Advanced control for constrained processes and systems a unified and practical approach

Control Engineering Series 75 This book provides a unified, practically-oriented treatment to many constrained control paradigms Recently proposed control strategies are unified in a generalised framework to deal with different kinds of constraints The book’s solutions are based on reference conditioning ideas implemented by means of supervisory loops, and they are complementary to any other control technique used for the main control loop Although design simplicity is a book priority, the use of well established sliding mode concepts for theoretical analysis make it also rigorous and self-contained The first part of the book focuses on providing a simple description of the method to deal with system constraints in SISO systems It also illustrates the design and implementation of the developed techniques through several case studies The second part is devoted to multivariable constrained control problems: improving system decoupling under different plant or controller constraints, and reducing the undesired effects caused by manual-automatic or controller switching The key aim of this book is to reduce the gap between the available constrained control literature and industrial applications Fabricio Garelli is currently Associate Professor at the National University of La Plata (UNLP) and Official Member of the National Research Council of Argentina (CONICET) He is the author of an awarded Ph.D Thesis and more than 30 journal and conference papers His research interests include multivariable systems and constrained control Ricardo J Mantz serves as Full Professor at UNLP and is an Official Member of the Scientific Research Commission (CICpBA) He is the author of a book and more than 150 papers in scientific journals and conferences His primary area of interest is nonlinear control Hernán De Battista is Senior Professor at UNLP and Official Member of CONICET He has published a book and more than 70 journal and conference papers His research interests are in the field of nonlinear control applications and renewable energy The three authors are with LEICI, EE Dept., UNLP, Argentina Constrained Control.indd Tai Lieu Chat Luong Garelli, Mantz and De Battista The Institution of Engineering and Technology www.theiet.org 978-1-84919-261-3 Advanced Control for Constrained Processes and Systems Advanced Control for Constrained Processes and Systems Advanced Control for Constrained Processes and Systems Fabricio Garelli, Ricardo J Mantz and Hernán De Battista 20/09/2011 14:21:44 IET CONTROL ENGINEERING SERIES 75 Advanced Control for Constrained Processes and Systems PRELIMS September 2011; 13:54:54 Other volumes in this series: Volume Volume Volume 14 Volume 18 Volume 20 Volume 28 Volume 32 Volume 33 Volume 34 Volume 35 Volume 37 Volume 39 Volume 40 Volume 41 Volume 42 Volume 44 Volume 47 Volume 49 Volume 50 Volume 51 Volume 52 Volume 53 Volume 54 Volume 55 Volume 56 Volume 57 Volume 58 Volume 59 Volume 60 Volume 61 Volume 62 Volume 63 Volume 64 Volume 65 Volume 66 Volume 67 Volume 68 Volume 69 Volume 70 Volume 71 Volume 73 Volume 74 Elevator traffic analysis, design and control, 2nd edition G.C Barney and S.M dos Santos A history of control engineering, 1800–1930 S Bennett Optimal relay and saturating control system synthesis E.P Ryan Applied control theory, 2nd edition J.R Leigh Design of modern control systems D.J Bell, P.A Cook and N Munro (Editors) Robots and automated manufacture J Billingsley (Editor) Multivariable control for industrial applications J O’Reilly (Editor) Temperature measurement and control J.R Leigh Singular perturbation methodology in control systems D.S Naidu Implementation of self-tuning controllers K Warwick (Editor) Industrial digital control systems, 2nd edition K Warwick and D Rees (Editors) Continuous time controller design R Balasubramanian Deterministic control of uncertain systems A.S.I Zinober (Editor) Computer control of real-time processes S Bennett and G.S Virk (Editors) Digital signal processing: principles, devices and applications N.B Jones and J.D.McK Watson (Editors) Knowledge-based systems for industrial control J McGhee, M.J Grimble and A Mowforth (Editors) A history of control engineering, 1930–1956 S Bennett Polynomial methods in optimal control and filtering K.J Hunt (Editor) Programming industrial control