Methods of system identification, parameter estimation and optimisation applied to problems of modelling and control in engineering and physiology

Mathematical and computer-based models provide the foundation of most methods of engineering design. They are recognised as being especially important in the development of integrated dynamic systems, such as “control-configured” aircraft or in complex robotics applications. These models usually involve combinations of linear or nonlinear ordinary differential equations or difference equations, partial differential equations and algebraic equations. In some cases models may be based on differential algebraic equations. Dynamic models are also important in many other fields of research, including physiology where the highly integrated nature of biological control systems is starting to be more fully understood. Although many models may be developed using physical, chemical, or biological principles in the initial stages, the use of experimentation is important for checking the significance of underlying assumptions or simplifications and also for estimating appropriate sets of parameters. This experimental approach to modelling is also of central importance in establishing the suitability, or otherwise, of a given model for an intended application – the so-called “model validation” problem. System identification, which is the broad term used to describe the processes of experimental modelling, is generally considered to be a mature field and classical methods of identification involve linear discrete-time models within a stochastic framework. The aspects of the research described in this thesis that relate to applications of identification, parameter estimation and optimisation techniques for model development and model validation mainly involve nonlinear continuous time models Experimentally-based models of this kind have been used very successfully in the course of the research described in this thesis very in two areas of physiological research and in a number of different engineering applications. In terms of optimisation problems, the design, experimental tuning and performance evaluation of nonlinear control systems has much in common with the use of optimisation techniques within the model development process and it is therefore helpful to consider these two areas together. The work described in the thesis is strongly applications oriented. Many similarities have been found in applying modelling and control techniques to problems arising in fields that appear very different. For example, the areas of neurophysiology, respiratory gas exchange processes, electro-optic sensor systems, helicopter flight-control, hydro-electric power generation and surface ship or underwater vehicles appear to have little in common. However, closer examination shows that they have many similarities in terms of the types of problem that are presented, both in modelling and in system design. In addition to nonlinear behaviour; most models of these systems involve significant uncertainties or require important simplifications if the model is to be used in a real-time application such as automatic control. One recurring theme, that is important both in the modelling work described and for control applications, is the additional insight that can be gained through the dual use of time-domain and frequency-domain information. One example of this is the importance of coherence information in establishing the existence of linear or nonlinear relationships between variables and this has proved to be valuable in the experimental investigation of neuromuscular systems and in the identification of helicopter models from flight test data. Frequency-domain techniques have also proved useful for the reduction of high-order multi-input multi-output models. Another important theme that has appeared both within the modelling applications and in research on nonlinear control system design methods, relates to the problems of optimisation in cases where the associated response surface has many local optima. Finding the global optimum in practical applications presents major difficulties and much emphasis has been placed on evolutionary methods of optimisation (both genetic algorithms and genetic programming) in providing usable methods for optimisation in design and in complex nonlinear modelling applications that do not involve real-time problems. Another topic, considered both in the context of system modelling and control, is parameter sensitivity analysis and it has been found that insight gained from sensitivity information can be of value not only in the development of system models (e.g. through investigation of model robustness and the design of appropriate test inputs), but also in feedback system design and in controller tuning. A technique has been developed based on sensitivity analysis for the semi-automatic tuning of cascade and feedback controllers for multi-input multi-output feedback control systems. This tuning technique has been applied successfully to several problems. Inverse systems also receive significant attention in the thesis. These systems have provided a basis for theoretical research in the control systems field over the past two decades and some significant applications have been reported, despite the inherent difficulties in the mathematical methods needed for the nonlinear case. Inverse simulation methods, developed initially by others for use in handling-qualities studies for fixed-wing aircraft and helicopters, are shown in the thesis to provide some important potential benefits in control applications compared with classical methods of inversion. New developments in terms of methodology are presented in terms of a novel sensitivity based approach to inverse simulation that has advantages in terms of numerical accuracy and a new search-based optimisation technique based on the Nelder-Mead algorithm that can handle inverse simulation problems involving hard nonlinearities. Engineering applications of inverse simulation are presented, some of which involve helicopter flight control applications while others are concerned with feed-forward controllers for ship steering systems. The methods of search-based optimisation show some important advantages over conventional gradient-based methods, especially in cases where saturation and other nonlinearities are significant. The final discussion section takes the form of a critical evaluation of results obtained using the chosen methods of system identification, parameter estimation and optimisation for the modelling and control applications considered. Areas of success are highlighted and situations are identified where currently available techniques have important limitations. The benefits of an inter-disciplinary and applications-oriented approach to problems of modelling and control are also discussed and the value in terms of cross-fertilisation of ideas resulting from involvement in a wide range of applications is emphasised. Areas for further research are discussed

