On the linear regulator with unknown stable exosystems

In this paper, we develop an output feedback adaptive control framework for continuous‐time nonminimum phase multivariable systems for output stabilization, command following, and disturbance rejection. The approach is based on a nonminimal state space realization that generates an expanded set of states using the filtered inputs and filtered outputs and their derivatives of the original system. Specifically, a direct adaptive controller for the nonminimal state space model is constructed using the expanded states of the nonminimal realization and is shown to be effective for multi‐input, multi‐output nonminimum phase systems with unstable dynamics. The adaptive controller does not require any model information nor does it require information of the system poles and system zeros or estimation of the system Markov parameters. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.

SummaryThe rejection of unknown periodic disturbances in the plant output through adaptive feedback has been an active area of research. In most successful efforts, it is assumed that the plant model is a known LTI stable system. In this paper, we relax the assumption of stable known plant and consider the case where the plant model can be unstable with unknown parameters. We do assume, however, that the plant model is minimum phase and use the model reference adaptive control structure to meet the objectives of reference tracking and unknown periodic disturbance rejection without amplifying the effect of broadband noises. The cost of achieving these objectives is the use of overparameterization that adds to the number of computations. The main contribution of this paper is that it shows that the problem of rejecting unknown periodic disturbances can be solved for unstable plants with unknown parameters as long as they are minimum phase. Numerical examples illustrate the effectiveness of the proposed control methodology.

Output regulation of unknown linear systems using average cost reinforcement learning

This paper studies energy storage based output tracking and disturbance rejection problems for a simple interconnected power system suffered from a periodic load disturbance with unknown amplitude and frequency. By constructing a new exosystem, the problem is converted into output regulation problem of a composite system. Internal model theorem is introduced for the composite system, and output regulation problem is changed into stabilization problem of a new augmented system by imposing an appropriate transformation. An adaptive dynamical energy storage based controller can solve stabilization problem of the augmented system as well as output tracking and disturbance rejection problem for the original system. Finally, simulation results show the effectiveness of the proposed controller.

Regulation of Linear Systems with Unknown Additive Sinusoidal Sensor Disturbances

Amplitude-Constrained Self-Tuning Control for Armax Systems with Unknown Order and Parameters

This paper develops a solution to the cooperative output tracking problem of a network of non-minimum phase (NMP) vehicles under a direct and time-varying communication topology. The desired trajectory is generated by a linear exo-system and accessible to partial vehicles. The solution consists of three modules: a distributed observer network (DON), a causal stable inversion (CSI), and a state trajectory tracker (LSTT), where DON generates an estimate of the desired trajectory for each vehicle and CSI gives a bounded state reference for LSTT. The solution is applicable to a wide range of situations where the vehicles may be homogeneous or heterogenous, minimum phase or NMP. In particular, for a network of N linear heterogenous NMP vehicles, we develop some conditions on the modules, present a specific realization and show the convergence of tracking errors and the boundedness of vehicles' internal states, and finally verify the realization by simulation.

SummaryAdaptive control schemes are developed for uncertain multivariable systems with unmatched input disturbances and are applied to an aircraft flight turbulence compensation problem. Key relative degree conditions from system input and disturbance are derived in terms of system interactor matrices for the design of a nominal state or output feedback control law that ensures desired asymptotic output tracking and disturbance rejection. To deal with an uncertain system high‐frequency gain matrix, a gain matrix decomposition technique is employed to parametrize an error system model in terms of the parameter and tracking errors, for the design of an adaptive parameter update law with reduced system knowledge. Both adaptive state and output feedback control schemes are presented in detail for systems with general interactor matrices, based on an LDS gain decomposition parametrization, and LDU and SDU decomposition‐based designs are also discussed, to develop unified adaptive disturbance rejection techniques for multivariable systems. All closed‐loop system signals are bounded, and the system output tracks a reference output asymptotically despite the system and disturbance parameter uncertainties. Simulation results of an aircraft flight control system with adaptive turbulence compensation are presented to show the desired system disturbance rejection performance. Copyright © 2015 John Wiley & Sons, Ltd.

We study robust output regulation for parabolic partial differential equations and other infinite-dimensional linear systems with analytic semigroups. As our main results we show that robust output tracking and disturbance rejection for our class of systems can be achieved using a finite-dimensional controller and present algorithms for construction of two different internal model based robust controllers. The controller parameters are chosen based on a Galerkin approximation of the original PDE system and employ balanced truncation to reduce the orders of the controllers. In the second part of the paper we design controllers for robust output tracking and disturbance rejection for a 1D reaction-diffusion equation with boundary disturbances, a 2D diffusion-convection equation, and a 1D beam equation with Kelvin-Voigt damping.