systems using IEC 1131-3 R.W Lewis Advanced robotics and intelligent machines J.O Gray and D.G Caldwell (Editors) Adaptive prediction and predictive control P.P Kanjilal Neural network applications in control G.W Irwin, K Warwick and K.J Hunt (Editors) Control engineering solutions: a practical approach P Albertos, R Strietzel and N Mort (Editors) Genetic algorithms in engineering systems A.M.S Zalzala and P.J Fleming (Editors) Symbolic methods in control system analysis and design N Munro (Editor) Flight control systems R.W Pratt (Editor) Power-plant control and instrumentation D Lindsley Modelling control systems using IEC 61499 R Lewis People in control: human factors in control room design J Noyes and M Bransby (Editors) Nonlinear predictive control: theory and practice B Kouvaritakis and M Cannon (Editors) Active sound and vibration control M.O Tokhi and S.M Veres Stepping motors: a guide to theory and practice, 4th edition P.P Acarnley Control theory, 2nd edition J.R Leigh Modelling and parameter estimation of dynamic systems J.R Raol, G Girija and J Singh Variable structure systems: from principles to implementation A Sabanovic, L Fridman and S Spurgeon (Editors) Motion vision: design of compact motion sensing solution for autonomous systems J Kolodko and L Vlacic Flexible robot manipulators: modelling, simulation and control M.O Tokhi and A.K.M Azad (Editors) Advances in unmanned marine vehicles G Roberts and R Sutton (Editors) Intelligent control systems using computational intelligence techniques A Ruano (Editor) Advances in cognitive systems S Nefti and J Gray (Editors) Adaptive Sampling with Mobile WSN K Sreenath, M.F Mysorewala, D.O Popa and F.L Lewis Eigenstructure Control Algorithms: applications to aircraft/rotorcraft handling qualities design S Srinathkumar PRELIMS September 2011; 13:54:55 Advanced Control for Constrained Processes and Systems Fabricio Garelli, Ricardo J Mantz and Herna´n De Battista The Institution of Engineering and Technology PRELIMS September 2011; 13:54:55 Published by The Institution of Engineering and Technology, London, United Kingdom The Institution of Engineering and Technology is registered as a Charity in England & Wales (no 211014) and Scotland (no SC038698) † 2011 The Institution of Engineering and Technology First published 2011 This publication is copyright under the Berne Convention and the Universal Copyright Convention All rights reserved Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may be reproduced, stored or transmitted, in any form or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency Enquiries concerning reproduction outside those terms should be sent to the publisher at the undermentioned address: The Institution of Engineering and Technology Michael Faraday House Six Hills Way, Stevenage Herts, SG1 2AY, United Kingdom www.theiet.org While the author and publisher believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgement when making use of them Neither the author nor publisher assumes any liability to anyone for any loss or damage caused by any error or omission in the work, whether such an error or omission is the result of negligence or any other cause Any and all such liability is disclaimed The moral rights of the author to be identified as author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988 British Library Cataloguing in Publication Data A catalogue record for this product is available from the British Library ISBN 978-1-84919-261-3 (hardback) ISBN 978-1-84919-262-0 (PDF) Typeset in India by MPS Ltd, a Macmillan Company Printed in the UK by CPI Antony Rowe, Chippenham, Wiltshire PRELIMS September 2011; 13:54:55 To Lau (F.G.), Lilian (R.M.) and Vale (H.D.B.) PRELIMS September 2011; 13:54:55 PRELIMS September 2011; 13:54:55 Contents An introduction to constrained control 1.1 Motivations 1.2 Types of constraints 1.2.1 Physical limits 1.2.2 Structural constraints 1.2.3 Dynamic restrictions 1.3 Some typical effects of constraints 1.3.1 Controller windup 1.3.2 Plant windup 1.3.3 Control directionality problem 1.4 Other constraint implications 1.5 Different approaches to constrained control 1.6 Book philosophy 1.7 Short outline of the main problems to be addressed 1 4 5 10 12 13 14 A practical method to deal with constraints 2.1 Introduction 2.2 Preliminary definitions 2.3 Sliding mode reference conditioning 2.3.1 Basic idea for biproper