Challenges and Paradigms in Applied Robust Control Edited by Andrzej Bartoszewicz CHALLENGES AND PARADIGMS IN APPLIED ROBUST CONTROL Edited by Andrzej Bartoszewicz INTECHOPEN.COM Challenges and Paradigms in Applied Robust Control http://dx.doi.org/10.5772/1024 Edited by Andrzej Bartoszewicz Contributors Abhijit Das, Frank L. Lewis, Jong Shik Kim, Han Me Kim, Sung Hwan Park, Euripedes Nobrega, Alysson Mazoni, Alberto Serpa, Benedikt Alt, Ferdinand Svaricek, Nelson Hernan Aros, Graciela Ingrid Suarez Segali, Joaquin Alvarez, David Rosas, Bruno Ferreira, Aníbal Matos, Nuno Alexandre Cruz, Wojciech Grega, Rafal Jastrzebski, Adam Pilat, Alexander Smirnov, Olli Pyrhonen, Takuma Suzuki, Masaki Takahashi, Takami Matsuo, Yusuke Totoki, Haruo Suemitsu, Tetsuo Shiotsuki, Toru Eguchi, Takaaki Sekiai, Naohiro Kusumi, Akihiro Yamada, Satoru Shimizu, Masayuki Fukai, Adolfo Sollazzo, Gianfranco Morani, Giovanni Cuciniello, Federico Corraro, Nitin Kaistha, V Pavan Kumar Malladi, Yang Bin, Keqiang Li, Nenglian Feng, He Chen, Hong Bai, Farhad Shahraki, Kiyanoosh Razzaghi, Mark Lawley, Shengyong Wang, Song Foh Chew, John Martin Anderies, Armando A Rodriguez, Jeffrey Dickeson, Oguzhan Cifdaloz © The Editor(s) and the Author(s) 2011 The moral rights of the and the author(s) have been asserted. 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For more information visit www.intechopen.com 4,100+ Open access books available 151 Countries delivered to 12.2% Contributors from top 500 universities Our authors are among the Top 1% most cited scientists 116,000+ International authors and editors 120M+ Downloads We are IntechOpen, the world’s leading publisher of Open Access books Built by scientists, for scientists Meet the editor Andrzej Bartoszewicz received M.Sc. degree in 1987 and Ph.D. degree in 1993, both from Technical University of Łódź, Poland. Then he obtained the degree of Assis - tant Professor in control engineering and robotics from Academy of Mining and Metallurgy in Cracow, Poland. He was visiting scholar at Purdue University, West La- fayette, In., USA and at Strathclyde University, Glasgow, UK. Then for one year he was at the University of Leicester, UK. Currently he is Professor at Technical University of Łódź, vice dean of Faculty of Electrical, Electronic, Computer and Control Engineering, head of Electric Drive and Industrial Automation Group and vice-director of Institute of Automatic Control. He has published three monographs and over 250 pa- pers, primarily in the fields of sliding mode control and congestion control in data transmission networks. Contents Preface XI Part 1 Robust Control in Aircraft, Vehicle and Automotive Applications 1 Chapter 1 Sliding Mode Approach to Control Quadrotor Using Dynamic Inversion 3 Abhijit Das, Frank L. Lewis and Kamesh Subbarao Chapter 2 Advanced Control Techniques for the Transonic Phase of a Re-Entry Flight 25 Gianfranco Morani, Giovanni Cuciniello, Federico Corraro and Adolfo Sollazzo Chapter 3 Fault Tolerant Depth Control of the MARES AUV 49 Bruno Ferreira, Aníbal Matos and Nuno Cruz Chapter 4 Robust Control Design for Automotive Applications: A Variable Structure Control Approach 73 Benedikt Alt and Ferdinand Svaricek Chapter 5 Robust Active Suspension Control for Vibration Reduction of Passenger's Body 93 Takuma Suzuki and Masaki Takahashi Chapter 6 Modelling and Nonlinear Robust Control of Longitudinal Vehicle Advanced ACC Systems 113 Yang Bin, Keqiang Li and Nenglian Feng Part 2 Control of Structures, Mechanical and Electro-Mechanical Systems 147 Chapter 7 A Decentralized and Spatial Approach to the Robust Vibration Control of Structures 149 Alysson F. Mazoni, Alberto L. Serpa and Eurípedes G. de O. Nóbrega X Contents Chapter 8 Robust Control of Mechanical Systems 171 Joaquín Alvarez and David Rosas Chapter 9 Robust Control of Electro-Hydraulic Actuator Systems Using the Adaptive Back-Stepping Control Scheme 189 Jong Shik Kim, Han Me Kim and Sung Hwan Park Chapter 10 Discussion on Robust Control Applied to Active Magnetic Bearing Rotor System 207 Rafal P. Jastrzebski, Alexander Smirnov, Olli Pyrhönen and Adam K. Piłat Part 3 Distillation Process Control and Food Industry Applications 233 Chapter 11 