A simple interconnected power system with periodic load disturbance is considered, an energy storage based adaptive controller is proposed to output tracking and disturbance completely rejection for the system. Since the periodic load disturbance is uncertain with both amplitude and frequency, by constructing a new exosystem, the output tracking and disturbance rejection problem is solved with output regulation theory. By designing an internal model for the complicated system and introducing an appropriate transformation, the output regulation problem is changed into the stabilization problem of a new augmented system. With the help of adaptive control technique, the designed dynamic energy storage controller can solve stabilization problem of the augmented systems as well as the output tracking and disturbance rejection problem for the original system. Finally, the simulation results show the effectiveness of the proposed control strategy.

Metaheuristics based global optimization technique is one among the state of art in soft sensing applications. The metaheuristic based soft sensor is capable of coping with the stochasticity of the process and as well as the corresponding nonlinearities in the dynamics. In this work, a multi-objective based parameter estimation and soft-sensing of unknown states are carried out for a modified version of Quadruple Tank Process (QTP). The effect of the outlet valve over the dynamics of the process is briefly investigated to emphasize the implication of these parameters in the process. The unknown parameters and unobserved states of the QTP are estimated through a Hybridized Grey Wolf Optimization (HGWO). The HGWO is a metaheuristic based optimization, hybridized with static Kalman Bucy (KB) algorithm. The hybridization is carried out to improve the convergence rate of the existing algorithm in terms of ideal computational cycle and proximity towards the global solution. Performance of the proposed HGWO is compared along with the conventional GWO algorithm. The estimation is executed for QTP operating in Non-Minimum Phase (NMP) mode and the simulated results proves the proposed HGWO based soft sensor provides a better result compared to the GWO algorithm.

In this short paper bounding estimators for uncertain systems are developed using the concept of Fuzzy Dynamic Programming. The estimator gives an upper bound to the error for any allowed system parameter variation. A dynamic system is considered where the uncertainty in initial state, additive plant disturbance measurement errors are modeled aS unknown but bounded (UBB). It is further assumed that there is a UBB uncertainty in the system parameters. The estimation problem for a nonlinear system with parameter uncertainty is first formulated as a constrained optimization problem and then using fuzzy dynamic programming the class of bounding estimators is derived. The results are applied to obtain a linear estimator for linear uncertain system. It is shown that such an estimator is precomputable and that it reduces to the optimum filter for a linear system with additive disturbances as the model uncertainty vanishes.

This article presents the central finite-dimensional H ∞ controller for linear time-varying systems with unknown parameters, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, this article reduces the original H ∞ controller problem to the corresponding H 2 controller problem, using the technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), ‘State-space Solutions to Standard H 2 and H Infinity Control Problems’, IEEE Transactions Automatic Control, 34, 831–847]. This article yields the central suboptimal H ∞ controller for linear systems with unknown parameters in a closed finite-dimensional form, based on the corresponding H 2 controller obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008), ‘Optimal LQG Controller for Linear Systems with Unknown Parameters’, Journal of The Franklin Institute, 345, 293–302]. Numerical simulations are conducted to verify performance of the designed central suboptimal controller for uncertain linear systems with unknown parameters against the conventional central suboptimal H ∞ controller for linear systems with exactly known parameter values.

This paper presents a robust control design methodology for a serial DC–AC converter based on 𝐻∞ synthesis and a MATLAB/Simulink modelling framework. A mathematical model of the converter is derived and linearized around a selected operating point to obtain a plant representation suitable for robust controller synthesis. Performance objectives related to output regulation, disturbance rejection, and control effort are formulated using appropriate weighting functions. An 𝐻∞ controller is then synthesized and evaluated under parameter variations and load disturbances. The results demonstrate improved robustness and dynamic performance compared to conventional linear control approaches, confirming the suitability of 𝐻∞-based design for power electronic converters operating under uncertainty.

In order to improve the performances of air conditioning systems, it is desirable to track time-varying trajectories generated by optimization algorithms, which H∞ synthesis techniques have been proved to successfully solve. However, the control-oriented models of vapor compressor cycles used for algorithm development, even if built from first-principles, suffer from model uncertainties introduced by modeling assumptions, calibration inaccuracies, and linearization errors. The differences between the actual plant and the control-oriented model, mainly in the form of unmodeled dynamics and parameter uncertainty, undermine the stable margin as well as the performance of the closed-loop system with H∞ controllers. In order to solve the problem, the concept of the structured singular value μ is used to analyze the influences of model uncertainties on robust stability and robust performance. Based on μ analysis results, μ synthesis techniques compared to H∞ methods achieve better stability and performance margins over the same set of uncertainties. Furthermore, simulation results show that the μ controller achieves better performances of output tracking and disturbance rejection than the H∞ controller for the automotive air conditioning system studied.