systems 2.3.2 Illustrative example 2.4 Biproper SMRC: features and analysis 2.4.1 VSS essentials 2.4.2 SMRC operation analysis 2.4.3 Implementation issues 2.5 Strictly proper SMRC 2.5.1 Normal form 2.5.2 Method reformulation 2.5.3 Illustrative examples 2.6 SMRC and non-linear systems 2.6.1 Geometrical interpretation of SM 2.6.2 Geometric invariance via SMRC 2.6.3 SMRC in strictly proper non-linear systems 2.7 Robustness properties 2.7.1 SM existence domain 2.7.2 SM dynamics 17 17 18 18 18 21 23 24 28 31 32 33 34 36 42 42 44 47 48 49 51 PRELIMS September 2011; 13:54:55 viii Advanced control for constrained processes and systems Some practical case studies 3.1 Pitch control in wind turbines 3.1.1 Brief introduction to the problem 3.1.2 Pitch actuator and control 3.1.3 SMRC compensation for actuator constraints in the pitch control loop 3.1.4 Application to a wind energy system for water pumping 3.2 Clean hydrogen production plant 3.2.1 Brief introduction to the problem 3.2.2 System description 3.2.3 SMRC algorithm to deal with electrolyser constraints 3.2.4 Simulation results 3.3 Robot path tracking 3.3.1 Brief introduction to the problem 3.3.2 Classical control scheme for robotic path tracking 3.3.3 Tracking speed autoregulation technique 3.3.4 Application to a 2R manipulator 3.4 Control of a fed-batch bioreactor 3.4.1 Brief introduction to the problem 3.4.2 Process model 3.4.3 Reference seeking for overflow avoidance 3.4.4 Simulations 53 53 53 55 56 57 59 61 62 66 67 70 70 71 73 75 80 80 80 82 84 Relevant tools for dynamic decoupling 4.1 Preliminary concepts 4.1.1 Multivariable system models 4.1.2 Multivariable poles and zeros 4.1.3 Closed-loop transfer matrices 4.1.4 Internal stability 4.2 MIMO controller parameterisation and approximate inverses 4.2.1 Stabilising controller parameterisation 4.2.2 Internal model control 4.2.3 Interactor matrices 4.2.4 Approximate model inverses 4.3 Dynamic decoupling of MIMO systems 4.3.1 Minimum phase systems 4.3.2 Non-minimum phase systems 4.3.3 Unstable systems 4.4 Performance limitations in non-minimum phase systems 87 87 87 88 90 92 92 93 94 95 99 99 100 102 106 107 Constrained dynamic decoupling 5.1 Introduction 5.2 Control directionality changes 5.3 Dynamic decoupling preservation by means of SMRC 111 111 112 115 PRELIMS September 2011; 13:54:55 Contents 5.3.1 Method formulation 5.3.2 Sliding surfaces design 5.3.3 SMRC dynamics 5.3.4 Operating issues 5.4 Minimum-phase example 5.5 Non-minimum phase examples 5.5.1 Revisiting Example 1.3 5.5.2 Sugar cane crushing station ix 115 117 117 120 122 124 124 125 Interaction limits in decentralised control architectures 6.1 Introduction to decentralised control 6.1.1 Architecture description 6.1.2 Interaction measure 6.1.3 Control structure selection: the TITO case 6.1.4 Decentralised integral controllability 6.2 Interaction effects on multiloop strategies 6.3 Limiting interactions in decentralised control via SMRC 6.3.1 Control scheme 6.3.2 Switching law 6.3.3 Output dynamics during conditioning 6.3.4 Behaviour in presence of output disturbances 6.4 Two-degrees of freedom PID controller with adaptive set-point weighting 6.5 Case study: Quadruple tank 6.5.1 Plant model analysis 6.5.2 Interactions limits in non-minimum phase setting 6.6 Delay example: catalytic reactor 149 150 151 155 161 Partial decoupling and non-minimum phase systems 7.1 Some introductory comments 7.2 Right-half plane zeros directionality and partial decoupling 7.2.1 Algebraic interpolation constraint 7.2.2 Inverse response on a particular output 7.3 Interpolating diagonal and partial decoupling 7.4 Partial decoupling with bounded interactions via SMRC 7.5 Numerical example 7.6 Case study: quadruple tank 163 163 164 164 167 170 170 172 175 MIMO bumpless transfer 8.1 Introduction 8.2 Switching at the plant input 8.3 A simple SMRC solution for SISO systems 8.4 MIMO bumpless transfer 8.4.1 Some concepts on collective sliding modes 8.4.2 A MIMO bumpless algorithm 181 181 182 183 185 185 188 PRELIMS September 2011; 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14:42:26 206 Advanced control for constrained processes and systems 158 H Zhang, Y Zheng, Q Liu, X Tao, W Zheng, X Ma, D Wei ‘Development of a fed-batch process for the production of anticancer drug tatm – survivin(t34a) in Escherichia coli’ Biochemical Engineering Journal of Bioscience and Bioengineering, 43:163–168, 