Reactive Distillation: Control Structure and Process Design for Robustness 235 V. Pavan Kumar Malladi and Nitin Kaistha Chapter 12 Robust Multivariable Control of Ill-Conditioned Plants – A Case Study for High-Purity Distillation 257 Kiyanoosh Razzaghi and Farhad Shahraki Chapter 13 Loop Transfer Recovery for the Grape Juice Concentration Process 281 Nelson Aros Oñate and Graciela Suarez Segali Part 4 Power Plant and Power System Control 303 Chapter 14 A Robust and Flexible Control System to Reduce Environmental Effects of Thermal Power Plants 305 Toru Eguchi, Takaaki Sekiai, Naohiro Kusumi, Akihiro Yamada, Satoru Shimizu and Masayuki Fukai Chapter 15 Wide-Area Robust H 2 / H ∞ Control with Pole Placement for Damping Inter-Area Oscillation of Power System 331 Chen He and Bai Hong Part 5 Selected Issues and New Trends in Robust Control Applications 347 Chapter 16 Robust Networked Control 349 Wojciech Grega Chapter 17 An Application of Robust Control for Force Communication Systems over Inferior Quality Network 373 Tetsuo Shiotsuki Contents XI Chapter 18 Robust Control for Single Unit Resource Allocation Systems 391 Shengyong Wang, Song Foh Chew and Mark Lawley Chapter 19 Design of Robust Policies for Uncertain Natural Resource Systems: Application to the Classic Gordon-Schaefer Fishery Model 415 Armando A. Rodriguez, Jeffrey J. Dickeson, John M. Anderies and Oguzhan Cifdaloz Chapter 20 Robustness and Security of H -Synchronizer in Chaotic Communication System 443 Takami Matsuo, Yusuke Totoki and Haruo Suemitsu Preface The main purpose of control engineering is to steer the regulated plant in such a way that it operates in a required manner. The desirable performance of the plant should be obtained despite the unpredictable influence of the environment on all parts of the control system, including the plant itself, and no matter if the system designer knows precisely all the parameters of the plant. Even though the parameters may change with time, load and external circumstances, still the system should preserve its nominal properties and ensure the required behavior of the plant. In other words, the principal objective of control engineering is to design and implement regulation systems which are robust with respect to external disturbances and modeling uncertainty. This objective may very well be obtained in a number of ways which are discussed and demonstrated in this book. Book is divided into five sections. In section 1 selected aircraft, vehicle and automotive applications are presented. That section begins with a contribution on rotorcraft control. The first chapter presents input-output linearization based on sliding mode controller for a quadrotor. Chapter 2 gives a comparison of different advanced control architectures for transonic phase of space re-entry vehicle flight. Then chapter 3 discusses the problem of robust fault tolerant, vertical motion control of modular underwater autonomous robot for environment sampling. The last three chapters in section 1 present solutions of the most important control problems encountered in automotive industry. They describe the second order sliding mode control of spark ignition engine idle speed, new active suspension control method reducing the passenger’s seat vibrations and advanced adaptive cruise control system design. Section 2 begins with a chapter on H-infinity active controller design for minimizing mechanical vibration of structures. Then it focuses on robust control of mechanical systems, i.e. uncertain Lagrangian systems with partially unavailable state variables, and adaptive back-stepping control of electro-hydraulic actuators. The last chapter in that section is concerned with the control of active magnetic bearing suspension system for high-speed rotors. Section 3 consists of three contributions on the control of distillation and multi-step evaporation processes. The first chapter, concerned with a generic double feed two- reactant two-product ideal reactive distillation and the methyl acetate reactive XIV Preface distillation systems, demonstrates the implications of the nonlinearity, and in particular input and output multiplicity, on the open and closed loop distillation system