Enhancing optimal controllers via techniques from robust and adaptive control

Optimal control strategies for both non-linear and linear plants and indices are notoriously sensitive to modelling errors and external noise disturbances. In this paper a general framework to enhance robustness of an optimal control law is presented, with emphasis on the non-linear case. The framework allows a blending of off-line non-linear optimal control, on-line linear robust feedback control for regulation about the optimal trajectory and on-line adaptive techniques to enhance performance/robustness. The adaptive-Q techniques are those developed in previous work based on the Youla-Kucera parametrization for the class of all stabilizing two-degree-of-freedom controllers. Some general fundamental stability properties are developed which are new, at least for the non-linear plant and linear robust controller case. Also, performance enhancement results in the presence of unmodelled linear dynamics based on an averaging analysis are reviewed. A convergence analysis based on averaging theory appears possible in principle for any specific non-linear system but is beyond the scope of the present paper. Certain model reference adaptive control algorithms come out as special cases. A non-linear optimal control problem is studied to illustrate the efficacy of the techniques, and the possibility of further performance enhancement based on functional learning is noted.     

Application of robust and adaptive pole placement

The previous investigation showed the usefulness of a two-degree-of-freedom configuration. Such a controller can also be designed using pole placement. An adaptive controller based on this concept is developed and applied to the problem with good results. Particular features, such as selection of model structure, design parameters and excitation, are also discussed.     

Example applications of the linear adaptive design technique

Adaptive controllers can be designed by a variety of different methodologies that have been developed over the past 35 years. However, all these methodologies have one thing in common; they lead to adaptive controllers that are intriniscatly non-linear in structure. Recently a new, unorthodox approach to the adaptive control problem has been developed. This new methodology leads to a new class of adaptive controllers that, in many cases, are entirely linear and have all-constant parameters (constant gains). In the present paper this new approach to adaptive control is used to design‘linear adaptive controllers’for two example applications, and the closed-loop adaptive performance obtained in each case is illustrated by digital simulation tests. These results demonstrate that the new linear adaptive controllers are able to produce a surprisingly high-degree of adaptation over significant ranges of plant parameter variations and disturbances.     

Transient bounds of dynamic certainty equivalent adaptive controllers

In this paper we show that the transient bounds of Morse's dynamic certainty equivalent adaptive controller established previously by us can be considerably strengthened. Specifically, we derive a computable bound on the ??_∞-norm of the tracking error which, in contrast with the local bound obtained previously by us, holds for all system initial conditions. Also, we add an ‘adaptation gain’ in the high-order estimator to prove that, by increasing this gain, the ??_∞-norm of the tracking error can be made arbitrarily small without increasing its ??_∞ norm. This is an improvement over the results obtained with backstepping designs, where these performance measures must be traded off in the selection of the adaptation speed.     

Experimental adaptive controllers for a class of electrohydraulic servosystems

This paper investigates experimentally the application of a class of adaptive control algorithms to hydraulic servosystems. These algorithms combine parameter identification algorithms and conventional discrete-time control design methods to continually update the coefficients of the control algorithm. Several versions of this approach were applied to the control of long-stroke pistons and rotary vane actuators. Experimental results demonstrate that this class of adaptive controllers work well in the presence of non-linearities such as Coulombic friction, servovalve saturation, flow non-linearities, and plant and significant initial parameter uncertainties.     

Robust pole placement indirect adaptive control

The problem of designing a robustly stable pole placement indirect adaptive controller in the presence of output disturbances and unmodelled dynamics is addressed. The key features of such a design are the following. (1) The unknown parameters are estimated by a normalized least-squares algorithm with a dead zone to provide the stability robustness with respect to bounded disturbances and ‘small’ unmodelled dynamics. (2) The estimated model controllability is ensured by modifying the control law over a finite time. The modification involved consists of adding an internal impulse excitation and ‘freezing’ the controller parameters.     

Example applications of an integrated indirect adaptive design technique

This paper illustrates an integrated indirect adaptive design technique using a case study example. Key features of this approach are the separate optimization of procedures for parameter estimation and control law synthesis as well as a mechanism for integrating robust and adaptive control design.     

