A survey on gain-scheduled control and filtering for parameter-varying systems

Copyright © 2014 Guoliang Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany

H∞ filtering for nonlinear discrete-time stochastic systems with randomly varying sensor delays

This is the post print version of the article. The official published version can be obained from the link - Copyright 2009 Elsevier LtdThis paper is concerned with the H∞ filtering problem for a general class of nonlinear discrete-time stochastic systems with randomly varying sensor delays, where the delayed sensor measurement is governed by a stochastic variable satisfying the Bernoulli random binary distribution law. In terms of the Hamilton–Jacobi–Isaacs inequalities, preliminary results are first obtained that ensure the addressed system to possess an l2-gain less than a given positive scalar γ. Next, a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the H∞ performance constraint for all nonzero exogenous disturbances under the zero-initial condition. Such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation. Furthermore, it is shown that our main results can be readily specialized to the case of linear stochastic systems. Finally, a numerical simulation example is used to demonstrate the effectiveness of the results derived.This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor James Lam under the direction of Editor Ian R. Petersen. This work was supported by the Shanghai Natural Science Foundation under Grant 07ZR14002, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany

Design of gain schedule fractional PID control for nonlinear thrust vector control missile with uncertainty

The purpose of this paper is to control the trajectory of the nonlinear missile model in the pitch channel by using Fractional PID controller (FPID) and Gain Schedule Fractional PID controller (GSFPID). FPID and GSFPID with nonlinear missile model are designed where their parameters are tuned by Simulink design optimization in the Matlab toolbox. This optimization method gives the optimal parameters that achieve the best tracking with step unit reference signal. The GSFPID controller compensates the restrictions that represent physical limits of actuators in the pitch channel. The GSFPID with nonlinear missile model is designed in two phases. The first phase is the boost phase where the thrust force is maximized and the second phase is sustain phase where the thrust force is minimized. The equations of motion for nonlinear missile model with FPID and GSFPID are modelled mathematically in the Matlab-Simulink environment. The results of FPID and GSFPID controllers with the nonlinear missile model are presented and compared. The wind effect and the dynamic uncertainties effects are researched and the results are compared. The closed-loop nonlinear system is linearized by the Simulink linear analysis tool at critical operating point t = 5.8 sec and the stability is studied

Equivalence of robust stabilization and robust performance via feedback

One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying (LPV) plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation (LFT) models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified $L^{2}$-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to Linear Matrix Inequality (LMI) conditions.Comment: 20 page

Observer-based controllers with data dropout rate adaptation

In this work, we address the observer-based control problem for networked control systems with an unknown time-varying packet arrival rate (PAR) and under root mean square-norm bounded disturbances. We assume packetized transmissions of both measurement and control input through a communication network with successful delivery acknowledgement. Using the measurement reception state and the control transmission acknowledgement, we derive a filter to estimate the PAR. We consider that the PAR changes sporadically from a constant value to another one; that is, it has two different behaviours: transient and steady state. While the observer only updates the state estimation using the current received measurements, the controller computes the control action employing the current state estimation and the previous applied control input. We propose to schedule both the observer and controller with rational functions of the PAR estimation. We show that the separation principle applies, and then, seeking higher performance accuracy, we develop an optimization math formula observer and controller design procedure that considers the two possible behaviours of the PAR. This optimization procedure attempts to maximize the estimation and control performances for each of the possible constant values of the PAR while offering robustness against PAR estimation errors and variations of the PAR. By exploiting sum-of-squares decomposition techniques, the design procedure involves an optimization problem over polynomials. A numerical example illustrates the effectiveness of the proposed approach.This work has been supported by MICINN project number TEC2015-69155-R from the Spanish government, project number P1·1B2015-42 and grant PI15734 from Universitat Jaume I

H∞ control for 2-D time-delay systems with randomly occurring nonlinearities under sensor saturation and missing measurements