operation. The next chapter shows that the desirable closed-loop performance can be achieved for an ill-conditioned high-purity distillation column by the use of a decentralized PID controller and the structured uncertainty model describing the column dynamics within its entire operating range. Then the last chapter of section 3 analyses a complex multi-stage evaporation process and presents a new full order Kalman filter based scheme to obtain full loop transfer recovery for the process. Section 4 comprises two chapters on the control of power plants and power systems. The first of the two chapters studies the problem of reducing environmental effects by operational control of nitrogen oxide and carbon monoxide emissions from thermal power plants. The second chapter is concerned with damping of inter-area oscillations in electric power systems. For that purpose a mixed H2/H-infinity output-feedback control with pole placement is applied. Section 5 presents a number of other significant developments in applied robust control. It begins with a noteworthy contribution on networked control which demonstrates that robust control system design not only requires a proper selection and tuning of control algorithms, but also must involve careful analysis of the applied communication protocols and networks, to ensure that they are appropriate for real- time implementation in distributed environment. A similar issue – in the context of force bilateral tele-operation – is discussed in the next chapter of that section, where it is shown that H-infinity design offers good robustness with reference to network induced time delays. Then the section discusses selected problems in resource allocation and control. These include development of robust controllers for single unit resource allocation systems with unreliable resources and real world natural resource robust management with the special focus on fisheries. The monograph concludes with the presentation of H-infinity synchronizer design and its application to improve the robustness of chaotic communication systems with respect to delays in the transmission line. In conclusion, the main objective of this book is to present a broad range of well worked out, recent engineering and non-engineering application studies in the field of robust control system design. We believe, that thanks to the authors, reviewers and the editorial staff of InTech Open Access Publisher this ambitious objective has been successfully accomplished. The editor and authors truly hope that the result of this joint effort will be of significant interest to the control community and that the contributions presented here will enrich the current state of the art, and encourage and stimulate new ideas and solutions in the robust control area. Andrzej Bartoszewicz Technical University of Ł ód ź Poland Part 1 Robust Control in Aircraft, Vehicle and Automotive Applications 1 Sliding Mode Approach to Control Quadrotor Using Dynamic Inversion Abhijit Das, Frank L. Lewis and Kamesh Subbarao Automation and Robotics Research Institute The University of Texas at Arlington USA 1. Introduction Nowadays unmanned rotorcraft are designed to operate with greater agility, rapid maneuvering, and are capable of work in degraded environments such as wind gusts etc. The control of this rotorcraft is a subject of research especially in applications such as rescue, surveillance, inspection, mapping etc. For these applications, the ability of the rotorcraft to maneuver sharply and hover precisely is important (Koo and Sastry 1998). Rotorcraft control as in these applications often requires holding a particular trimmed state; generally hover, as well as making changes of velocity and acceleration in a desired way (Gavrilets, Mettler, and Feron 2003). Similar to aircraft control, rotorcraft control too involves controlling the pitch, yaw, and roll motion. But the main difference is that, due to the unique body structure of rotorcraft (as well as the rotor dynamics and other rotating elements) the pitch, yaw and roll dynamics are strongly coupled. Therefore, it is difficult to design a decoupled control law of sound structure that stabilizes the faster and slower