FORCE CONTROL USING PREDICTIVE FUNCTIONAL CONTROL (PFC)

ALGORITHM FOR TWO CHAMBERS SOFT ACTUATOR

NAJIB KABIR DANKADAI

A project report submitted in partial fulfilment of the

requirements for the award of the degree of

Masters of Engineering (Electrical-Mechatronics & Automatic Control)

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

JUNE 2014

iii

This project is dedicated to my beloved mother Haj. Nafisa Habib, father

Alh. Kabir.M. Dankadai, my brothers my sisters and Rabi’u Kwankwaso for their

encouragement and blessing, support and caring.

iv

ACKNOWLEDGEMENT

In The Name of God.

I am particularly grateful to ALLAH (S.W.T.) for giving me the courage,

strength and ability to successfully undertake and complete this report work.

I would like to express my gratitude to my project supervisor, Dr. Ahmad

Athif Mohd Faudzi for his moral support, making useful corrections, comments,

suggestions to improve the quality of this project and took the pains in reading the

entire thesis scripts.

I am indebted to express my thanks to my friends Amiru Bature, Usman

Tasi’u, Shahrul Hamzah bin Abdul Razak, Khairuddin Osman and Muhammad

Rusydi and also the entire staffs of Electrical Engineering Department.

Finally I would like to dedicate this achievement to my parents, family and

friends who have helped me directly or indirectly and sacrificed a lot in the

completion of this study.

v

ABSTRACT

The current trend in the world of automation and robotics heavily applies

metal structure type of the actuators which are heavy, rigid, difficult and expensive

to develop. Other areas of applications like medical, agriculture, biological and

welfare requires less rigid and safer robots. Thus, a biologically inspired robot is

required to meet this certain criteria. This lead to the recent attraction in the study

and development of Pneumatic Soft Actuator (PSA) because it has more advantages

over hard actuators to suit the applications mentioned above due to its simple

structure, low cost, high efficiency, high compliance, high power to weight ratio and

ensures safe and more natural way of interaction. Despite the advantages of

pneumatic soft actuator it has nonlinearity and hysteresis, which makes them

difficult to model and control. The main objective of this study was to obtain

mathematical model and control the force of a two chamber pneumatic soft actuator.

Obtaining nonlinear mathematical model accurately to be used in controller design

needs to determine all physical parameters of the real system which is very

expensive and time consuming, to simplifying this procedure, model of system was

analysed and obtained using system identification toolbox in MATLAB software.

Input and output data was acquired from an experimental setup which was used to

obtain a transfer function force model of the system. The best model was accepted

based on the best fit criterion through SI toolbox. Predictive Functional Controller

(PFC) was designed and simulated for the model via MATLAB/Simulink. The

results showed that PFC controller provides better output than a conventional PID

controller when tested using several references. PFC controller exhibits faster

response to the system with desired transient error. The study represented in this

project can be further broaden by taken position control into account and validation

of the simulated control can be done on the experimental setup.

vi

ABSTRAK

Trend semasa di dalam dunia automasi dan robotik banyak bergantung

kepada jenis penggerak dari struktur logam yang berat, tegar, mahal dan sukar untuk

dibangunkan. Antara bidang lain yang menggunakan aplikasi ini adalah seperti

perubatan, pertanian, biologi dan kebajikan yang memerlukan robot yang kurang

tegar dan lebih selamat. Oleh itu, sebuah robot yang berinspirasikan biologi

diperlukan untuk memenuhi kriteria yang tertentu. Hal ini membawa kepada tarikan

terbaru dalam kajian dan pembangunan penggerak pneumatik lembut kerana ia

mempunyai banyak kebaikan berbanding penggerak kasar untuk disesuaikan dengan

aplikasi yang disebutkan di atas kerana ia mempunyai struktur yang mudah, kos

rendah, kecekapan tinggi, pematuhan yang tinggi, kuasa tinggi kepada nisbah berat

dan menjamin keselamatan serta interaksi yang lebih semula jadi. Walaupun

penggerak pneumatik lembut mempunyai pelbagai kebaikan, namun sifatnya yang

tidak linear dan histerisis, menjadikan ianya sukar untuk dimodel dan dikawal.

