The design of periodic excitations for dynamic system identification

System identification techniques are developed for modelling linear and nonlinear systems. The main results of the work are concerned with the design and utilisation of periodic perturbation signals in general areas of time- and frequency-domain system identification. A design strategy is given for a new class of perturbation signals, together with examples of their use in system identification applications. Signal processing procedures are developed for the practical treatment of drift disturbances and transient effects, and also for the detection of nonlinear contributions to the measurement data. The techniques rely completely on the periodicity of the excitation, and so the advantageous properties of periodic input signals are considered in detail. The use of periodic excitations in discrete- and continuous-time nonlinear system identification is also reported, with the identification methods illustrating the worth of frequency-domain measurements in this area. An automatic tuning procedure for PID controllers is also developed, which illustrates an application of system identification techniques to control problems

Study of the best linear approximation of nonlinear systems with arbitrary inputs

System identification is the art of modelling of a process (physical, biological, etc.) or to predict its behaviour or output when the environment condition or parameter changes. One is modelling the input-output relationship of a system, for example, linking temperature of a greenhouse (output) to the sunlight intensity (input), power of a car engine (output) with fuel injection rate (input). In linear systems, changing an input parameter will result in a proportional increase in the system output. This is not the case in a nonlinear system. Linear system identification has been extensively studied, more so than nonlinear system identification. Since most systems are nonlinear to some extent, there is significant interest in this topic as industrial processes become more and more complex. In a linear dynamical system, knowing the impulse response function of a system will allow one to predict the output given any input. For nonlinear systems this is not the case. If advanced theory is not available, it is possible to approximate a nonlinear system by a linear one. One tool is the Best Linear Approximation (Bla), which is an impulse response function of a linear system that minimises the output differences between its nonlinear counterparts for a given class of input. The Bla is often the starting point for modelling a nonlinear system. There is extensive literature on the Bla obtained from input signals with a Gaussian probability density function (p.d.f.), but there has been very little for other kinds of inputs. A Bla estimated from Gaussian inputs is useful in decoupling the linear dynamics from the nonlinearity, and in initialisation of parameterised models. As Gaussian inputs are not always practical to be introduced as excitations, it is important to investigate the dependence of the Bla on the amplitude distribution in more detail. This thesis studies the behaviour of the Bla with regards to other types of signals, and in particular, binary sequences where a signal takes only two levels. Such an input is valuable in many practical situations, for example where the input actuator is a switch or a valve and hence can only be turned either on or off. While it is known in the literature that the Bla depends on the amplitude distribution of the input, as far as the author is aware, there is a lack of comprehensive theoretical study on this topic. In this thesis, the Blas of discrete-time time-invariant nonlinear systems are studied theoretically for white inputs with an arbitrary amplitude distribution, including Gaussian and binary sequences. In doing so, the thesis offers answers to fundamental questions of interest to system engineers, for example: 1) How the amplitude distribution of the input and the system dynamics affect the Bla? 2) How does one quantify the difference between the Bla obtained from a Gaussian input and that obtained from an arbitrary input? 3) Is the difference (if any) negligible? 4) What can be done in terms of experiment design to minimise such difference? To answer these questions, the theoretical expressions for the Bla have been developed for both Wiener-Hammerstein (Wh) systems and the more general Volterra systems. The theory for the Wh case has been verified by simulation and physical experiments in Chapter 3 and Chapter 6 respectively. It is shown in Chapter 3 that the difference between the Gaussian and non-Gaussian Bla’s depends on the system memory as well as the higher order moments of the non-Gaussian input. To quantify this difference, a measure called the Discrepancy Factor—a measure of relative error, was developed. It has been shown that when the system memory is short, the discrepancy can be as high as 44.4%, which is not negligible. This justifies the need for a method to decrease such discrepancy. One method is to design a random multilevel sequence for Gaussianity with respect to its higher order moments, and this is discussed in Chapter 5. When estimating the Bla even in the absence of environment and measurement noise, the nonlinearity inevitably introduces nonlinear distortions—deviations from the Bla specific to the realisation of input used. This also explains why more than one realisation of input and averaging is required to obtain a good estimate of the Bla. It is observed that with a specific class of pseudorandom binary sequence (Prbs), called the maximum length binary sequence (Mlbs or the m-sequence), the nonlinear distortions appear structured in the time domain. Chapter 4 illustrates a simple and computationally inexpensive method to take advantage this structure to obtain better estimates of the Bla—by replacing mean averaging by median averaging. Lastly, Chapters 7 and 8 document two independent benchmark studies separate from the main theoretical work of the thesis. The benchmark in Chapter 7 is concerned with the modelling of an electrical Wh system proposed in a special session of the 15th International Federation of Automatic Control (Ifac) Symposium on System Identification (Sysid) 2009 (Schoukens, Suykens & Ljung, 2009). Chapter 8 is concerned with the modelling of a ‘hyperfast’ Peltier cooling system first proposed in the U.K. Automatic Control Council (Ukacc) International Conference on Control, 2010 (Control 2010)

