Dynamics and control of quasirational systems

Systems having transfer functions of the form documentclass{article}pagestyle{empty}begin{document}$$G_P (s) = frac{{P_1 (s) - P_2 (s)e^{ - t_d s} }}{{Q(s)}},$$end{document} where P 1 ( s ), P 2 ( s ) and Q ( s ) are polynomials, are called quasirational distributed systems (QRDS). They are encountered in processes modeled by hyperbolic partial differential equations. QRDS can have an infinity of right half-plane zeros which causes large phase lags and can result in poor performance of the closed-loop system with PID controllers. Theory on the asymptotic location of zeros of quasipolynomials is used to predict the nonminimum phase characteristics of QRDS and formulas are presented for factoring QRDS models into minimum and non-minimum phase elements. A generalized Smith predictor controller design procedure for QRDS, based on this factorization, is derived. It uses pole placement to obtain a controller parameterization that introduces free poles which are selected to satisfy robustness specifications. The use of pole placement allows for the design of robust control systems in a transparent manner. Controller selection is generally better, simpler and more direct with this procedure than searching for optimal PID controller settings.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/37408/1/690350615_ftp.pd

A classification of techniques for the compensation of time delayed processes. Part 2: Structurally optimised controllers

Following on from Part 1, Part 2 of the paper considers the use of structurally optimised controllers to compensate time delayed processes

An investigation into the merits of fuzzy logic control versus classical control.

A project report submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering.Up to now the benefits and problems with fuzzy control have not been fully identified and its role in the control domain needs investigation. The past trend has been to show that a fuzzy controller can provide better control than classical control, without examining what is actually being achieved. The aim in this project report is to give a fair comparison between classical and fuzzy control. Robustness, disturbance rejection, noise suppression" nonminimurn phase and dead time are examined for both controllers. The comparison is performed through computer simulation of classical and fuzzy controlled plant models. Fuzzy control has the advantage of non-linear performance and the ability to capture linguistic information. Translating quantitative information into the fuzzy domain is difficult; therefore when the system is easily mathematically modelled and linear, classical control is usually better. Which controller should be used depends on the application, control designer and information available.Andrew Chakane 201

Continuous-time self-tuning algorithms

This thesis proposes some new self-tuning algorithms. In contrast to the conventional discrete-time approach to self-tuning control, the continuous-time approach is used here, that is continuous-time design but digital implementation is used. The proposed underlying control methods are combined with a continuous-time version of the well-known discrete recursive least squares algorithms. The continuous-time estimation scheme is chosen to maintain the continuous-time nature of the algorithms. The first new algorithm proposed is emulator-based relay control (which has already been described in a paper by the author). The algorithm is based on the idea of constructing the switching surface by emulators; that is, unrealisable output derivatives are replaced by their emulated values. In particular, the relay is forced to operate in the sliding mode. In this case, it is shown that emulator-based control and its proposed relay version become equivalent in the sense that both give the same control law. The second new algorithm proposed is a continuous-time version of the discrete-time generalized predictive control (GPC) of Clarke et al (which has already been described in a paper by the author). The algorithm, continuous-time generalized predictive control (CGPC), is based on similar ideas to the GPC, however the formulation is very different. For example, the output prediction is accomplished by using the Taylor series expansion of the output and emulating the output derivatives involved. A detailed closed-loop analysis of this algorithm is also given. It is shown that the CGPC control law only changes the closed-loop pole locations leaving the open-loop zeros untouched (except one special case). It is also shown that LQ control can be considered in the CGPC framework. Further, the CGPC is extended to include some design polynomials so that the model-following and pole-placement control can be considered in the same framework. A third new algorithm, a relay version of the CGPC, is described. The method is based on the ideas of the emulator-based relay control and again it is shown that the CGPC and its relay version become equivalent when the relay operates in the sliding mode. Finally, the CGPC ideas are extended to the multivariable systems and the resulting closed-loop system is analysed in some detail. It is shown that some special choice of design parameters result in a decoupled closed-loop system for certain systems. In addition, it is shown that if the system is decouplable, it is possible to obtain model-following control. It is also shown that LQ control, as in the scalar case, can be considered in the same framework. An illustrative simulation study is also provided for all of the above methods throughout the thesis