dynamics simultaneously. On the contrary, for a fixed wing aircraft it is relatively easy to design decoupled standard control laws with intuitively comprehensible structure and guaranteed performance (Stevens and F. L. Lewis 2003). There are many different approaches available for rotorcraft control such as (Altug, Ostrowski, and Mahony 2002; Bijnens et al. 2005; T. Madani and Benallegue 2006; Mistler, Benallegue, and M'Sirdi 2001; Mokhtari, Benallegue, and Orlov 2006) etc. Popular methods include input-output linearization and back-stepping. The 6-DOF airframe dynamics of a typical quadrotor involves the typical translational and rotational dynamical equations as in (Gavrilets, Mettler, and Feron 2003; Castillo, Lozano, and Dzul 2005; Castillo, Dzul, and Lozano 2004). The dynamics of a quadrotor is essentially a simplified form of helicopter dynamics that exhibits the basic problems including under- actuation, strong coupling, multi-input/multi-output, and unknown nonlinearities. The quadrotor is classified as a rotorcraft where lift is derived from the four rotors. Most often they are classified as helicopters as its movements are characterized by the resultant force and moments of the four rotors. Therefore the control algorithms designed for a quadrotor could be applied to a helicopter with relatively straightforward modifications. Most of the papers (B. Bijnens et al. 2005; T. Madani and Benallegue 2006; Mokhtari, Benallegue, and Orlov 2006) etc. deal with either input-output linearization for decoupling pitch yaw roll or back-stepping to deal with the under-actuation problem. The problem of coupling in the Challenges and Paradigms in Applied Robust Control 4 yaw-pitch-roll of a helicopter, as well as the problem of coupled dynamics-kinematic underactuated system, can be solved by back-stepping (Kanellakopoulos, Kokotovic, and Morse 1991; Khalil 2002; Slotine and Li 1991). Dynamic inversion (Stevens and F. L. Lewis 2003; Slotine and Li 1991; A. Das et al. 2004) is effective in the control of both linear and nonlinear systems and involves an inner inversion loop (similar to feedback linearization) which results in tracking if the residual or internal dynamics is stable. Typical usage requires the selection of the output control variables so that the internal dynamics is guaranteed to be stable. This implies that the tracking control cannot always be guaranteed for the original outputs of interest. The application of dynamic inversion on UAV’s and other flying vehicles such as missiles, fighter aircrafts etc. are proposed in several research works such as (Kim and Calise 1997; Prasad and Calise 1999; Calise et al. 1994) etc. It is also shown that the inclusion of dynamic neural network for estimating the dynamic inversion errors can improve the controller stability and tracking performance. Some other papers such as (Hovakimyan et al. 2001; Rysdyk and Calise 2005; Wise et al. 1999; Campos, F. L. Lewis, and Selmic 2000) etc. discuss the application of dynamic inversion on nonlinear systems to tackle the model and parametric uncertainties using neural nets. It is also shown that a reconfigurable control law can be designed for fighter aircrafts using neural net and dynamic inversion. Sometimes the inverse transformations required in dynamic inversion or feedback linearization are computed by neural network to reduce the inversion error by online learning. In this chapter we apply dynamic inversion to tackle the coupling in quadrotor dynamics which is in fact an underactuated system. Dynamic inversion is applied to the inner loop, which yields internal dynamics that are not necessarily stable. Instead of redesigning the output control variables to guarantee stability of the internal dynamics, we use a sliding mode approach to stabilize the internal dynamics. This yields a two-loop structured tracking controller with a dynamic inversion inner loop and an internal dynamics stabilization outer loop. But it is interesting to notice that unlike normal two loop structure, we designed an inner loop which controls and stabilizes altitude and attitude of the quadrotor and an outer loop which controls and stabilizes the position (x,y) of the quadrotor. This yields a new structure of the autopilot in contrast to the conventional loop linear or nonlinear autopilot. Section 2 of this chapter discusses the basic quadrotor dynamics which is used for control law formulation. Section 3 shows dynamic inversion of a nonlinear state-space model of a quadrotor. Sections 4 discuss the robust control method using sliding mode approach to stabilize the internal dynamics. In the final section, simulation results are shown to validate the control law discussed in this chapter. 