Optimal tuning of linear controllers for power electronics/power systems applications

This paper presents a new method for tuning various linear controllers such as Proportional-Integral (PI), Proportional-Integral-Derivative (PID) and Proportional-Resonant (PR) structures which are frequently used in power electronics and power system applications. The linear controllers maintain a general structure defined by the Internal Model Principle (IMP) of control theory. The proposed method in this paper is twofold. The first perspective uses the well-known concept of the Linear Quadratic Regulator (LQR) to address the problem as a regulation problem. The Q matrix of the LQR design is then finely adjusted in order to assure the desired transient response for the system. The second perspective redefines the LQR in order to add capability to address the optimal tracking problem and is then generalized to systems with more than two states. These methods are then applied to two specific examples, one in an uninterruptible power supply (UPS) inverter system and the other one in a distributed generation (DG) system. In these examples, the tuning of PR and PI controllers is studied in great detail. These proposed design methods provide an easy and algorithmic procedure without jeopardizing stability or robustness. These tuning methods can also be utilized for linear state-space realization of any power converters. Both examples are supported via simulation and the results, which confirm analytical derivations, are presented and discussed.     

A showcase of adaptive controller designs

The adaptive control literature contains hundreds of technical papers on many different approaches to the subject. However, engineers who are not specialists in adaptive theory often have difficulty selecting which approach to use in any given problem. This series of papers addresses this situation by defining a set of standard problems which are then solved by several distinct approaches to adaptive control. This introductory paper defines the problems and guidelines which have been used in this process.     

A new approach to adaptive robust control

A new approach is given for the design of adaptive robust control in the frequency domain. Starting with an initial model of a stable plant and a robust stabilizing controller, the new (windsurfer) approach allows the bandwidth of the closed-loop system to be increased progressively through an iterative control-relevant system identification and control design procedure. The method deals with both undermodelling and measurement noise issues. Encouraging results are obtained in the simulations that illustrate the new idea.     

An advanced showcase of adaptive controller designs

The adaptive control literature contains numerous theories for deriving adaptive controllers. However, practising engineers who are not specialists in adaptive theory often have difficulty selecting which approach to use in a given application. The papers in this special issue address this situation by defining a set of standard problems which are then solved by several distinct adaptive control approaches. This introductory paper provides the motivation for the issue (why it is important, who is the target audience, what is the goal of the process), defines the standard problems to be considered and explains the rationale for their formulation, and describes the guidelines which were established for the participants. In addition, this paper defines the ‘ideal’ closed-loop responses for each standard problem, from which the results of the subsequent papers can be judged.     

Adaptive performance enhancement by iterative identification and control design

In this paper we combine adaptation and robust control by an iterative scheme of system identification and control design. A nominal model is identified for robust control design and the controller is applied to the plant to gather new data for an update of the nominal model. Our objective is to improve the plant performance with every iteration right from the start. We tackle this problem with frequency domain identification and a control design method that optimizes robustness against coprime factor perturbations. Our approach is illustrated by simulated and practical examples.     

Simple adaptive control of uncertain systems

This paper considers adaptive control of various systems with unknown time-varying or non-linear dynamics in an attempt to show that practical adaptive control can be simple and robust. The simplified adaptive control methodology used is based on the observation that most real-world systems, even non-stationary or non-linear, can be stabilized by simple controller configurations. More complex controllers may be needed only in order to improve the performance of the control systems. In the adaptive scheme, the stabilizability properties of the plants are used only to satisfy the necessary conditions that guarantee robustness of simple adaptive controllers. The desired performance is then imposed upon the plant by these adaptive controllers, which force the plant to follow the input-output behaviour of low-order reference models. Examples from the recent literature of control with uncertainty are used to illustrate the power of these adaptive techniques.     