Multivariable System Controller Tuning Techniques Based on Sensitivity Measures

A controller tuning technique using sensitivity functions of the controller parameters is proposed which does not require a detailed model of the plant either based on physical principles or through system identification. Only simple signal processing is required in the tuning process. The sensitivity information is used by an adjustment algorithm involving a least squares type of criterion function. The generation of the sensitivity functions which are of central importance in this approach is described in this thesis, involving use of a signal convolution approach and a two-stage method both in the time-domain and frequency-domain. Three different forms of input signal, which involve the step input, the impulse input and the extended pseudorandom binary sequence (PRBS) input signal are selected in the calculation of the sensitivity functions. The two-stage approach to generating the sensitivity functions of the controller parameters in systems with unknown plants has been investigated for the first time in this research work. The advantage of this novel approach is that there is no limitation on the form of the test input signal. The sensitivity functions can be obtained from measurements directly without any calculations. No problems of implementation arise with the sensitivity filters required. In the controller tuning process, the least squared approach is used to provide the figure of merit for each projected system response. The changes of the controller parameters are altered to minimise the difference between the response of the actual system and the desired response. The details of an application of the tuning procedure using the signal convolution approach for generating the sensitivity functions for a two-tank system with two inputs two outputs both in the time-domain and the frequency-domain are given. Special consideration is given to the accurate modelling of the two-tank system upon which this work is based. Questions of plant nonlinearity and measurement noise and their effects on the tuning process are given careful consideration but no significant problems were encountered. In order to prove that the technique is suitable for more complex problems, the technique has also been applied successfully to helicopter flight control system design optimisation. This is of potential interest as a means of reducing the period of time for test flying and design modification for practical helicopter flight control systems. The tuning process is a very "visible" one and likely to be attractive for applications of this kind. From the results of these two applications of the tuning technique it can be seen that the tuning process is very effective although the initial responses of the system may be far from the desired responses. In fact, the adjustment procedure provides fast is convergence in the cases considered. Significant progress is made at each adjustment without any oscillations in parameter values. The number of experiments needed to generate the sensitivity information needed for controller tuning is, in general, significantly smaller than that required for a traditional parameter perturbation method for sensitivity function generation

Modelling and Control of Small-Scale Helicopter on a Test Platform

The helicopter is a Multiple-Input Multiple-Output (MIMO) system with highly coupled characteristics, which increases the complexity of the system dynamics. In addition, the system dynamics of the helicopter are unstable, referring to its tendency to deviate from an equilibrium when disturbed. Despite the complexity in its modelling and control, the benefit of using a helicopter for unmanned, autonomous applications can be tremendous. One particular application that motivates this research is the use of an unmanned small-scale helicopter in an autonomous survey mission over an area struck by disaster, such as an earthquake. The work presented in this thesis provides a framework for utilizing a platform system for research and development of small-scale helicopter systems. A platform system enables testing and analysis to be performed indoor in a controlled environment. This can provide a more convenient mean for helicopter research since the system is not affected by environmental elements, such as wind, rain or snow condition. However, the presence of the platform linkages poses challenges for analysis and controller design as it alters the helicopter system flight dynamics. Through a six degree-of-freedom (6 DOF) platform model derived in this research, the criteria for matching the trim conditions between the platform system and a stand alone helicopter have been identified. With the matched trim conditions, linearization is applied to perform analysis on the effects that the platform has on the system dynamics. The results of the analysis provide insights into both the limitations and benefits of utilizing the platform system for helicopter research. Finally, a Virtual Joint Control scheme is proposed as an unified control strategy for both the platform and the stand alone helicopter systems. Having a consistent control scheme between the two systems allows for comparisons between simulation and experimental results for the two systems to be made more readily. Furthermore, the Virtual Joint Control scheme represents a novel flight control strategy for stand alone helicopter systems