Meta-heuristic global optimization algorithms for aircraft engines modelling and controller design; A review, research challenges, and exploring the future

Utilizing meta-heuristic global optimization algorithms in gas turbine aero-engines modelling and control problems is proposed over the past two decades as a methodological approach. The purpose of the review is to establish evident shortcomings of these approaches and to identify the remaining research challenges. These challenges need to be addressed to enable the novel, cost-effective techniques to be adopted by aero-engine designers. First, the benefits of global optimization algorithms are stated in terms of philosophy and the nature of different types of these methods. Then, a historical coverage is given for the applications of different optimization techniques applied in different aspects of gas turbine modelling, controller design, and tuning fields. The main challenges for the application of meta-heuristic global optimization algorithms in new advanced engine designs are presented. To deal with these challenges, two efficient optimization algorithms, Competent Genetic Algorithm in single objective feature and aggregative gradient-based algorithm in multi-objective feature are proposed and applied in a turbojet engine controller gain-tuning problem as a case study. A comparison with the publicly available results show that optimization time and convergence indices will be enhanced noticeably. Based on this comparison and analysis, the potential solutions for the remaining research challenges for application to aerospace engineering problems in the future include the implementation of enhanced and modified optimization algorithms and hybrid optimization algorithms in order to achieve optimal results for the advanced engine modelling and controller design procedure with affordable computational effort

A DATA-DRIVEN PID CONTROLLER FOR FLEXIBLE JOINT MANIPULATOR USING NORMALIZED SIMULTANEOUS PERTURBATION STOCHASTIC APPROXIMATION

This paper presents a data-driven PID controller based on Normalized Simultaneous Perturbation Stochastic Approximation (SPSA). Initially, an unstable convergence of conventional SPSA is illustrated, which motivate us to introduce its improved version. The unstable convergence always happened in the data-driven controller tuning, when the closed-loop control system became unstable. In the case of flexible joint manipulator, it will exhibit unstable tip angular position with high magnitude of vibration. Here, the conventional SPSA is modified by introducing a normalized gradient approximation to update the design variable. To be more specific, each measurement of the cost function from the perturbations is normalized to the maximum cost function measurement at the current iteration. As a result, this improvement is expected to avoid the updated control parameter from producing an unstable control performance. The effectiveness of the normalized SPSA is tested to the data-driven PID control scheme of a flexible joint plant. The simulation result shows that the data-driven controller tuning using the normalized SPSA is able to provide a stable convergence with 76.68 % improvement in average cost function. Moreover, it also exhibits lower average and best values for both norms of error and input performances as compared to the existing modified SPSA.A DATA-DRIVEN PID CONTROLLER FOR FLEXIBLE JOINT MANIPULATOR USING NORMALIZED SIMULTANEOUS PERTURBATION STOCHASTIC APPROXIMATIO

A Data-Driven PID Controller For Flexible Joint Manipulator Using Normalized Simultaneous Perturbation Stochastic Approximation

This paper presents a data-driven PID controller based on Normalized Simultaneous Perturbation Stochastic Approximation (SPSA). Initially, an unstable convergence of conventional SPSA is illustrated, which motivate us to introduce its improved version. The unstable convergence always happened in the data-driven controller tuning, when the closed-loop control system became unstable. In the case of flexible joint manipulator, it will exhibit unstable tip angular position with high magnitude of vibration. Here, the conventional SPSA is modified by introducing a normalized gradient approximation to update the design variable. To be more specific, each measurement of the cost function from the perturbations is normalized to the maximum cost function measurement at the current iteration. As a result, this improvement is expected to avoid the updated control parameter from producing an unstable control performance. The effectiveness of the normalized SPSA is tested to the data-driven PID control scheme of a flexible joint plant. The simulation result shows that the data-driven controller tuning using the normalized SPSA is able to provide a stable convergence with 76.68 % improvement in average cost function. Moreover, it also exhibits lower average and best values for both norms of error and input performances as compared to the existing modified SPSA