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

Optimised configuration of sensing elements for control and fault tolerance applied to an electro-magnetic suspension system

New technological advances and the requirements to increasingly abide by new safety laws in engineering design projects highly affects industrial products in areas such as automotive, aerospace and railway industries. The necessity arises to design reduced-cost hi-tech products with minimal complexity, optimal performance, effective parameter robustness properties, and high reliability with fault tolerance. In this context the control system design plays an important role and the impact is crucial relative to the level of cost efficiency of a product. Measurement of required information for the operation of the design control system in any product is a vital issue, and in such cases a number of sensors can be available to select from in order to achieve the desired system properties. However, for a complex engineering system a manual procedure to select the best sensor set subject to the desired system properties can be very complicated, time consuming or even impossible to achieve. This is more evident in the case of large number of sensors and the requirement to comply with optimum performance. The thesis describes a comprehensive study of sensor selection for control and fault tolerance with the particular application of an ElectroMagnetic Levitation system (being an unstable, nonlinear, safety-critical system with non-trivial control performance requirements). The particular aim of the presented work is to identify effective sensor selection frameworks subject to given system properties for controlling (with a level of fault tolerance) the MagLev suspension system. A particular objective of the work is to identify the minimum possible sensors that can be used to cover multiple sensor faults, while maintaining optimum performance with the remaining sensors. The tools employed combine modern control strategies and multiobjective constraint optimisation (for tuning purposes) methods. An important part of the work is the design and construction of a 25kg MagLev suspension to be used for experimental verification of the proposed sensor selection frameworks

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

Fixed-Order Robust Controller Design by Convex Optimization Using Spectral Models

This thesis proposes a new method to design fixed-order controllers in frequency domain using convex optimization. The method is based on the shaping of open-loop transfer function in the Nyquist diagram with infinity norm constraints on weighted closed-loop transfer functions. A parametric model is not required in this method as it directly uses frequency-domain data. Furthermore, systems with multi-model uncertainty as well as systems with frequency-domain uncertainties can be considered. Fixed-order linearly parameterized controllers are designed with the proposed method for single-input single-output (SISO) linear time-invariant plants. The shaping of the open-loop transfer function is performed based on the minimization of the difference with a desired open-loop transfer function under H∞ constraints on the closed-loop sensitivity functions. Since these constraints represent a nonconvex set in the space of the controller parameters, an inner convex approximation of this set is proposed using the desired open-loop transfer function. This approximation makes the problem of robust fixed-order controller design a convex optimization problem. An extension of the method is proposed to design two-degree-of-freedom (2DOF) controllers for SISO plants. The method is also extended to tune fixed-order linearly parameterized multivariable controllers for multiple-input multiple-output (MIMO) linear time-invariant plants where the stability of the closed-loop system is guaranteed using Gershgorin bands. The control problem is solved only using a finite number of frequency-domain samples. However, the stability and performance conditions between frequency samples are also verified if a frequency-domain uncertainty is considered. It is shown that this adds some conservatism to the solution. The proposed frequency-domain method has been tested on many simulation examples. The method has been applied to a flexible transmission benchmark for robust controller design giving extremely good results. Additionally, the method has also been implemented on an experimental high-precision double-axis positioning system. These results show the effectiveness of the proposed methods

Model predictive controller tuning by machine learning and ordinal optimisation

While for the past several decades model predictive control (MPC) has been an established control strategy in chemical process industries, more recently there has been increased collaboration in MPC research between academia and automotive companies. Despite the promising work thus far, one particular challenge facing the widespread adoption of MPC in the automotive industry is the increased calibration requirement. The focus of the research in this thesis is to develop methods towards reducing the calibration effort in designing and implementing MPC in practice. The research is tailored by application to offline tuning of quadratic-cost MPC for an automotive diesel air-path, to address the limited time-availability to perform online tuning experiments. Human preferences can be influential in automotive engine controller tuning. Some earlier work has proposed a machine learning controller tuning framework (MLCTF), which learns preferences from numeric data labelled by human experts, and as such, these learned preferences can be replicated in automated offline tuning. Work done in this thesis extends this capability by allowing for preferences to be learned from pairwise comparison data, with monotonicity constraints in the features. Two methods are proposed to address this: 1) an algorithm based around Gaussian process regression; and 2) a Bayesian estimation procedure using a Dirichlet prior. These methods are successfully demonstrated in learning monotonicity-constrained utility functions in time-domain features from data consisting of pairwise rankings for diesel air-path trajectories. The MLCTF also constitutes a plant model, yet there will typically be some uncertainty in an engine model, especially if it has been identified from data collected with a limited amount of experimentation time. To address this, an active learning framework is proposed for selection of the next operating points in the design of experiments, for identifying linear parameter-varying systems. The approach is based on exploiting the probabilistic features of Gaussian process regression to quantify the overall model uncertainty across locally identified models, resulting in a flexible methodology which accommodates for various techniques to be applied for estimation of local linear models and their corresponding uncertainty. The framework is applied to the identification of a diesel engine air-path model, and it is demonstrated that measures of model uncertainty can be quantified and subsequently reduced. To make the most of the limited availability for online tuning experiments, an ordinal optimisation (OO) approach is proposed, which seeks to ensure that offline tuned controllers can perform acceptably well, once tested online with the physical system. Via the use of copula models, an OO problem is formulated to be compatible with the tuning of controllers over an uncountable search space, such as quadratic-cost MPC. In particular, results are obtained which formally characterise the copula dependence conditions required for the OO success probability to be non-decreasing in the number of offline controllers sampled during OO. A gain-scheduled MPC architecture was designed for the diesel air-path, and implemented on an engine control unit (ECU). The aforementioned non-decreasing properties of the OO success probability are then specialised to tuning gain-scheduled controller architectures. Informed by these developments, the MPC architecture was firstly tuned offline via OO, and then tested online with an experimental diesel engine test rig, over various engine drive-cycles. In the experimental results, it was found that some offline tuned controllers outperformed a manually tuned baseline MPC, the latter which has comparable performance to proprietary production controllers. Upon additional manual tuning online, the performance of the offline tuned controllers could also be further refined, which illustrates how offline tuning via OO may complement online tuning approaches. Lastly, using an analytic lower bound developed for OO under a Gaussian copula model, a sequential learning algorithm is developed to address a probabilistically robust offline controller tuning problem. The algorithm is formally proven to yield a controller which meets a specified probabilistic performance specification, assuming that the underlying copula is not too unfavourably far from a Gaussian copula. It is demonstrated in a simulation study that the algorithm is able to successfully tune a single controller to meet a desired performance threshold, even in the presence of probabilistic uncertainty in the diesel engine model. This is applied to two case studies: 1) `hot-starting' an online tuning procedure; and 2) tuning for uncertainty inherent across a fleet of vehicles

