Evolutionary learning and global search for multi-optimal PID tuning rules

With the advances in microprocessor technology, control systems are widely seen not only in industry but now also in household appliances and consumer electronics. Among all control schemes developed so far, Proportional plus Integral plus Derivative (PID) control is the most widely adopted in practice. Today, more than 90% of industrial controllers have a built-in PID function. Their wide applications have stimulated and sustained the research and development of PID tuning techniques, patents, software packages and hardware modules. Due to parameter interaction and format variation, tuning a PID controller is not as straightforward as one would have anticipated. Therefore, designing speedy tuning rules should greatly reduce the burden on new installation and ‘time-to-market’ and should also enhance the competitive advantages of the PID system under offer. A multi-objective evolutionary algorithm (MOEA) would be an ideal candidate to conduct the learning and search for multi-objective PID tuning rules. A simple to implement MOEA, termed s-MOEA, is devised and compared with MOEAs developed elsewhere. Extensive study and analysis are performed on metrics for evaluating MOEA performance, so as to help with this comparison and development. As a result, a novel visualisation technique, termed “Distance and Distribution” (DD)” chart, is developed to overcome some of the limitations of existing metrics and visualisation techniques. The DD chart allows a user to view the comparison of multiple sets of high order non-dominated solutions in a two-dimensional space. The capability of DD chart is shown in the comparison process and it is shown to be a useful tool for gathering more in-depth information of an MOEA which is not possible in existing empirical studies. Truly multi-objective global PID tuning rules are then evolved as a result of interfacing the s-MOEA with closed-loop simulations under practical constraints. It takes into account multiple, and often conflicting, objectives such as steady-state accuracy and transient responsiveness against stability and overshoots, as well as tracking performance against load disturbance rejection. These evolved rules are compared against other tuning rules both offline on a set of well-recognised PID benchmark test systems and online on three laboratory systems of different dynamics and transport delays. The results show that the rules significantly outperform all existing tuning rules, with multi-criterion optimality. This is made possible as the evolved rules can cover a delay to time constant ratio from zero to infinity based on first-order plus delay plant models. For second-order plus delay plant models, they can also cover all possible dynamics found in practice

Evolutionary design automation for control systems with practical constraints

The aim of this work is to explore the potential and to enhance the capability of evolutionary computation in the development of novel and advanced methodologies that enable control system structural optimisation and design automation for practical applications. Current design and optimisation methods adopted in control systems engineering are in essence based upon conventional numerical techniques that require derivative information of performance indices. These techniques lack robustness in solving practical engineering problems, which are often of a multi-dimensional, multi-modal nature. Using those techniques can often achieve neither global nor structural optimisation. In contrast, evolutionary mechanism learning tools have the ability to search in a multi-dimensional, multi-modal space, but they can not approach a local optimum as a conventional calculus-based method. The first objective of this research is to develop a reliable and effective evolutionary algorithm for engineering applications. In this thesis, a globally optimal evolutionary methodology and environment for control system structuring and design automation is developed, which requires no design indices to be differentiable. This is based on the development of a hybridised GA search engine, whose local tuning is tremendously enhanced by the incorporation of Hill-Climbing (HC), Simulated Annealing (SA) and Simplex techniques to improve the performance in search and design. A Lamarckian inheritance technique is also developed to improve crossover and mutation operations in GAs. Benchmark tests have shown that the enhanced hybrid GA is accurate, and reliable. Based on this search engine and optimisation core, a linear and nonlinear control system design automation suite is developed in a Java based platform-independent format, which can be readily available for design and design collaboration over corporate Intranets and the Internet. Since it has also made cost function unnecessary to be differentiable, hybridised indices combining time and frequency domain measurement and accommodating practical constraints can now be incorporated in the design. Such type of novel indices are proposed in the thesis and incorporated in the design suite. The Proportional plus Integral plus Derivative (PID) controller is very popular in real world control applications. The development of new PID tuning rules remains an area of active research. Many researchers, such as Åström and Hägglund, Ho, Zhuang and Atherton, have suggested many methods. However, their methods still suffer from poor load disturbance rejection, poor stability or shutting of the derivative control etc. In this thesis, Systematic and batch optimisation of PID controllers to meet practical requirements is achieved using the developed design automation suite. A novel cost function is designed to take disturbance rejection, stability in terms of gain and phase margins and other specifications into account in-the same time. Comparisons made with Ho's method confirm that the derivative action can play an important role to improve load disturbance rejection yet maintaining the same stability margins. Comparisons made with Åström’s method confirm that the results from this thesis are superior not only in load disturbance rejection but also in terms of stability margins. Further robustness issues are addressed by extending the PID structure to a free form transfer function. This is realised by achieving design automation. Quantitative Feedback Theory (QFTX, method offers a direct frequency-domain design technique for uncertain plants, which can deal non-conservatively with different types of uncertainty models and specifications. QFT design problems are often multi-modal and multi-dimensional, where loop shaping is .the most challenging part. Global solutions can hardly be obtained using analytical and convex or linear programming techniques. In addition, these types of conventional methods often impose unrealistic or unpractical assumptions and often lead to very conservative designs. In this thesis, GA-based automatic loop shaping for QFT controllers suggested by the Research Group is being furthered. A new index is developed for the design which can describe stability, load rejection and reduction of high frequency gains, which has not been achieved with existing methods. The corresponding prefilter can also be systematically designed if tracking is one of the specifications. The results from the evolutionary computing based design automation suite show that the evolutionary technique is much better than numerical methods and manual designs, i.e., 'high frequency gain' and controller order have been significantly reduced. Time domain simulations show that the designed QFT controller combined with the corresponding prefilter performs more satisfactorily

