perform accurate control. It has low wear rate because the hydraulic fluid is acting as a lubricant (Rydberg, 2009). The systems can be operated under several conditions such as continuous, reversing or stalled. The flexibility of the hydraulic power element can be found in both linear and rotary actuators. Moreover, the protection for overloading in the system operation is easy to implement. The system also has longer component life and available in smaller and lighter compact system. The disadvantage of hydraulic system is the response dynamic. The hydraulic system is highly non-linear and the movement is relatively difficult to precisely control. A good system requires a controller to perform a stable and a desired performance. There are various control techniques applied on hydraulic system, such as adaptive control, nonlinear control, intelligent control and servo control.
22 8 Servo control is the most common controller design in application involving position control. Next section will discuss the servo control of the hydraulic system. In addition, it will also explain the various control techniques of hydraulic system Proportional Valve One of important mechanical part in hydraulic system is proportional valve. The term proportional valve refers to a specific type of valve which is quite distinctive to servo valves. The proportional valves are about a solenoid activated valve with very distinctive operating characteristics (BTP, 2012). The proportional valves are used to provide a smooth and continuous variation in flow or pressure in response to an electrical input (Lunge et al., 2013). Table 2.1 is defined the differences between the more conventional servo valves and proportional valves. Fundamentally, it shows the construction and flow pressure-current characteristics that will mark the differences. Table 2.1: Characteristics difference between servo valve and proportional valve Proportional valve Servo valve Open loop control Less costly then servo valve Required more power (50W) Closed loop control Very expensive Low power input (.1-.3W) Moderate filtration (30 m) High filtration (1-5 m) Spools are overlapped Flow-current characteristic very nonlinear Spools critically lapped Flow-current characteristic very linear Hysteresis large 0.5% Very low hysteresis 0.1% Can be used as flow, pressure and directional valves (pressure compensation) Can be used in closed loop control if expectations not high Used primarily in closed loop to create flow and pressure control When used in closed loop, high performance is expected Source: Jelali and Kroll (2002)
23 9 There are three types of proportional valves in hydraulics as following (Jelali and Kroll, 2002): such as flow valve, pressure valves and directional valves. The directional valves are useful and popular for a wide range of hydraulic applications. Directional valves are used as multi-polar switches (Jelali & Kroll 2002). The proportional valve is proposed to improve the function of directional valve. They were used to control the directional of actuator motion. The fundamental principle of operation of proportional valves is based on the use of a proportional solenoid. The use of proportional solenoid is to moves the valve spool to the desired position. It normally used because of less expensive with fewer performance demands such as larger values of hysteresis and dead-bands (Jelali & Kroll, 2002). The development of proportional valves for application such as the precision of a servo valve is not needed, but more accuracy is needed than a conventional valves. The proportional valve is also functioning to provide a smooth and continuous variation in flow or pressure in response to input signal (Lunge et al., 2013). Figure 2.1 shows a partly cross sectional view of the proportional valve for 3/4 way types Figure 2.1: Proportional valve Source: Besch (2012)
24 10 The electrical operator of proportional valve is using proportional solenoid In electronic concept that applying a current to a coil creates a magnetic field which when passed through an appropriate core material can produces in a magnetic force (BTP, 2012). The force when applied to a movable armature will result in a motion towards the core. The proportional solenoids are shaped (armature, coil and pole piece) such that the force of attraction is relatively constant over the stroke. This is illustrated schematically in Figure 2.2. The mathematical expression of the relation between force and stroke can be described based on this statement: If i is held constant, then the force of attraction is approximately constant over the working stroke. Thus, F i ; F k i, whereby F.is proportional to i. i Figure 2.2: Proportional solenoid Source: BTP (2012)
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