Bing Chu

Iterative learning control for constrained linear systems

This article considers iterative learning control (ILC) for linear systems with convex control input constraints. First, the constrained ILC problem is formulated in a novel successive projection framework. Then, based on this projection method, two algorithms are proposed to solve this constrained ILC problem. The results show that, when perfect tracking is possible, both algorithms can achieve perfect tracking. The two algorithms differ, however, in that one algorithm needs much less computation than the other. When perfect tracking is not possible, both algorithms can exhibit a form of practical convergence to a ‘best approximation’. The effect of weighting matrices on the performance of the algorithms is also discussed and finally, numerical simulations are given to demonstrate the effectiveness of the proposed methods.

Energy-Based

Using an energy-based method, this paper investigates the L 2 disturbance attenuation excitation control of multimachine power system connected with constant power loads. First, a general result is presented for the L 2 disturbance attenuation control of nonlinear differential algebraic systems with dissipative Hamiltonian realization. Then, pre-feedback is employed to transform the power system into a dissipative Hamiltonian form. Based on this, a decentralized L 2 excitation control scheme is proposed to improve the transient stability of the system. Simulation results demonstrate the effectiveness of the controller.

L_2

This article proposes a novel technique for accelerating the convergence of the previously published norm-optimal iterative learning control (NOILC) methodology. The basis of the results is a formal proof of an observation made by D.H. Owens, namely that the NOILC algorithm is equivalent to a successive projection algorithm between linear varieties in a suitable product Hilbert space. This leads to two proposed accelerated algorithms together with well-defined convergence properties. The results show that the proposed accelerated algorithms are capable of ensuring monotonic error norm reductions and can outperform NOILC by more rapid reductions in error norm from iteration to iteration. In particular, examples indicate that the approach can improve the performance of NOILC for the problematic case of non-minimum phase systems. Realisation of the algorithms is discussed and numerical simulations are provided for comparative purposes and to demonstrate the numerical performance and effectiveness of the proposed methods.

Disturbance Attenuation Excitation Control of Differential Algebraic Power Systems

This paper presents a boost-multilevel inverter design with integrated battery energy storage system for standalone application. The inverter consists of modular switched-battery cells and a full-bridge. It is multifunctional and has two modes of operation: 1) the charging mode, which charges the battery bank and 2) the inverter mode, which supplies ac power to the load. This inverter topology requires significantly less power switches compared to conventional topology such as cascaded H-bridge multilevel inverter, leading to reduced size/cost and improved reliability. To selectively eliminate low-order harmonics and control the desired fundamental component, nonlinear system equations are represented in fitness function through the manipulation of modulation index and the genetic algorithm (GA) is employed to find the optimum switching angles. A seven-level inverter prototype is implemented and experimental results are provided to verify the feasibility of the proposed inverter design.

Accelerated norm-optimal iterative learning control algorithms using successive projection

The paper describes a substantial extension of norm optimal iterative learning control (NOILC) that permits tracking of a class of finite dimensional reference signals whilst simultaneously converging to the solution of a constrained quadratic optimisation problem. The theory is presented in a general functional analytical framework using operators between chosen real Hilbert spaces. This is applied to solve problems in continuous time where tracking is only required at selected intermediate points of the time interval but, simultaneously, the solution is required to minimise a specified quadratic objective function of the input signals and chosen auxiliary (state) variables. Applications to the discrete time case, including the case of multi-rate sampling, are also summarised. The algorithms are motivated by practical need and provide a methodology for reducing undesirable effects such as payload spillage, vibration tendencies and actuator wear whilst maintaining the desired tracking accuracy necessary for task completion. Solutions in terms of NOILC methodologies involving both feedforward and feedback components offer the possibilities of greater robustness than purely feedforward actions. Results describing the inherent robustness of the feedforward implementation are presented and the work is illustrated by experimental results from a robotic manipulator.

Switched-Battery Boost-Multilevel Inverter with GA Optimized SHEPWM for Standalone Application

This brief investigates the asymptotic stability of positive 2D systems described by the Roesser model. A necessary and sufficient condition is derived for the asymptotic stability, which amounts to checking the spectrum radius of the system matrix. Furthermore, it can be shown that the asymptotic stability of positive 2D systems is equivalent to that of the traditional 1D systems. This observation would greatly facilitate the analysis and synthesis of positive 2D systems.