2009 159 A Zheng, M V Kothare, M Morari ‘Anti-windup design for internal model control’ International Journal of Control, 60(5):1015–1024, 1994 160 K Zheng, A Lee, J Bentsman, C Taft ‘Steady-state bumpless transfer under controller uncertainty using the state/output feedback topology’ IEEE Transactions on Control Systems Technology, 14:3–17, 2006 REFERENCE September 2011; 14:42:26 Index algebraic interpolation constraint 164–7 anti-windup (AW) algorithms 53 anti-windup (AW) techniques 12–13 automatic–automatic commutation 193–5 auxiliary compensation loop 56 AW: see anti-windup (AW) algorithms; anti-windup (AW) techniques BDFG: see brushless doubly fed generator (BDFG) BIBO: see bounded-input bounded-output (BIBO) stable biomass production 81 biproper SMRC features and analysis 23–32 implementation issues 31–2 SMRC operation analysis 28–31 VSS essentials 24–8 biproper systems conditioning loop for constraints in 18–23 SMRC as AW algorithm for 21 blade pitch rotation 53 bounded-input bounded-output (BIBO) stable 92 Bristol interaction index 135–6, 137, 154 brushless doubly fed generator (BDFG) 57 bumpless transfer defined 11 MIMO systems 185–91 overview 181–2 index in quadruple tank process 191–5 simple SMRC solution for SISO systems 183–5 switching at the plant input (SISO system) 182–3 bumpy transfer 11, 181, 182, 183, 193 see also bumpless transfer catalytic reactor 161–2 see also decentralised control system chattering effect 31 classical control for robot path tracking 71–3 closed-loop decoupling 9, 14 closed-loop system output/state limiter for 36–7 response of decentralised PI controller 139–43 closed-loop transfer matrices MIMO systems 90–1 compensation, pitch control 56–7 auxiliary compensation loop 56 main pitch control loop 56 in wind energy system 57–9 complementary sensitivity function matrix 91 conditioned reference signals 22 conditioned system 21, 22 condition number kðPÞ defined 136 and RGA, correlation between 136 constrained control 1–15 different approaches to 12–13 September 2011; 15:45:20 208 Advanced control for constrained processes and systems constrained dynamic decoupling control directionality changes 112–15 minimum-phase example 122–3 NMP examples 124–9 overview 111–12 SMRC loop to preserve 115–21 constrained unstable system 38–41 constraints in biproper systems 18–23 control directionality problem 9–10 controller windup effect 5–7 dynamic implications 10–11 methods for, dealing 17–51 physical 2–3 plant windup effect 7–8 structural 4, 59 typical effects of 5–10 continuous equivalent control for SM 26–7 for SMRC 29 control directionality constrained dynamic decoupling and 112–15 defined 112 problem 9–10 controller outputs 174 controller windup 5–7 SMRC for biproper controllers and 21 control loops wind turbines 53 decentralised control system architecture description 131–2 catalytic reactor (delay example) 161–2 decentralised integral controllability 137–8 2DOF-PI controller with adaptive set-point weighting 149–50 interaction effects on 139–43 interaction measure 132–4 index limiting interactions with SMRC technique 143–9 behaviour in presence of output disturbances 148–9 control scheme 143–5 output dynamics during conditioning 147–8 switching law 145–7 ‘pairing’ of variables in 132 practical advantages of 132 quadruple tank (case study) 150–60 relative gain array 132–4 structure of 131–2 TITO system under 134–7 see also quadruple-tank system decentralised integral controllable (DIC) systems defined 137 theorems 138 decoupling closed-loop 9, 14 diagonal 170 partial: see partial decoupling static 167–8 triangular: see triangular decoupling decoupling, dynamic full 99–100 of MIMO systems 99–107 tools for 87–109 diagonal decoupling 170 DIC systems: see decentralised integral controllable (DIC) systems digital position controller 71 directional derivative 42, 43 directionality-preserving saturation 72, 73 2DOF-PID controller: see two-degrees of freedom PID (2DOF-PID) controller dynamic analysis SMRC loop 117–20 dynamic decoupling, constrained control directionality changes 112–15 minimum-phase example 122–3 September 2011; 15:45:21 Index NMP examples 124–9 overview 111–12 SMRC loop to preserve 115–21 dynamic restrictions 4, 11, 80 dynamics hidden 30 reduced 27–8, 30, 35–6 robust 30, 35–6 SM 51 electrolyser 64 current–voltage characteristic of 64 SMRC algorithm for constraints 66–7 electronic converter 63–4 