Model-based and data-based frequency domain design of fixed structure robust controller: a polynomial optimization approach

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Robust stabilisation of multivariable systems: A super-optimisation approach

The work aims to derive extended robust stability results for the case of unstructured uncertainty models of multivariable systems. More specifically, throughout the thesis, additive and coprime unstructured perturbation models are considered. Refined robust stabilisation problems of MIMO systems are defined and maximally robust controllers are synthesised in a state-space form. Unstructured perturbations which destabilise the feedback system for every optimal (maximally robust) controller are identified on the boundary of the optimal ball, i.e. the set of all admissible perturbations with norm equal to the maximum robust stability radius. Boundary perturbations are termed "uniformly destabilising" if they destabilise the closed-loop system for every optimal controller and it is shown that they all share a common characteristic, i.e. a projection of magnitude equal to the maximal robust stability radius, along a fixed direction defined by a pair of maximising vectors (scaled Schmidt pair) of a Hankel operator related to the problem. By imposing a directionality constraint it is shown that it is possible to increase the robust stability radius in every other direction by a subset of all optimal controllers. In order to solve this problem, super-optimisation techniques are developed. Independently a natural extension of Hankel norm approximations, the so-called super­ optimisation problem is posed and solved explicitly for the case of one-block problems in a state-space setting. It is thus shown that a subset of all maximally robust controllers, namely the class of super-optimal controllers, stabilises all perturbed plants within an extended stability radius 11,*(b), subject to a directionality constraint. In addition, the work is related to robust stabilisation subject to structured perturbations. The notions of structured robust stabilisation problem, and structured set approximation are defined in connection with the maximised set of permissible perturbations. It is further shown that µ*(J) can serve as an upper bound the structured robust stabilisation problem. The effect of µ*(J) as an upper bound depends on the compatibility between the two structures, the true structure and the artificial structure of the extended permissible set. [Look inside the thesis' abstract for an exact version of formulas and equations

New Approaches in Automation and Robotics

The book New Approaches in Automation and Robotics offers in 22 chapters a collection of recent developments in automation, robotics as well as control theory. It is dedicated to researchers in science and industry, students, and practicing engineers, who wish to update and enhance their knowledge on modern methods and innovative applications. The authors and editor of this book wish to motivate people, especially under-graduate students, to get involved with the interesting field of robotics and mechatronics. We hope that the ideas and concepts presented in this book are useful for your own work and could contribute to problem solving in similar applications as well. It is clear, however, that the wide area of automation and robotics can only be highlighted at several spots but not completely covered by a single book

Automotive Driveline Control by Nonparametric QFT Methods

This thesis develops and applies novel identification and control methods for automotive vehicle driveline control. The driveline system has internal backlash combined with resonances which make its control a difficult nonlinear problem. The automotive industry has become very competitive during the last few years and in addition to style and fuel economy, the vehicle performance is a very important issue for the customer. The driveline response to driver demand is a key factor in the customer perception of vehicle quality. A major challenge in its control is that individual driving skills differ greatly among drivers, which leads to a large uncertainty in uncontrolled vehicle response. Current industrial methodologies for the driveline control problem are heuristic and trial and error and require considerable time and resources including extensive on-road vehicle testing. The presented work in thesis in contrast, presents a rapid and systematic methodology which allows the control engineer to achieve pre-determined quantified tracking bounds on the driveline response despite significant system nonlinearity and uncertainty. Firstly a novel mathematical model of the drive line is presented which is subsequently used as one means to evaluate the proposed control methods. Both clutch and backlash nonlinearities are included in the model, and unlike in other published models, backlash is more realistically sandwiched between the compliant clutch and compliant drive shafts. The thesis integrates a Nonparametric (NP) identification approach with Quantitative Feedback Theory (QFT) control methods to result in a novel NP QFT method for nonlinear systems. A NP frequency response identification method is proposed for obtaining a Linear Time Invariant Equivalent (LTIE) sets for the nonlinear system using a frequency weighted windowing method to allow the use of experimentally obtained finite Input/Output (I/O) data records. The NP model is obtained by a local frequency smoothing estimation method in which a frequency set is selected to cover the system bandwidth. This novel NP QFT method has the usual benefits of NP identification such as avoiding concentrating the system information in a limited number of parameters and also permits the acknowledged benefits of QFT control such as the effective linear controller design for nonlinear systems which cannot otherwise be applied without parametric models. A novel technique, based on the discrete Hilbert transform is presented for obtaining an equivalent Minimum Phase (MP) plant for a None Minimum Phase (NMP) nominal plant and determining their phase shift difference which allows the QFT design of such systems based on NP data for the first time. Another application of the NP identification method which is presented is to parameter space control and develops a novel NP parameter space method which has the advantage over QFT of simplicity of controller design and structure at the expense of reduced performance. This method is validated experimentally on the vehicle Internal Combustion (IC) engine idle speed problem. The presented NP QFT method is used to design a controller for a gasoline electronic throttle valve which is a key component of all driveline control systems. Although nonlinear compensation could significantly enhance the outcomes of the process further, it is shown that an effective linear controller can be designed by the NP QFT method without any nonlinear compensation and with an acceptable time response in a quick and systematic method from readily obtained test-data. All used experimental validation approaches use an entirely black box approach in which the controllers are developed directly from experimental testing. The experimental results show that both the new NP parameter space and new NP QFT methods are able to robustly achieve good engine idle speed control and good driveline wheel speed control respectively. In driveline control, the wheel speed response was experimentally found to be always inside the pre-designed boundaries and the controlled system was found able to reject the external disturbances within the desired boundary. The presented techniques can be applied to any similar systems where only experimental test data is available without any need to change the methodology or to use any trial and error sequences. The presented methods provide considerable reduction in the design and testing effort for driveline, electronic throttle valve and idle speed control problems