In this paper, the H∞ output-feedback control problem is investigated for a class of two-dimensional (2-D) nonlinear systems with time-varying delays under imperfect measurements. Randomly occurring nonlinearities (RONs) are introduced in the system to account for probabilistic nonlinear disturbances typically caused by networked environments and governed by a sequence of random variables obeying the Bernoulli distribution. The imperfect measurement outputs are subject to both data missing and randomly occurring sensor saturations (ROSSs), which are put forward to characterize the network-induced phenomena such as probabilistic communication failures and limited capacity of the communication devices. The aim of this paper is to design an output-feedback controller such that the closed-loop system is globally asymptotically stable in the mean square and the prescribed H∞ performance index is satisfied. Sufficient conditions are presented by resorting to intensive stochastic analysis and matrix inequality techniques, which not only guarantee the existence of the desired controllers for all possible time-delays, RONs, missing measurements and ROSSs but also lead to the explicit expressions of such controllers. Finally, a numerical simulation example is given to demonstrate the applicability of the proposed control scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61174136, 61134009 and 61329301, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the “333 Project” Foundation of Jiangsu Province, the Programme for New Century Excellent Talents in University under Grant NCET-12-0117, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Iterative learning control: algorithm development and experimental benchmarking

This thesis concerns the general area of experimental benchmarking of Iterative Learning Control (ILC) algorithms using two experimental facilities. ILC is an approach which is suitable for applications where the same task is executed repeatedly over the necessarily finite time duration, known as the trial length. The process is reset prior to the commencement of each execution. The basic idea of ILC is to use information from previously executed trials to update the control input to be applied during the next one. The first experimental facility is a non-minimum phase electro-mechanical system and the other is a gantry robot whose basic task is to pick and place objects on a moving conveyor under synchronization and in a fixed finite time duration that replicates many tasks encountered in the process industries. Novel contributions are made in both the development of new algorithms and, especially, in the analysis of experimental results both of a single algorithm alone and also in the comparison of the relative performance of different algorithms. In the case of non-minimum phase systems, a new algorithm, named Reference Shift ILC (RSILC) is developed that is of a two loop structure. One learning loop addresses the system lag and another tackles the possibility of a large initial plant input commonly encountered when using basic iterative learning control algorithms. After basic algorithm development and simulation studies, experimental results are given to conclude that performance improvement over previously reported algorithms is reasonable. The gantry robot has been previously used to experimentally benchmark a range of simple structure ILC algorithms, such as those based on the ILC versions of the classical proportional plus derivative error actuated controllers, and some state-space based optimal ILC algorithms. Here these results are extended by the first ever detailed experimental study of the performance of stochastic ILC algorithms together with some modifications necessary to their configuration in order to increase performance. The majority of the currently reported ILC algorithms mainly focus on reducing the trial-to-trial error but it is known that this may come at the cost of poor or unacceptable performance along the trial dynamics. Control theory for discrete linear repetitive processes is used to design ILC control laws that enable the control of both trial-to-trial error convergence and along the trial dynamics. These algorithms can be computed using Linear Matrix Inequalities (LMIs) and again the results of experimental implementation on the gantry robot are given. These results are the first ever in this key area and represent a benchmark against which alternatives can be compared. In the concluding chapter, a critical overview of the results presented is given together with areas for both short and medium term further researc

Stabilization of uncertain linear systems: an LFT approach

This paper develops machinery for control of uncertain linear systems described in terms of linear fractional transformations (LFTs) on transform variables and uncertainty blocks with primary focus on stabilization and controller parameterization. This machinery directly generalizes familiar state-space techniques. The notation of Q-stability is defined as a natural type of robust stability, and output feedback stabilizability is characterized in terms of Q-stabilizability and Q-detectability which in turn are related to full information and full control problems. Computation is in terms of convex linear matrix inequalities (LMIs), the controllers have a separation structure, and the parameterization of all stabilizing controllers is characterized as an LFT on a stable, free parameter

Robust Fault-Tolerant Tracking Control for Nonlinear Networked Control System: Asynchronous Switched Polytopic Approach

This paper is concerned with the robust fault-tolerant tracking control problem for networked control system (NCS). Firstly, considering the locally overlapped switching law widely existed in engineering applications, the NCS is modeled as a locally overlapped switched polytopic system to reduce designing conservatism and solving complexity. Then, switched parameter dependent fault-tolerant tracking controllers are constructed to deal with the asynchronous switching phenomenon caused by the updating delays of the switching signals and weighted coefficients. Additionally, the global uniform asymptotic stability in the mean (GUAS-M) and desired weighted l2 performance are guaranteed by combining the switched parameter dependent Lyapunov functional method with the average dwell time (ADT) method, and the feasible conditions for the fault-tolerant tracking controllers are obtained in the form of linear matrix inequalities (LMIs). Finally, the performance of the proposed approach is verified on a highly maneuverable technology (HiMAT) vehicle’s tracking control problem. Simulation results show the effectiveness of the proposed method

Measurements, Models, Systems and Design

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