equivalent control, continuous 26–7, 29 Escherichia coli 80 ethanol 80 concentration 83 oxidation of 81 explicit invariance condition, defined 45 fed-batch bioreactor, SMRC and 80–6 overflow avoidance, reference seeking for 82–4 process model 80–2 simulations 84–6 feedback error-based control 75 feedforward trajectory generator 75 filtered references 174 geometric invariance with SMRC 44–6 geometric multiplicity 89 glucose oxidation of 81 reduction of 81 hidden dynamics SMRC 30 Hurwitz polynomials 97 hydrogen production plant, SMRC and 59–70 conventional MPPT control scheme 65 index 209 plant description 62–4 simulation results 67–70 SMRC algorithm for electrolyser constraints 66–7 IAE: see integral absolute error (IAE) ideal sliding mode defined 26 IMC: see internal model control (IMC) implicit invariance condition, defined 45 improper systems, defined 18 improper transfer matrices 88 independent saturation 72 input direction of zero 88 input sensitivity matrix 91 integral absolute error (IAE) 178 integral square error (ISE) 160 integrator windup interaction bounds, output signals with 173, 174 interaction limits defined 146 different rates of approach to 175 interaction measures of decentralised control system 132–4 relative gain array (RGA) as 132–4 interactor matrices 95–7 constructing 97–9 left 97 right 97 interactors 168 see also interactor matrices internal model control (IMC) 87, 94–5, 112 internal stability 92 interpolating diagonal, and partial decoupling 170 interpolation constraint, algebraic 164–7 invariance, geometric with SMRC 44–6 inverse response, on particular output 167–70 September 2011; 15:45:21 210 Advanced control for constrained processes and systems I–P structure 149 ISE: see integral square error (ISE) Jacobian matrix 72 joint controllers 71 kinematic function of robot model 72 left-half plane (LHP) 92 left interactor matrices 97 LHP: see left-half plane (LHP) Lie derivative 42, 43 limiting element 19 linear matrix inequalities (LMI) 112 linear parameter-varying (LPV) 112 LMI: see linear matrix inequalities (LMI) LPV: see linear parameter-varying (LPV) manual–automatic switching 181, 191–2 matching condition 120, 121, 148 defined 51 maximum power point tracking (MPPT) 54–5, 65 maximum power tracking algorithm 53 maximum power tracking control 67–8 MIMO: see multiple-input multipleoutput (MIMO) systems MIMO bumpless transfer algorithm for 188–91 collective sliding modes concepts 185–8 hidden SM dynamics 190–1 reaching condition 189–90 minimum phase (MP), defined 18 minimum phase (MP) systems 87, 90, 100–2 minimum-phase plants SMRC strategy in 122–3 model predictive control (MPC) 12 motion parameter 71 MP: see minimum phase (MP) systems MPC: see model predictive control (MPC) index MPPT: see maximum power point tracking (MPPT) multiloop control system: see decentralised control system multiple-input multiple-output (MIMO) systems 1–2, 112 approximate inverses 92–9 basic concepts of 87–92 closed-loop transfer matrices 90–1 dynamic decoupling of 99–107 internal stability 92 multivariable poles and zeros 88–90 multivariable system models 87–8 SMRC loop to preserve dynamic decoupling of 115–21 state-space models 87 transfer matrices 88–90 multivariable controller parameterisation 92–9 multivariable system models 87–8 non-minimum phase 89–90 poles 89 zeros 88–9 see also multiple-input multipleoutput (MIMO) systems NMP: see non-minimum phase (NMP) systems NMP plants: see non-minimum phase (NMP) plants non-linear systems robustness properties of SM 48–51 SMRC and 42–8 strictly proper, SMRC in 47–8 non-minimum phase (NMP) plants interactions limits in quadruple-tank system 155–60 SMRC strategy in 124–9 non-minimum phase (NMP) systems 87, 89–90, 102–6, 163–79 performance limitations in 107–9 triangular decoupling in 163 normal canonical form 33–4 September 2011; 15:45:21 Index one-step algorithms, for constraints 12 output direction of zero 88 overflow metabolism 80 oxidation of ethanol 81 of glucose 81 ‘pairing’ of variables in decentralised control system 132 parameterisation, MIMO systems 92–9 interactor matrices 95–7 internal model control 94–5 stabilising 93–4 partial decoupling 163–79 with bounded interactions via SMRC 170–2 case study 175–9 interpolating diagonal and 170 numerical example 172–5 overview 163–4 RHP zeros directionality in 164–70 path following speed 73 perfect control 93, 100 permanent magnet