Nonlinear continuous-time generalised predictive control

The development of the nonlinear version of the Continuous-time Generalised Predictive Control (NCGPC) is presented. Unlike the linear version, the nonlinear version is developed in state-space form and shown to include Nonlinear Generalised Minimum Variance (NGMV), and a new algorithm, Nonlinear Predictive Generalised Minimum Variance (NPGMV), as special cases. Through simulations, it is demonstrated that NCGPC can deal with nonlinear systems whose relative degree is not well defined and nonlinear systems with unstable zero dynamics. Geometric approaches, such as exact linearisation, are shown to be included in the NCGPC as special cases

Retrospective Cost Adaptive Control with Concurrent Closed-Loop Identification

Retrospective cost adaptive control (RCAC) is a discrete-time direct adaptive control algorithm for stabilization, command following, and disturbance rejection. RCAC is known to work on systems given minimal modeling information which is the leading numerator coefficient and any nonminimum-phase (NMP) zeros of the plant transfer function. This information is normally needed a priori and is key in the development of the filter, also known as the target model, within the retrospective performance variable. A novel approach to alleviate the need for prior modeling of both the leading coefficient of the plant transfer function as well as any NMP zeros is developed. The extension to the RCAC algorithm is the use of concurrent optimization of both the target model and the controller coefficients. Concurrent optimization of the target model and controller coefficients is a quadratic optimization problem in the target model and controller coefficients separately. However, this optimization problem is not convex as a joint function of both variables, and therefore nonconvex optimization methods are needed. Finally, insights within RCAC that include intercalated injection between the controller numerator and the denominator, unveil the workings of RCAC fitting a specific closed-loop transfer function to the target model. We exploit this interpretation by investigating several closed-loop identification architectures in order to extract this information for use in the target model.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138440/1/fsobolic_1.pd

Advances in PID Control

Since the foundation and up to the current state-of-the-art in control engineering, the problems of PID control steadily attract great attention of numerous researchers and remain inexhaustible source of new ideas for process of control system design and industrial applications. PID control effectiveness is usually caused by the nature of dynamical processes, conditioned that the majority of the industrial dynamical processes are well described by simple dynamic model of the first or second order. The efficacy of PID controllers vastly falls in case of complicated dynamics, nonlinearities, and varying parameters of the plant. This gives a pulse to further researches in the field of PID control. Consequently, the problems of advanced PID control system design methodologies, rules of adaptive PID control, self-tuning procedures, and particularly robustness and transient performance for nonlinear systems, still remain as the areas of the lively interests for many scientists and researchers at the present time. The recent research results presented in this book provide new ideas for improved performance of PID control applications

Development of adaptive control methodologies and algorithms for nonlinear dynamic systems based on u-control framework

Inspired by the U-model based control system design (or called U-control system design), this study is mainly divided into three parts. The first one is a U-model based control system for unstable non-minimum phase system. Pulling theorems are proposed to apply zeros pulling filters and poles pulling filters to pass the unstable non-minimum phase characteristics of the plant model/system. The zeros pulling filters and poles pulling filters derive from a customised desired minimum phase plant model. The remaining controller design can be any classic control systems or U-model based control system. The difference between classic control systems and U-model based control system for unstable non-minimum phase will be shown in the case studies.Secondly, the U-model framework is proposed to integrate the direct model reference adaptive control with MIT normalised rules for nonlinear dynamic systems. The U-model based direct model reference adaptive control is defined as an enhanced direct model reference adaptive control expanding the application range from linear system to nonlinear system. The estimated parameter of the nonlinear dynamic system will be placement as the estimated gain of a customised linear virtual plant model with MIT normalised rules. The customised linear virtual plant model is the same form as the reference model. Moreover, the U-model framework is design for the nonlinear dynamic system within the root inversion.Thirdly, similar to the structure of the U-model based direct model reference adaptive control with MIT normalised rules, the U-model based direct model reference adaptive control with Lyapunov algorithms proposes a linear virtual plant model as well, estimated and adapted the particular parameters as the estimated gain which of the nonlinear plant model by Lyapunov algorithms. The root inversion such as Newton-Ralphson algorithm provides the simply and concise method to obtain the inversion of the nonlinear system without the estimated gain. The proposed U-model based direct control system design approach is applied to develop the controller for a nonlinear system to implement the linear adaptive control. The computational experiments are presented to validate the effectiveness and efficiency of the proposed U-model based direct model reference adaptive control approach and stabilise with satisfied performance as applying for the linear plant model