Frequency domain design conditions for robust direct model reference adaptive controllers

This paper presents the design of a robust direct model reference adaptive control (DMRAC) algorithm with focus on the satisfaction of an almost strictly positive real (ASPR) condition in the presence of plant uncertainty represented as either variations in plant parameters or unmodelled dynamics in the form of additive or multiplicative norm bounded perturbations in the transfer function. Both the time and frequency domain design conditions for a feedforward compensator have been developed utilizing the robust stability analysis and optimization methods. Illustrative examples are presented to validate the algorithm's use and applicability to control systems with parametric uncertainty or unmodelled dynamics.

The control of hemodynamic variables, particularly mean arterial pressure (MAP) and cardiac output (CO), is a challenging problem. A good controller is difficult to design, due to the complex, nonlinear behavior of the system. Adding to this are the significant changes in dynamics from one patient to another, and even variations in the patients response to the drugs as his condition evolves. A robust direct model reference adaptive controller (DMRAC), modified to handle infusion constraints (saturation and rate limiting) is validated with dog experiments.

As control systems become integrated with structures in such applications as vibration suppression and structural shape modification, a damage tolerance/mitigation concern must be addressed. The fundamental issue of this concern is whether the controller is robust enough to remain stable after a step change in the structural parameters as a result of impact damage. A secondary issue is whether the controller can continue to perform its intended function (even if at some reduced level of effectiveness) following impact damage. Due to the complexity of the structural system such a controller must be lower-order than the structure that is controlled. This paper builds on previous research by Waters and Balas to demonstrate the effectiveness and limitations of a reduced- order direct model reference adaptive control (DMRAC) algorithm for damage mitigation. The reduced-order model matching conditions for implementing this algorithm and the theoretical stability results are presented. Also presented are simulation results demonstrating the effectiveness of the DMRAC algorithm in forcing a higher-order damaged plant to track a lower-ordered reference model. These simulation results look at matching a second-order plant to a first-order reference model, and a fourth-order plant to both a first- and second-order reference model. The results of these simulations indicate that a reduced-order DMRAC algorithm can, in some cases, effectively stabilize the system following severe damage to the structure, even if the system become inherently unstable. Additionally, the reduced-order DMRAC algorithm still allows for steady state tracking by the damaged smart structure of a reference input.

Comments on a robust model reference adaptive control for non-minimum phase systems with unknown or time-varying delay

For a class of discrete-time systems with unmodeled dynamics and bounded disturbance, the design and analysis of robust indirect model reference adaptive control (MRAC) with normalized adaptive law are investigated. The main work includes three parts. Firstly, it is shown that the constructed parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms, but also avoids the possibility of division by zero. Secondly, by establishing a relationship between the plant parameter estimate and the controller parameter estimate, some similar properties of the latter are also established. Thirdly, by using the relationship between the normalizing signal and all the signals of the closed-loop system, and some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and robustness analysis approach to the discrete indirect robust MRAC scheme is developed rigorously.

Model reference adaptive controllers with improved performance for applications in LCL-filtered grid-connected converters

This paper presents a direct model reference adaptive controller for multi-input multi-output linear systems with known nonminimum-phase zeros. This controller uses a surrogate tracking error, which approximates the true tracking error. The recursive-least-squares-based adaptive law is developed by minimizing an integral quadratic cost of the surrogate tracking error.

A Design of Decentralized Robust Model Reference Adaptive Control System

This paper presents the development of an equilibrated three-phase power source, which is able to generate sinusoidal waveforms with adjustable amplitudes and frequencies, as well as several arbitrary waveforms. The setup is based on a computer-controlled three-phase PWM inverter system, whose model is rewritten using /spl alpha//spl beta/0 transformation. A robust model reference adaptive controller (RMRAC) is used to assure system robustness and performance. Simulation and experimental results are used to show the closed-loop system performance, when different waveforms are generated under several operation conditions.

A recently introduced class of the well-posed error systems and the corresponding robust model reference adaptive control (MRAC) laws for systems represented by parabolic or hyperbolic partial differential equations (PDEs) with spatially varying parameters is extended to encompass the disturbance rejection capability. The disturbance is modeled as a space-time-varying signal generated by a parabolic PDE with known parameters or as a spatially-varying time-invariant signal.

In this paper, a robust model reference adaptive controller is presented for robots based on neural network parametrization. The controller is based on applying direct adaptive techniques to a basic fixed controller for better control performance, while a sliding mode control is introduced to guarantee robust closed-loop stability. It is shown that if bounded basis function networks are used for the parallel NN, uniformly stable adaptation is assured and asymptotic tracking of the reference signal is achieved.

ABSTRACTIn this paper, we address the robust control design problem for nonlinear dynamical systems tracking unreliable reference signals. Specifically, we present robust model reference adaptive control laws that guarantee uniform ultimate boundedness of the trajectory tracking error for nonlinear plants that are affected by matched, unmatched, and parametric uncertainties, and are subject to constraints on the state space and the measured output. These control laws guarantee satisfactory results even in case the reference trajectory or the reference output signal do not verify the given constraints and hence, may draw the plant's trajectory or measured output outside their constraint sets. A numerical example involving the attitude control of a spacecraft illustrates the feasibility of the theoretical results presented.

This paper proposes the application of a combined adaptive controller for the current control loop of a Shunt Active Power Filter (Shunt APF). The proposed approach uses a Variable Structure Controller (VS) together with a Robust Model Reference Adaptive Controller (RMRAC), leading to a VS-RMRAC algorithm. The control law u = ¿ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> ¿ is comprised by two set of parameters. One set is related with the RMRAC while the other part is related with the VS controller. The VS parameters are used to improve the transient response, and its effect increases when the estimation error increases. The VS-RMRAC is experimentally tested and compared with a Dead Beat current controller in a three-phase four-wire Shunt APF.

DIRECT MODEL REFERENCE ADAPTIVE CONTROL AND SATURATION CONSTRAINTS

SUMMARY We study the convergence properties of a direct model reference adaptive control system by applying techniques from numerical analysis. In particular, a first-order discrete system coupled to a minimal control synthesis algorithm discretized by the one-step one-stage zero-order-hold sampling is studied. This results in a strongly non-linear dynamic system owing to the adaptive mechanism where stability at steady state, i.e. at the operating point, equates to successful control. This paper focuses on the convergence analysis of the overall dynamical system for understanding accuracy, stability and performance at steadystate. The local stability of the steady state solution is considered by linearizing the system in the neighbourhood of an operating point when the input is a step function. This analysis allows us to specify two gain space domains which define the region of local stability. Moreover, both the accuracy and the frequency-domain analyses give insight into the range of adaptive control weightings that results in optimal performance of the minimal control synthesis algorithm and also highlights a possible approach to a priori selection of the time step and adaptive weighting values. The effectiveness of the proposed analysis is further demonstrated by simulations and experiments on a first-order plant. Copyright # 2006 John Wiley & Sons, Ltd.