synchronous generator (PMSG) 63 PI controller 4–6, 19, 21, 23, 36, 39, 65, 66, 139–143, 149, 150, 155, 162, 179, 182 pitch actuators 53, 55 pitch control in wind turbines, SMRC and 53–9 simulation results 59 system description 57–9 pitch control loop 54 actuator constraints in 56–7 designing 55 SMRC compensation for actuator constraints in 56–7 plant model analysis quadruple-tank system 151–4 plant windup effect 7–8 prevention of 37–8, 39 index 211 PMSG: see permanent magnet synchronous generator (PMSG) Poisson integral 109 poles, multivariable system 89 position reference (pref) 71 power conditioning via SMRC 68–70 power electronic devices 53 proper systems, defined 18 proper transfer matrices 88 proportional controller plant windup in 7–8 Q-parameterisation: see Youla parameterisation quadruple tank 175–9 quadruple-tank system bumpless algorithm in 191–5 automatic–automatic commutation 193–5 manual–automatic switching 191–2 interactions limits in NMP setting 155–60 parameter values 152 plant model analysis 151–4 SMRC technique in 156–9 structural overview 150–1 see also decentralised control system reaching mode 32 reduced dynamics SM 27–8 SMRC 30, 35–6 reduction of glucose 81 relative degree defined 18 RHP zero directions and 168–70 relative gain array (RGA) 132–4 and condition number kðPÞ, correlation between 136 defined 133 properties 134 for TITO systems 135–6 September 2011; 15:45:21 212 Advanced control for constrained processes and systems RGA: see relative gain array (RGA) RHP: see right-half plane (RHP) RHP zeros: see right-half plane (RHP) zeros right-half plane (RHP) zeros 4, 87, 90, 111, 147–8 algebraic interpolation constraint and 164–7 directionality, in partial decoupling 164–70 directions, relative degrees and 168–70 inverse response on a particular output 167–70 right interactor matrices 97 2R manipulator robot path tracking, SMRC and 75–9 robot path tracking, SMRC and 70–9 classical control for 71–3 physical limitations 70 2R manipulator, application in 75–9 speed autoregulation technique 73–5 robust dynamics SMRC 30, 35–6 robustness properties, of SM control 48–51 Rosenbrock system 139–40, 141 Saccharomyces cerevisiae 80 sensitivity function matrix 91 single-input single-output (SISO) systems 1, 87, 90, 112, 181 SMRC solution for 183–5 switching at the plant input 182–3 SISO: see single-input single-output (SISO) systems SISO systems: see single-input singleoutput (SISO) systems sliding manifold/surface, defined 24 sliding mode reference conditioning (SMRC) 18–53, 111, 131, 163, 181 algorithm for electrolyser constraints 66–7 index as AW algorithm for biproper controllers 21 biproper, features and analysis 23–32 in biproper systems 18–23 clean hydrogen production plant 59–70 see also hydrogen production plant, SMRC and condition for transient 30–1 continuous equivalent control for 29 for delimiting internal state 36 fed-batch bioreactor, control of 80–6 see also fed-batch bioreactor, SMRC and geometric invariance with 44–6 necessary and sufficient condition for 29–30 necessary condition for 28–9 and non-linear systems 42–8 operation analysis 28–31 partial decoupling with bounded interactions 170–2 pitch control in wind turbines 53–9 see also pitch control in wind turbines, SMRC and power conditioning 68–70 reduced and robust dynamics 30, 35–6 robot path tracking 70–9 see also robot path tracking, SMRC and SM operation in 28 strictly proper 32–41 in strictly proper non-linear systems 47–8 behaviour of the whole system and 121 biproper transfer functions 119 disturbance rejection 120–1 dynamic analysis 117–20 dynamic decoupling preservation 115–21 limiting interactions in decentralised control with 143–9 September 2011; 15:45:22 Index behaviour in presence of output disturbances 148–9 control scheme 143–5 output dynamics during conditioning 147–8 quadruple-tank system 156–9 switching law 145–7 method formulation 115–17 minimum-phase example 122–3 NMP examples 124–9 operating issues 120–1 for SISO systems 183–5 strictly proper transfer functions 119–20 sliding mode (SM) 13 continuous equivalent control for 26–7 defined 24 description 24–5 dynamics 51 existence domain 49–50 geometrical interpretation of 42–4 ideal 26 necessary and sufficient condition for 27 necessary conditions for 25–6, 27 operation in SMRC 28 reduced dynamics 27–8 robustness properties of 48–51 SM: see sliding mode (SM) Smith predictor PI