Objektif utama kajian ini adalah untuk mendapatkan model matematik dan

mengawal daya pada sebuah penggerak pneumatik lembut yang mempunyai dua

kebuk. Data bagi masukan dan keluaran diperolehi daripada eksperimen yang

dijalankan dan ianya digunakan untuk medapatkan model persamaan daya bagi

sistem ini. Model terbaik yang diterima adalah berdasarkan kepada kriteria sesuai

yang terbaik melalui kelengkapan pengenalan sistem (SI Toolbox). Pengawal fungsi

ramalan (PFC) telah direkabentuk dan model telah disimulasikan dengan

menggunakan perisian MATLAB/SIMULINK. Hasil kajian menunjukkan pengawal

PFC mampu menyediakan keluaran yang lebih baik berbanding pengawal PID

konvensional apabila diuji dengan beberapa rujukan.

vii

TABLE OF CONTENTS

CHAPTER CONTENT PAGE

DECLARATION

ii

DEDICATION

iii

ACKNOWLEDGEMENT iv

ABSTRACT

v

ABSTRAK

vi

TABLE OF CONTENTS vii

LIST OF TABLES

ix

LIST OF FIGURES

x

LIST OF ABBREVIATIONS xii

1 INTRODUCTION

1

1.1 Project background 1

1.2 Problem Statement 3

1.3 Project Objectives 4

1.4 Project scope 4

1.5 Project Report Outline 5

2 LITERATURE REVIEW 6

2.1 Introduction 6

2.2 System Model 6

2.2.1 Analytical Modeling 7

2.2.2 Numerical Modeling 10

2.2.3 Artificial Intelligence based Modeling 11

2.3 Control Strategies 13

viii

2.4 Summary 16

3 PROJECT METHODOLOGY 18

3.1 Introduction 18

3.2 Mathematical Modeling 20

3.2.1 Components used for the System

Identification

22

3.2.1.1 Control valve 23

3.3 Transfer Function of Pneumatic Soft Actuator 25

3.3.1 Transfer Function using System Identification 25

3.4 Controller Design 32

3.3.1 PFC control algorithm 32

3.4.1 PID control algorithm 36

3.5 Conclusion 40

4 RESULT & DISCUSSION 41

4.1 Introduction 41

4.2 Model Simulation 41

4.2.1 Transfer Function Model Simulation 42

4.3 PFC Controller 44

4.4 PID Controller 47

4.5 Complete Controller System Performance 50

4.6 Summary 52

5 CONCLUSION

54

5.1 Project Conclusion 54

5.2 Recommendations 55

REFERENCES

56

Appendices A-B

59

ix

LIST OF TABLES

TABLE NO. TITLE PAGE

1.1 Advantages of soft actuators over hard actuators 2

3.1 Some type of Valves and their application 24

and functions

3.2 PSO selection initializing parameters 39

4.1 PID controller parameter 49

5.1 Table5.2: Common Valve Specifications 60

5.2 Table 5.3: Valve Controller Specifications 61

x

LIST OF FIGURES

FIGURE TITLE PAGE

1.1 A two chamber pneumatic soft actuator. 3

2.1 Contraction-Force graph comparing experimental and

derived model at 4 bar

8

2.2 Three element mechanical components 9

2.3 Three types of Fuzzy optimization approaches and

Estimation using neural network .

12

2.4 Dynamic simulation model of the pneumatic actuator based

on geometric model of two artificial muscles in antagonistic

connection.

14

2.5 Block diagram of the control system. 15

3.1 Research methodology flow 19

3.2 Flowchart for System Identification Process 21

3.3 Experimental for System Identification Process 22

3.4 Experimental Setup Component for data acquisition in this

Project

23

3.5 Schematic Diagram of Valve Spool 25

3.6 TF Model Structure 28

3.7 Sine shape input Signal. 28

3.8 Acquired output data 28

3.9 Importing data sets to MATLAB system ID toolbox 29

3.1 System Id Toolbox Window on MATLAB 30

xi

3.11 Normalized and Divided Input and Output Data for

Estimation and Validation

30

3.12 Selecting TF Model with Order of 31. 31

3.13 Estimated Output versus Actual Output 32

3.14 Block Diagram of PFC for Force Model. 34

3.15 PFC Control Strategy Simulink Diagram 37

3.16 Flow chart for PSO algorithm 40

4.1 Simulink Block Diagram for the System Identification

Process

43

4.2 Input and output signals used for System ID. 44

4.3 Block Diagram of Open Loop Pneumatic System. 44

4.4 The measured and simulated model output for 2-chamber

Pneumatic Soft Actuator When Sine Wave Signal is used as

an Input.