Design of robust decentralised controllers for MIMO plants with delays through network structure exploitation

International audienceA methodology is proposed for the design of robust controllers for retarded and neutral-type time-delay systems, focusing on decentralised and overlapping fixed-order controllers for Multiple Input Multiple Output (MIMO) systems. The methodology is grounded in a direct optimisation approach and relies on the minimisation of spectral abscissa and H∞ cost functions, as a function of the controller or design parameters. First, an approach applicable to generic MIMO systems is presented, which imposes a suitable sparsity pattern with the possibility of fixing elements in the controller parameterisation. Second, if the system to be controlled has the structure of a network of coupled identical subsystems, then it is shown that this structure can be exploited by an improved algorithm for the design of decentralised controllers, thereby improving computational efficiency and scalability with the number of subsystems. Several numerical examples illustrate the effectiveness of the methodology, and its extension towards consensus type problems

Dynamical Analysis and Robust Control Synthesis for Water Treatment Processes

Nowadays, water demand and water scarcity are very urgent issues due to population growth, drought and poor water quality all over the world. Therefore, water treatment plants are playing a vital role for good living condition of human. Water area needs more concentration study to increase water productivity and decrease water cost. This dissertation presents the analysis and control of water treatment plants using robust control techniques. The applied control algorithms include H∞, gain scheduled and observer-based loop-shaping control technique. They are modern control algorithms and very powerful in robust controlling of systems with uncertainties and disturbances. The water treatment plants include a desalination system and a wastewater process. Since fresh water scarcity is getting more serious, the desalination plants are to produce drinking water and wastewater treatment plants give the reusable water. The desalination system is a RO one used to produce drinking water from seawater and brackish water. The nonlinear behaviors of this system is carefully analyzed before the linearization. Due to the uncertainty caused by concentration polarization, the system is linearized using linear state-space parametric uncertainty framework. The system also suffer from many disturbances which water hammer is one of the most influential one. The mixed robust H∞ and μ-synthesis control algorithm is applied to control the RO system coping with large uncertainties, disturbances and noises. The wastewater treatment process is an activated sludge process. This biological process use microorganisms to convert organic and certain inorganic matter from wastewater into cell mass. The process is very complex with many coupled biological and chemical reactions. Due to the large variation in the influent flow, the system is modelized and linearized as a linear parametric varying system using affine parameter-dependent representation. Since the influent flow is quickly variable and easily to be measured, the robust gain scheduled robust controller is applied to deal with the large uncertainty caused by the scheduled parameter. This control algorithm often gives better performances than those of general robust H∞ one. In the wastewater treatment plant, there exist an anaerobic digestion, which is controlled by the observer-based loop-shaping algorithm. The simulations show that all the controllers can effectively deal with large uncertainties, disturbances and noises in water treatment plants. They help improve the system performances and safeties, save energy and reduce product water costs. The studies contribute some potential control approaches for water treatment plants, which is currently a very active research area in the world.Contents ······················································································· iv List of Tables ··············································································· viii List of Figures ··············································································· ix Chapter 1. Introduction ···································································· 1 1.1 Reverse osmosis process ···································································· 2 1.2 Activated sludge process ···································································· 6 1.3 Robust H∞ and gain scheduling control ··················································· 10 Chapter 2. Robust H∞ controller ······················································· 13 2.1 Introduction ·················································································· 13 2.2 Uncertainty modelling ······································································ 13 2.2.1 Unstructured uncertainties ···························································· 14 2.2.2 Parametric uncertainties ······························································· 15 2.2.3 Structured uncertainties ································································ 16 2.2.4 Linear fractional transformation ······················································ 16 2.3 Stability criterion ············································································ 17 2.3.1 Small gain theorem ····································································· 17 2.3.2 Structured singular value (muy) synthesis brief definition ·························· 19 2.4 Robustness analysis and controller design ··············································· 20 2.4.1 Forming generalised plant and N-delta structure ····································· 20 2.4.2 Robustness analysis ···································································· 24 2.5 Reduced controller ·········································································· 26 2.5.1 Truncation ··············································································· 27 2.5.2 Residualization ········································································· 