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This paper presents the synthesis of an optimal robust controller with the use of pole placement technique. The presented method includes solving a polynomial equation on the basis of the chosen fixed characteristic polynomial and introduced parametric solutions with a known parametric structure of the controller. Robustness criteria in an unstructured uncertainty description with metrics of norm ℋ∞ are for a more reliable and effective formulation of objective functions for optimization presented in the form of a spectral polynomial with positivity conditions. The method enables robust low-order controller design by using plant simplification with partial-fraction decomposition, where the simplification remainder is added to the performance weight. The controller structure is assembled of well-known parts such as disturbance rejection, and reference tracking. The approach also allows the possibility of multiobjective optimization of robust criteria, application of mixed sensitivity problem, and other closed-loop limitation criteria, where the common criteria function can be composed from different unrelated criteria. Optimization and controller design are performed with iterative evolution algorithm

Control of fluid flows and other systems governed by partial differential-algebraic equations

The motion of fluids, such as air or water, is central to many engineering systems of significant economic and environmental importance. Examples range from air/fuel mixing in combustion engines to turbulence induced noise and fatigue on aircraft. Recent advances in novel sensor/actuator technologies have raised the intriguing prospect of actively sensing and manipulating the motion of the fluid within these systems, making them ripe for feedback control, provided a suitable control model exists. Unfortunately, the models for many of these systems are described by nonlinear, partial differential-algebraic equations for which few, if any, controller synthesis techniques exist. In stark contrast, the majority of established control theory assumes plant models of finite (and typically small) state dimension, expressed as a linear system of ordinary differential equations. Therefore, this thesis explores the problem of how to apply the mainstream tools of control theory to the class of systems described by partial differential-algebraic equations, that are either linear, or for which a linear approximation is valid. The problems of control system design for infinite-dimensional and algebraically constrained systems are treated separately in this thesis. With respect to the former, a new method is presented that enables the computation of a bound on the n-gap between a discretisation of a spatially distributed plant, and the plant itself, by exploiting the convergence rate of the v-gap metric between low-order models of successively finer spatial resolution. This bound informs the design, on loworder models, of H[infinity] loop-shaping controllers that are guaranteed to robustly stabilise the actual plant. An example is presented on a one-dimensional heat equation. Controller/estimator synthesis is then discussed for finite-dimensional systems containing algebraic, as well as differential equations. In the case of fluid flows, algebraic constraints typically arise from incompressibility and the application of boundary conditions. A numerical algorithm is presented, suitable for the semi-discrete linearised Navier-Stokes equations, that decouples the differential and algebraic parts of the system, enabling application of standard control theory without the need for velocity-vorticity type methods. This algorithm is demonstrated firstly on a simple electrical circuit, and secondly on the highly non-trivial problem of flow-field estimation in the transient growth region of a flat-plate boundary layer, using only wall shear measurements. These separate strands are woven together in the penultimate chapter, where a transient energy controller is designed for a channel-flow system, using wall mounted sensors and actuators

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