45

4.5 Response of close-loop the system to Step input signal

(PFC)

44

4.6 Response of close-loop the system to Sinusoidal input signal

(PFC)

45

4.7 Response of close-loop the system to Multi Step input signal

(PFC)

48

4.8 PFC step tracking control signal. 48

4.9: Response of close-loop the system to Step input signal (PID) 49

4.10 Response of the close-loop system to sine wave input signal

(PID)

50

4.11 Response Of The Close-Loop System To Multi Step Input

Signal (PID)

50

4.12 Complete Block Diagram of PID and PFC Controller 51

4.13 Performance comparison of PFC with PID for Step input

signal

52

4.14 Performance comparison of PFC with PID for Sinusoidal

input signal

52

xii

4.15 Performance comparison of PFC with PID for Multi Step

input signal

53

xiii

LIST OF ABBREVIATIONS

AI - Artificial Intelligence

ARX - Auto-Regressive with Exogenous

ARMAX - Auto-Regressive Moving Average with Exogenous

BJ - Box-Jenkins

DC - Direct Current

FIS - Fuzzy Inference System

GA - Genetic Algorithms

GD - Gradient Descent

ID - Identification

LMS - Least Mean-Squares

MGA - Modified Genetic Algorithm

MPC - Model Predictive Control

NN - Neural Network

N-PID - Nonlinear Proportional Integral Derivative

NARX - Nonlinear Auto-Regressive with Exogenous

OE - Output Error

PAM - Pneumatic Artificial Muscle

PFC - Predictive Functional Controller

PI - Proportional – Integral

PD - Proportional - Derivative

PID - Proportional Integral Derivative

PSA - Pneumatic Soft Actuators

PSO - Particle Swarm Optimization

SI - System Identification

CHAPTER 1

INTRODUCTION

1.1 Project background

In the use of pneumatic system is rapidly increasing in the sector of

automation and modern industry. Therefore nowadays a lot of pneumatic actuation

tools are being developed, studied and used in order to convert compressed gas

energy to mechanical energy [1]. Some of the pneumatic actuators used include tie

rod cylinders, rotary actuators, grippers, rodless actuators with magnetic linkage or

rotary cylinders, Rodless actuators with mechanical linkage, pneumatic artificial

muscle and Vacuum generators e.t.c. The current trend in the world of automation

and robotics heavily applies metal structure type of the actuators which is heavy

rigid difficult and expensive to develop and not suitable for human interaction.

Other areas of applications like medical, agriculture, biological and welfare requires

less rigid and safer robots. A biologically inspired is required to meet this criterion

in order to perform tasks with more safety. This leads to the recent attraction in the

study and development of pneumatic artificial muscle (soft actuator). This type of

soft actuator has its own advantages over the hard type. Table 1.1 shows some of the

qualifications.

A 2- chambers pneumatic soft actuator will be considered in this project. A

2- chambers Soft pneumatic Actuator is made of rubber with fiber reinforce and has

a cylindrical shape with two symmetrical holes (chambers) as shown in Figure 1.1.

2

It can deform in three motions of shorten, elongate and bend. It uses only pneumatic

input to move and having a soft motion in its movements.

Table 1.1: Advantages of soft actuators over hard actuators.

PROPERTIES SOFT ACTUATOR HARD

ACTUATOR

Safety Safe Dangerous

Working Environment Structured and unstructured Structure only

Degree of freedom/compliance Infinite Few

Cost Low High

Robotic actuation Under Actuated Fully actuated

Due to the soft actuator type of applications, the need for a robust, flexible

and precise control of soft actuator is required. Soft actuators are difficult to control

using classical control because they have nonlinearity; hysteresis and their behavior

also change with time. In addition to that soft actuators are also difficult to obtain

accurate and parsimonious model that adequately describe the behavior of the

system [1]

Many methods which are categorized as analytical modeling, numerical

Modeling and artificial Intelligence based modeling [2] has been used to build

dynamic equations that best represent the soft actuator. One of the most popular and

effective way is to chose a given model structure based on the prior knowledge of

the system and identify the system parameters by estimation method using

experimentally acquired data. This method is known as System ID method

3

Figure 1.1 A two chamber pneumatic soft actuator [27].