29 2.5.3 Balanced realization···································································· 29 2.5.4 Optimal Hankel norm approximation ················································ 31 Chapter 3. Robust gain scheduling controller ······································· 37 3.1 Introduction ·················································································· 37 3.2 Linear parameter varying (LPV) system ·················································· 39 3.3 Matrix Polytope ·············································································· 40 3.4 Polytope and affine parameter-dependent representation ······························· 41 3.4.1 Polytope representation ································································ 41 3.4.2 Affine parameter-dependent representation ········································· 42 3.5 Quadratic stability of LPV systems and quadratic (robust) H∞ performance ········· 43 3.6 Robust gain scheduling ····································································· 44 3.6.1 LPV system linearization ······························································ 44 3.6.2 Polytope-based gain scheduling ······················································ 45 3.6.3 LFT-based gain scheduling ··························································· 48 Chapter 4. Mixed robust H∞ and μ-synthesis controller applied for a reverse osmosis desalination system ····························································· 52 4.1 RO principles ················································································ 52 4.1.1 Osmosis and reverse osmosis ························································· 52 4.1.2 Dead-end filtration and cross-flow filtration ········································ 53 4.2 Membranes ··················································································· 54 4.2.1 Structure and material ································································· 54 4.2.2 Hollow fine fiber membrane module ················································ 55 4.2.3 Spiral wound membrane module ····················································· 57 4.3 Nonlinear RO modelling and analysis ···················································· 58 4.3.1 RO system introduction ······························································· 58 4.3.2 Modelling ··············································································· 60 4.3.3 Nonlinear analysis ······································································ 62 4.3.4 Concentration polarization ···························································· 64 4.4 Water hammer phenomenon ······························································· 66 4.4.1 Water hammer, column separation and vaporous cavitation ······················ 66 4.4.2 Water hammer analysis and simulation ·············································· 69 4.4.3 Prevention of water hammer effect··················································· 78 4.5 RO linearization ············································································· 79 4.5.1 Nominal linearization ·································································· 79 4.5.2 Uncertainty modeling ·································································· 81 4.5.3 Parametric uncertainty linearization ················································· 83 4.6 Robust H∞ controller design for RO system ·············································· 85 4.6.1 Control of uncertain RO system ······················································ 85 4.6.2 Robustness analysis and H∞ controller design ······································ 86 4.7 Simulation result and discussion··························································· 90 4.8 Conclusion ··················································································· 95 Chapter 5. Robust gain scheduling control of activated sludge process ······· 96 5.1 Introduction about activated sludge process ············································· 96 5.1.1 State variables ·········································································· 98 5.1.2 ASM1 processes ······································································ 100 5.1.3 The control problem of activated sludge process ································· 102 5.2 System modelling ········································································· 104 5.3 Model linearization ········································································ 107 5.4 Robust gain-schedule controller design for activated sludge process ··············· 109 5.5 Simulation result and discussion························································· 115 5.6 Conclusion ················································································· 120 Chapter 6. Observer-based loop-shaping control of anaerobic digestion ···· 121 6.1 Introduction ················································································ 121 6.1.1 Control problem in anaerobic digestion ··········································· 122 6.2 System modelling ········································································· 123 6.3 Controller design ·········································································· 124 6.3.1 H∞ loop-shaping controller ························································· 125 6.3.2 Coprime factor uncertainty ·························································· 126 6.3.3 Control synthesis ····································································· 127 6.4 Simulation result ··········································································· 131 6.5 Conclusion ················································································· 133 Chapter 7. Conclusion ··································································· 134 References ·················································································· 136 Appendices ················································································· 144Docto

Systems and control : 21th Benelux meeting, 2002, March 19-21, Veldhoven, The Netherlands