controller, for plant 5–7 SMRC: see sliding mode reference conditioning (SMRC) speed autoregulation technique robot path tracking 73–5 state-space models MIMO systems 87 static decoupling 167–8 strictly proper SMRC 32–41 examples 36–41 method reformulation 34–6 in normal canonical form 33–4 strictly proper transfer matrices 88 index 213 structural constraints 4, 59 signal-bound requirements from 11 sugar cane milling process SMRC strategy in 125–9 switching block 171, 172 overview 181 at the plant input 182–3 switching function (s), defined 19 switching law closed-loop interactions and 145–7 graphical interpretation of 20 TITO systems: see two inputs–two outputs (TITO) systems tracking speed autoregulation technique, SMRC and 73–5 effect of chattering 75 effect of feedback 75 effect of robot Jacobian 75 transfer functions biproper 119 strictly proper 119–20 transfer matrices 88–90 transmission zeros 88 transversality condition 26 defined 25 triangular decoupling closed-loop constraints of 164–5 in NMP systems 163 upper and lower 168–70 two-degrees of freedom PID (2DOF-PID) controller 149–50 two inputs–two outputs (TITO) systems control scheme 143–4 under decentralised control structure 134–7 2DOF-PI controller for 149–50 RGA for 135–6 two-step algorithms, for constraints 12–13 unstable systems 106–7 September 2011; 15:45:22 214 Advanced control for constrained processes and systems variable-pitch wind rotors 53 variables ‘pairing,’ in decentralised control system 132 variable structure systems (VSS) 13 chattering effect in 31 essentials 24–8 reaching mode in 32 SM and: see sliding mode (SM) VSS: see variable structure systems (VSS) index Weller–Goodwin method 171, 178 wind rotor 62–3 wind turbines control loops 53 pitch control, SMRC technique 53–9 Youla parameterisation 93, 94 zeros, multivariable system 88–9 z-interactors 99, 168 see also interactor matrices September 2011; 15:45:22 Control Engineering Series 75 This book provides a unified, practically-oriented treatment to many constrained control paradigms Recently proposed control strategies are unified in a generalised framework to deal with different kinds of constraints The book’s solutions are based on reference conditioning ideas implemented by means of supervisory loops, and they are complementary to any other control technique used for the main control loop Although design simplicity is a book priority, the use of well established sliding mode concepts for theoretical analysis make it also rigorous and self-contained The first part of the book focuses on providing a simple description of the method to deal with system constraints in SISO systems It also illustrates the design and implementation of the developed techniques through several case studies The second part is devoted to multivariable constrained control problems: improving system decoupling under different plant or controller constraints, and reducing the undesired effects caused by manual-automatic or controller switching The key aim of this book is to reduce the gap between the available constrained control literature and industrial applications Fabricio Garelli is currently Associate Professor at the National University of La Plata (UNLP) and Official Member of the National Research Council of Argentina (CONICET) He is the author of an awarded Ph.D Thesis and more than 30 journal and conference papers His research interests include multivariable systems and constrained control Ricardo J Mantz serves as Full Professor at UNLP and is an Official Member of the Scientific Research Commission (CICpBA) He is the author of a book and more than 150 papers in scientific journals and conferences His primary area of interest is nonlinear control Hernán De Battista is Senior Professor at UNLP and Official Member of CONICET He has published a book and more than 70 journal and conference papers His research interests are in the field of nonlinear control applications and renewable energy The three authors are with LEICI, EE Dept., UNLP, Argentina Constrained Control.indd Garelli, Mantz and De Battista The Institution of Engineering and Technology www.theiet.org 978-1-84919-261-3 Advanced Control for Constrained Processes and Systems Advanced Control for Constrained Processes and Systems Advanced Control for Constrained Processes and Systems Fabricio Garelli, Ricardo J Mantz and Hernán De Battista 20/09/2011 14:21:44