Based on all that mentioned before, it can be learnt that pneumatics soft

actuator are a qualified alternative over pneumatic hard actuator systems if there is a

solution to tackle its problems. Thus, controller design and its implementation for

pneumatic soft actuators is one of the challenging problems in control engineering.

Predictive Functional Control (PFC) design is selected as the control strategy

for the pneumatic system. Performance assessment of the PFC controller is

performed in MATLAB. Result shows that the PFC controller is adapted to the

system and able to control successfully in the simulation.

1.2 Problem statement

Due to its type of applications, the need for a robust, flexible and more

accurate force control arises.

Soft actuators are difficult to control using classical control because they

have:

i. nonlinearity.

4

ii. hysteresis .

iii. it’s behavior also varies with time.

Difficult to obtain accurate and parsimonious model that adequately describe

the behavior of the system

1.3 Project Objectives

The objective of this project is to precisely control the bending force exerted

by the two chamber pneumatic soft actuator with an accurate and fast enough

response are desired. So regarding to this aim, overall objective can be divided into

three. Which are:

To develop a force mathematical model of a 2- chambers pneumatic soft

actuator.

i. To design a controller using Predictive functional control for a soft actuator

flexible mechanism.

ii. To simulate and analyze the characteristics of the force control in

MATLAB/simulink software.

1.4 Project scope

The scope of work in fulfilling the project objectives are;

i. A two chamber pneumatic soft actuator will be considered.

ii. The mathematical model of force for the two chamber pneumatic soft

actuator will be obtained by implementing system identification method.

5

iii. Predictive functional control will be studied, designed, tuned and

implemented using MATLAB /simulink.

iv. Also, the force control will be simulated using MATLAB/Simulink.

1.5 Project Report Outline

This project thesis is organized in five chapters. Chapter one gives an

overview of the system, objectives and scope of the project and also gives

introduction regarding the problem to be solved. Chapter two reviews some

previous research and literatures related to this project. Chapter three provides steps

of the methodology and description of each procedure to be followed in order to

solve the problem at in view. Chapter four gives a detailed explanation of the results

obtained from simulation and experiment and discuses the outcomes from the

followed methodology. And finally chapter five presents conclusion on the

achievements in the project and also set forth some recommendations for further

future works.

REFERENCES

[1] Hazem I. Ali, Samsul Bahari B Mohd Noor, S. M. Bashi, M. H. Marhaban,

2009. A Review of Pneumatic Actuators (Modeling and Control). Australian

Journal of Basic and Applied Sciences, 3(2): 440-454.

[2] Prashant K. Jamwal, Shahid Hussain and Sheng Quan Xie ‘Dynamic

Modeling of Pneumatic Muscles Using Modified Fuzzy Inference

Mechanism’ Proceedings of the 2009 IEEE International Conference on

Robotics and Biomimetics December 19 -23, 2009, Guilin, China..

[3] Khairuddin Osman, Member, IEEE, Ahmad 'Athif Mohd Faudzi, Member,

IEEE, M.F. Rahmat, Nu'man Din Mustafa and Koichi Suzumori, Member,

IEEE “Predictive Functional Controller Design for Pneumatic Actuator.

[4] Mingcong Deng, aihui Wang, Shuichi Wskimoto, and Tashihiro Kawashima

”Characteristic Analysis and modeling of a Miniature Pneumatic Rubber

Actuator” processing of the 2011 inernational Conference on Advance

Mechatronics systems, Zhengzhou, China, August 11-13-2011.

[5] Li Songbo, Jin Jian and He Qingwei(1)‘Modelling and assessment of

pneumatic artificial muscle’ School of Mechanical Engineering, Shanghai

Jiaotong University, Shanghai, P.R. CHINA ,2006.

[6] S. W. Chan, John H> Lilly “Adaptive Tracking for Pneumatic Muscle

Actuators. in Bicep and Tricep Configurations” IEEE transactions on neural

systems and rehabilitation engineering , vol. 11, no. 3, september 2003.

[7] Tamas Szepe ‘Accurate force function approximation for pneumatic artificial

muscles’ 3rd IEEE International Symposium on Logistics and Industrial

Informatics August 25–27, 2011, Budapest, Hungary.

[8] Mervin Chandrapal, XiaoQi Chen, and Wenhui Wang “Self Organizing Fuzzy

Control of Pneumatic Artificial Muscle for Active Orthotic Device” 6th

annual IEEE Conference on Automation Science and Engineering, 2010.