2. Quadrotor dynamics Fig. 1 shows a basic model of an unmanned quadrotor. The quadrotor has some basic advantage over the conventional helicopter. Given that the front and the rear motors rotate counter-clockwise while the other two rotate clockwise, gyroscopic effects and aerodynamic torques tend to cancel in trimmed flight. This four-rotor rotorcraft does not have a swash- plate (P. Castillo, R. Lozano, and A. Dzul 2005). In fact it does not need any blade pitch control. The collective input (or throttle input) is the sum of the thrusts of each motor (see Fig. 1). Pitch movement is obtained by increasing (reducing) the speed of the rear motor while reducing (increasing) the speed of the front motor. The roll movement is obtained similarly using the lateral motors. The yaw movement is obtained by increasing (decreasing) Sliding Mode Approach to Control Quadrotor Using Dynamic Inversion 5 the speed of the front and rear motors while decreasing (increasing) the speed of the lateral motors (Bouabdallah, Noth, and Siegwart 2004). Fig. 1. A typical model of a quadrotor helicopter In this section we will describe the basic state-space model of the quadrotor. The dynamics of the four rotors are relatively much faster than the main system and thus neglected in our case. The generalized coordinates of the rotorcraft are ( , , , , , ) q x y z , where ( , , ) x y z represents the relative position of the center of mass of the quadrotor with respect to an inertial frame , and ( , , ) are the three Euler angles representing the orientation of the rotorcraft, namely yaw-pitch-roll of the vehicle. Let us assume that the transitional and rotational coordinates are in the form 3 ( , , ) T x y z R and 3 ( , , ) R . Now the total transitional kinetic energy of the rotorcraft will be 2 T trans m T where m is the mass of the quadrotor. The rotational kinetic energy is described as 1 2 T rot T J , where matrix ( ) J J is the auxiliary matrix expressed in terms of the generalized coordinates . The potential energy in the system can be characterized by the gravitational potential, described as U m g z . Defining the Lagrangian trans rot L T T U , where ( / 2) T trans T m is the translational kinetic energy, (1 / 2) T rot T I is the rotational kinetic energy with as angular speed, U m g z is the potential energy, z is the quadrotor altitude, I is the body inertia matrix, and g is the acceleration due to gravity. Then the full quadrotor dynamics is obtained as a function of the external generalized forces ( , ) F F as d L L F dt q q (1) l 1 f 1 M 2 M 2 f 3 M 3 f 4 M 4 f b x b z b y x y z l 1 f 1 M 2 M 2 f 3 M 3 f 4 M 4 f b x b z b y x y z Challenges and Paradigms in Applied Robust Control 6 The principal control inputs are defined as follows. Define 0 0 R F u (2) where u is the main thrust and defined by 1 2 3 4 u f f f f (3) and i f ’s are described as 2 i i i f k , where i k are positive constants and i are the angular speed of the motor i . Then F can be written as R F RF (4) where R is the transformation matrix representing the orientation of the rotorcraft as c c s s s R c s s s c s s s c c c s c s c s s s s c c s c c (5) The generalized torque for the variables are (6) where 4 1 2 3 4 1 ( ) i M i c f f f f (7) 2 4 ( ) f f l (8) 3 1 ( ) f f l (9) Thus the control distribution from the four actuator motors of the quadrotor is given by 1 2 3 4 1 1 1 1 0 0 0 0 f u f l l f l l f c c c c f C (10) where l is the distance from the motors to the center of gravity, i M is the torque produced by motor i M , and c is a constant known as force-to-moment scaling factor. So, if a required thrust and torque vector are given, one may solve for the rotor force using (10).