Multivariable norm optimal iterative learning control with auxiliary optimisation

Reducing greenhouse gas emissions is now an important and pressing matter. Systems control theory, and in particular feedback control, can contribute to the design of policies that achieve sustainable levels of emissions of CO2 (and other greenhouse gases) while minimizing the impact on the economy, and at the same time explicitly addressing the high levels of uncertainty associated with predictions of future emissions. In this paper, preliminary results are described for an approach where economic Model Predictive Control (MPC) is applied to a Regional dynamic Integrated model of Climate and the Economy (RICE model) as a test bed to design savings rates and global carbon tax for greenhouse gas emissions. Using feedback control, the policies are updated on the basis of the observed emissions, rather than on the predicted level of emissions. The basic structure and principle of the RICE model is firstly introduced and some key equations are described. The idea of introducing feedback control is then explained and economic MPC is applied to design policies for CO2 emissions. Simulation results are presented to demonstrate the effectiveness of the proposed method for two different scenarios. Feedback control design provides a degree of robustness against disturbances and model uncertainties, which is illustrated through a simulation study with two particular types of uncertainties. The results obtained in this paper illustrate the strength of the proposed design approach and form the basis for future research on using systems control theory to design optimal sustainable policies.

On the Asymptotic Stability of Positive 2-D Systems Described by the Roesser Model

The subject of this article is the modelling of the influence of non-minimum phase discrete-time system dynamics on the performance of norm optimal iterative learning control (NOILC) algorithms with the intent of explaining the observed phenomenon and predicting its primary characteristics. It is established that performance in the presence of one or more non-minimum phase plant zeros typically has two phases. These consist of an initial fast monotonic reduction of the L 2 error norm (mean square error) followed by a very slow asymptotic convergence. Although the norm of the tracking error does eventually converge to zero, the practical implications over a finite number of trials is apparent convergence to a non-zero error. The source of this slow convergence is identified using the singular value distribution of the systems all pass component. A predictive model of the onset of slow convergence behaviour is developed as a set of linear constraints and shown to be valid when the iteration time interval is sufficiently long. The results provide a good prediction of the magnitude of error norm where slow convergence begins. Formulae for this norm and associated error time series are obtained for single-input single-output systems with several non-minimum phase zeros outside the unit circle using Lagrangian techniques. Numerical simulations are given to confirm the validity of the analysis.

Using economic Model Predictive Control to design sustainable policies for mitigating climate change

Motivated by the commonly encountered problem in which tracking is only required at selected intermediate points within the time interval, a general optimisation-based iterative learning control (ILC) algorithm is derived that ensures convergence of tracking errors to zero whilst simultaneously minimising a specified quadratic objective function of the input signals and chosen auxiliary (state) variables. In practice, the proposed solutions enable a repeated tracking task to be accurately completed whilst simultaneously reducing undesirable effects such as payload spillage, vibration tendencies and actuator wear. The theory is developed using the well-known norm optimal ILC (NOILC) framework, using general linear, functional operators between real Hilbert spaces. Solutions are derived using feedforward action, convergence is proved and robustness bounds are presented using both norm bounds and positivity conditions. Algorithms are specified for both continuous and discrete-time state-space representations, with the latter including application to multi-rate sampled systems. Experimental results using a robotic manipulator confirm the practical utility of the algorithms and the closeness with which observed results match theoretical predictions.

Modelling of non-minimum phase effects in discrete-time norm optimal iterative learning control

A novel design approach is proposed for point-to-point iterative learning control (ILC), enabling system constraints to be satisfied while simultaneously addressing the requirement for high-performance tracking. It is shown that point-to-point ILC design can be formulated and solved using a successive projection first proposed by J. von Neumann, allowing a number of new point-to-point ILC algorithms to be developed and analyzed. To illustrate this framework, two new algorithms are derived with different convergence and computational properties for the constrained point-to-point ILC design problem. The proposed algorithms are validated on a robotic arm with experimental results demonstrating their effectiveness.