Book of abstract

NON-LINEAR MODEL PREDICTIVE CONTROL STRATEGIES FOR PROCESS PLANTS USING SOFT COMPUTING APPROACHES

The developments of advanced non-linear control strategies have attracted a considerable research interests over the past decades especially in process control. Rather than an absolute reliance on mathematical models of process plants which often brings discrepancies especially owing to design errors and equipment degradation, non-linear models are however required because they provide improved prediction capabilities but they are very difficult to derive. In addition, the derivation of the global optimal solution gets more difficult especially when multivariable and non-linear systems are involved. Hence, this research investigates soft computing techniques for the implementation of a novel real time constrained non-linear model predictive controller (NMPC). The time-frequency localisation characteristics of wavelet neural network (WNN) were utilised for the non-linear models design using system identification approach from experimental data and improve upon the conventional artificial neural network (ANN) which is prone to low convergence rate and the difficulties in locating the global minimum point during training process. Salient features of particle swarm optimisation and a genetic algorithm (GA) were combined to optimise the network weights. Real time optimisation occurring at every sampling instant is achieved using a GA to deliver results both in simulations and real time implementation on coupled tank systems with further extension to a complex quadruple tank process in simulations. The results show the superiority of the novel WNN-NMPC approach in terms of the average controller energy and mean squared error over the conventional ANN-NMPC strategies and PID control strategy for both SISO and MIMO systemsPetroleum Training Development Fun

Model predictive fuzzy control of a steam boiler

This thesis is devoted to apply a Model Predictive Fuzzy Controller (MPC and Takagi-Sugeno) to a specific Steam Boiler Plant. This is a very common problem in control. The considered plant is based on the descriptions obtained from the data of a referenced boiler in the combined cycle plant as Abbot in Champaign, Illinois. The idea is to take all the useful data from the boiler according to its performance and capability in different operation points in order to model the most accurate plant for control. The considered case study is based in a modification of a model proposed by Pellegrinetti and Bentsman in 1996, considering to be tested under the demands of the Control Engineering Association (CEA). The system is Multi-Input and Multi-Output (MIMO), where each controlled output has a specific weight in order to measure the performance. The objective is to minimize cost index but also make it operative and robust for a wide range of variables, discovering the limits of the plant and its behaviour. The model is supposed to manage real data and was constructed under real physical descriptions. However, this model is not a white box, so the analysis and development of the model to be used with the MPC strategy have to be identified to continue with the evaluation of the controlled plant. There are some physical variables that have to be taken into account (Drum Pressure, Excess of Oxygen, Water Level, Water Flow, Fuel Flow, Air Flow and Steam Demand) to know if these variables and other parameters are evolving in the correct way and satisfy the logic of the mass and energy balances in the system. After measuring and analysing the data, the model is validated testing it for different values of steam demands. The controller is tuned for every one of the considered demands. Once tuned, the controller computes the manipulated variables receiving information from the controlled ones, including their references. Finally, the resulting controller is a combination of a set of local controllers using the Takagi-Sugeno approach using the steam demand setpoint as scheduling variable. To apply this approach, a set of local models approximating the non-linear boiler behaviour around a set of steam demand set-points are obtained and then their a fused using the Takagi-Sugeno approach to approximate any unknown steam demand located in the valid range of values

A Linear Parameter Varying Controller for Grid-tied Converters under Unbalanced Voltage Network Conditions

This thesis focuses on the development and practical assessment of a contemporary Linear Parameter Varying (LPV) controller for grid-tied converters. The increasing popularity of renewable energy resources necessitates intelligent power converters to interface with utility network. The proposed control methodology can effectively regulate converter powers/currents under highly unbalanced voltage conditions. The methodology can be easily applied to rotating electrical machines that have similar dynamic models. A LPV model of grid-tied converter with filters are derived in synchronous positive and negative rotating frames and a detailed controller design procedure is then carried out using Matrix Linear Inequality technique. The proposed controller uses network frequency as a reference and it has the capability to handle the system frequency variations. Off-line controller design stage is computed by Matlab software while on-line controller calculations are dealt by a Digital Signal Processor (DSP). The highly distorted voltage at the point of common coupling between Voltage Source Inverter (VSI) and utility network may degrade the outputs of the phase locked loop (PLL) module and overall controller performance. An enhanced version of PLL technique is proposed to overcome the voltage distortions and a significant reduction of Total Harmonic Distortion has been recorded. The harmonic issue is successfully treated further with an additional harmonic observer supporting the main controller. To verify the proposed control approach, studies are carried out using Matlab/SIMULINK platform with the code-based simulation. This simulation method can ensure the results close to a real DSP system and enables the user to transfer the simulation studies effectively to the experimental setup without major modifications. A prototype of a three phase VSI with a DSP controller is then investigated using dSPACE DS1104 development board. Experimental results from this system validate the proposed control technique and its benefits