57

[9] B. Tondu and P. Lopez, "Theory of an artificial pneumatic muscle and

application to the modelling of McKibben artificial muscle," Theorie d'un

muscle artificiel pneumatique et application a la modelisation du muscle

artificiel de McKibben, vol. 320, pp. 105- 114, 1995.

[10] D. Schindele and H. Aschemann, "Nonlinear model predictive control of a

high-speed linear axis driven by pneumatic muscles," in Proceedings of the

American Control Conference, 2008, pp. 3017- 3022.

[11] H. P. H. Anh and K. K. Ahn, "Identification of pneumatic artificial muscle

manipulators by a MGA-based nonlinear NARX fuzzy model," Mechatronics,

vol. 19, pp. 106-133.

[12] . Chang and J. H. Lilly, "Fuzzy control for pneumatic muscle tracking via

evolutionary tuning," Intelligent Automation and Soft Computing, vol. 9, pp.

227-244, 2003.

[13] K. K. Ahn and H. P. H. Anh, "A new approach for modelling and

identification of the pneumatic artificial muscle manipulator based on

recurrent neural networks," Proceedings of the Institution of Mechanical

Engineers. Part I: Journal of Systems and Control Engineering, vol. 221, pp.

1101-1121, 2007.

[14] Marcel More and Ondrej Líška “Comparison of different methods for

pneumatic artificial muscle control” Technical University of Košice/ Faculty

of Mechanical Engineering/ Department of Automation, Control and Human

Machine Interaction / Košice, Slovakia.

[15] Ján Pite, Mária Tóthová ” Dynamic Modeling of PAM Based Actuator Using

Modified Hill´s Muscle Model ‘ 14th International Carpathian Control

Conference (ICCC), 2013.

[16] A. Calanca, S. Piazza, P. Fiorini]’ Force Control System for Pneumatic

Actuators of an Active Gait Orthosis’ Proceedings of the 3rd IEEE RAS &

EMBS International Conference on Biomedical Robotics and

Biomechatronics, The University of Tokyo, Tokyo, Japan, September 26-29,

2010.

[17] F. Rahmat, S. N. S. Salim, A. A. M. Faudzi, Z. H. Ismail, S.I.Samsudin,

N.H.Sunar, and K.Jusoff . “Non-linear Modeling and Cascade Control of an

Industrial Pneumatic Actuator System.” Australian Journal of Basic and

Applied Sciences, 5(8): 465-477. 2011.

58

[18] J. A. Rossiter and J. Richalet, "Handling constraints with predictive functional

control of unstable processes," in Proceedings of the American Control

Conference, 2002, pp. 4746-4751 vol.6.

[19] L. Wang, Model Predictive Control System Design and Implementation Using

MATLAB: Springer, 2009.

[20] S. J. Qin and T. A. Badgwell, "A survey of industrial model predictive control

technology," Control Engineering Practice, vol. 11, pp. 733- 764, 2003.

[21] J. A. Rossiter and J. Richalet, "Handling constraints with predictive functional

control of unstable processes," in Proceedings of the American Control

Conference, vol.6, 2002, pp. 4746-4751.

[22] K.E.Parsopoulos and M.N.Vrahatis,“Particle swarm optimizer in noisy and

continuously changing environment”,Indianapolis.IN (2001).

[23] Hirotaka Yoshida, Kenichi Kawata, yoshikazuFukuyana, yosuke Nakanishi,

“A particle swarm optimization for reactive power and voltage control

considering voltage stability”, IEEE international conference on intelligent

system applications to power systems(ISAP‟99), Rio de Janeiro, April 4-8

(1999).

[24] Jun Zhao, Tianpeng Li and JixinQian “Application of Particle Swarm

Optimization Algorithm on Robust PID controller Tuning”, Springerlink-

Verlag Berlin Heidelberg , pp. 948-957, (2005).

[25] Zwe-Lee Gaing “A Particle Swarm Optimization Approach for Optimum

Design of PID Controller in AVR System” IEEE Transactions On Energy

Conversion, Vol. 19, No. 2, June 2004

[26] Suzumori, K., Endo, S., Kanda, T., Kato, N. & Suzuki, H. Year. A bending

pneumatic rubber actuator realizing soft-bodied manta swimming robot. In,

2007. 4975-4980.