Design of Low-Order Controllers using Optimization Techniques

In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers. The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency sensitivity subject to constraints that ensure robustness to process variations and limitations of control signal effort. The second part of this thesis deals with tuning of feedforward controllers. Tuning rules that minimize the integrated-squared-error arising from measurable step disturbances are derived for a controller that can be interpreted as a filtered and possibly time-delayed PD controller. Using a controller structure that decouples the effects of the feedforward and feedback controllers, the controller is optimal both in open and closed loop settings. To improve the high-frequency noise behavior of the feedforward controller, it is proposed that the optimal controller is augmented with a second-order filter. Several aspects on the tuning of this filter are discussed. For systems with PID controllers, the response to step changes in the reference can be improved by introducing set-point weighting. This can be interpreted as feedforward from the reference signal to the control signal. It is shown how these weights can be found by solving a convex optimization problem. Proportional set-point weight that minimizes the integrated-absolute-error was obtained for a batch of over 130 different processes. From these weights, simple tuning rules were derived and the performance was evaluated on all processes in the batch using five different feedback controller tuning methods. The proposed tuning rules could improve the performance by up to 45% with a modest increase in actuation

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate physical models for these plants using first principles may be impossible. With the increased developments in the computing world, large amounts of measured data can be easily collected and stored for processing purposes. Data can also be collected and used in an on-line fashion. Thus it would be very sensible to make full use of this data for controller design, performance evaluation, and stability analysis. The design methods imposed in this work ensure that the dynamics of a system are captured in an experiment and avoids the problem of unmodeled dynamics associated with parametric models. The devised methods consider robust designs for both linear-time-invariant (LTI) single-input-single-output (SISO) systems and certain classes of nonlinear systems. In this dissertation, a data-driven approach using the frequency response function of a system is proposed for designing robust controllers with H∞ performance. Necessary and sufficient conditions are derived for obtaining H∞ performance while guaranteeing the closed-loop stability of a system. A convex optimization algorithm is implemented to obtain the controller parameters which ensure system robustness; the controller is robust with respect to the frequency-dependent uncertainties of the frequency response function. For a certain class of nonlinearities, the proposed method can be used to obtain a best-linear-approximation with an associated frequency dependent uncertainty to guarantee the stability and performance for the underlying linear system that is subject to nonlinear distortions. The concepts behind these design methods are then used to devise necessary and sufficient conditions for ensuring the closed-loop stability of systems with sector-bounded nonlinearities. The conditions are simple convex feasibility constraints which can be used to stabilize systems with multi-model uncertainty. Additionally, a method is proposed for obtaining H∞ performance for an approximate model (i.e., describing function) of a sector-bounded nonlinearity. This work also proposes several data-driven methods for designing robust fixed-structure controllers with H∞ performance. One method considers the solution to a non-convex problem, while another method convexifies the problem and implements an iterative algorithm to obtain the local solution (which can also consider H2 performance). The effectiveness of the proposed method(s) is illustrated by considering several case studies that require robust controllers for achieving the desired performance. The main applicative work in this dissertation is with respect to a power converter control system at the European Organization for Nuclear Research (CERN) (which is used to control the current in a magnet to produce the desired field in controlling particle trajectories in accelerators). The proposed design methods are implemented in order to satisfy the challenging performance specifications set by the application while guaranteeing the system stability and robustness using data-driven design strategies