Adaptive lqg controller with loop transfer recovery

In this paper we propose for scalar plants an adaptive LQG controller with adaptive input sensitivity function/loop transfer recovery of an associated adaptive LQ design. The sensitivity recovery can be viewed as a frequency-shaped loop recovery where the weights involve a sensitivity function. The adaptive loop/sensitivity recovery is achieved by feeding back the estimation residuals to the control through a stable bounded input, bounded output (BIBO) adaptive filter Q_k. For simplicity we consider fixed but uncertain plants in the model set and identification schemes where there are consistent parameter estimates. For non-minimum phase plants an asymptotic partial recovery is achieved via a recursive least squares update of the BIBO filter Q_k. The degree of recovery can be prescribed a priori between zero and the maximum possible. For the case of minimum phase plant estimates, full loop recovery may be achieved asymptotically by prescribing a maximum degree of recovery. The motivation for proposing the new adaptive control algorithm is to enhance robustness of adaptive LQG designs, taking advantage of the robustness enhancement properties of sensitivity/loop recovery for off-line designs. The robustness properties of the new algorithm are demonstrated by simulation results.     

Example applications of the partial state model reference adaptive design technique

This paper presents an implementation methodology for adaptive control schemes. The latter have been developed bearing in mind the available theoretical results as well as the practical requirements. This leads to an adaptive control software package which can run on several digital computers, including the IBM-PC and compatibles. Simulation results involving two adaptive control benchmarks are presented.     

Optimization of stochastic terminal control systems adapting to changes in disturbance characteristics

The optimization problem of adaptive stochastic terminal control systems accommodating to changing disturbance characteristics is considered. It is assumed that a plant with randomly changing or fixed structure is operated under non-Gaussian disturbances described by non-linear models. Direct information about random structural changes of the disturbance model is absent. For systems with various types of structural changes the optimal adaptive terminal control laws are obtained in analytical form. Filtering-prediction-recognition algorithms are designed for realization of these control laws. It is found that the synthesized regulators provide a disturbance accommodation control strategy with adaptation to structural changes of the disturbance model. A principal difference from traditional control laws is illustrated by simulation studies.     

Power quality enhancement in islanded microgrids via closed-loop adaptive virtual impedance control

The high proportion of nonlinear and unbalanced loads results in power quality issues in islanded microgrids. This paper presents a novel control strategy for harmonic and unbalanced power allocation among distributed generators (DGs) in microgrids. Different from the existing sharing strategies that allocate the harmonic and unbalanced power according to the rated capacities of DGs, the proposed control strategy intends to shape the lowest output impedances of DGs to optimize the power quality of the microgrid. To achieve this goal, the feasible range of virtual impedance is analyzed in detail by eigenvalue analysis, and the findings suggest a simultaneous adjustment of real and imaginary parts of virtual impedance. Because virtual impedance is an open-loop control that imposes DG to the risk of overload, a new closed-loop structure is designed that uses residual capacity and absorbed power as feedback. Accordingly, virtual impedance can be safely adjusted in the feasible range until the power limit is reached. In addition, a fuzzy integral controller is adopted to improve the dynamics and convergence of the power distribution, and its performance is found to be superior to linear integral controllers. Finally, simulations and control hardware-in-the-loop experiments are conducted to verify the effectiveness and usefulness of the proposed control strategy.     

Further evaluation of partial,state model reference adaptive design

This paper is a follow up to Reference 1. It presents further evaluation of the partial state model reference adaptive control approach proposed in Reference 2. This evaluation involves suitable benchmark examples that have been proposed in Reference 3 to illustrate the essence of today's adaptive control design techniques. Particular emphasis is put on the ability of the considered adaptive controller to accommodate state disturbances, sensor noise and unmodelled dynamics.     

Applications of the passive systems approach to the stability analysis of adaptive controllers for robot manipulators

Utilizing the fact that a manipulator composed of rigid links is a passive system, an approach based on the properties of interconnected passive systems is proposed for the analysis and synthesis of fixed and adaptive controllers for robot manipulators. This approach clarifies the rationale behind the various fixed and adaptive control laws synthesized using Lyapunov functions and provides new adaptation algorithms.