Multivariable Model Reference Adaptive Control System Research Articles

Combustion Control of Diesel Engine using Feedback Error Learning with Kernel Online Learning Approach

This paper shows how to design Multivariable Model Reference Adaptive Control System (MRACS) for “Tokyo University discrete-time engine model” proposed by Yasuda et al (2014). This controller configuration has the structure of “Feedback error learning (FEL)” and adaptive law is based on kernel method. Simulation results indicate that “kernelized” adaptive controllers can improve the tracking performance, the speed of convergence and the robustness to disturbances.

Modeling and Model Reference Adaptive Control of Aircraft with Asymmetric Damage

This paper addresses some fundamental issues in adaptive control of aircraft with struc- tural damage. It presents a thorough study of linearized aircraft models with damage to obtain new details of system descriptions, such as coupling and partial derivatives of lateral and longitudinal dynamics. A detailed study of system invariance under damage conditions is performed for generic aircraft models to obtain key system characterizations for model reference adaptive control (MRAC), such as infinite zero structure and signs of high frequency gain matrices. A comprehensive study of multivariable MRAC systems in the presence of damage is performed to obtain critical design specifications for adaptive flight control, such as system and controller parametrizations and adaptive parameter up- date laws. Both analytical and simulation results are given to illustrate the design and performance of adaptive control systems for aircraft flight control. Adaptive control of aircraft in the presence of damage has been an important topic in the research of flight control design for aircraft safety. Damage can cause uncertain parametric and structural variations, which requires new aircraft modeling and control approaches. In Reference (1), a study of aircraft dynamics with damage is presented, and a neural network based adaptive control algorithm is introduced for control of aircraft in the presence of structure uncertainties. In (2), equations of motion are introduced in detail for aircraft with asymmetric mass loss. In (3), we introduced a nonlinear aircraft model with partial wing damage, and illustrated linearization of such a model. In (4), real time identification of a damaged aircraft model is studied. A two-step identification process is introduced, which consists of an aircraft state estimation phase and an aerodynamic model identification step. With such a two-step process, the nonlinear part of the model identification is isolated in the first phase, and the aerodynamic parameter identification procedure is simplified to a linear one. A hybrid adaptive control method is proposed in (5) for control of aircraft with damage. The control design is based on a neural network parameter estimation blended with a direct adaptive law. A stability and convergence analysis is presented for this adaptive control methodology. For accommodating unknown changes in the structure and parameters, multivariable MRAC designs offer many advantages. In (6), we introduced an MRAC design based on the LDS decomposition of the high frequency gain matrix for the control of aircraft with multiple wing damage. The key design conditions are that, both the nominal and post-damage systems should have a uniform known modified interactor matrix, and the leading principal minors of their high frequency gain matrices should be nonzero with their signs unchanged. In (7), we studied linearization of nonlinear aircraft models under damage conditions and designed a multivariable MRAC scheme which does not require the knowledge of the signs of the high frequency gain matrix. Potential extension to aircraft flight control systems with changing signs of the high frequency gain matrix remains a topic of future research.

Gain Margins of Adaptive Control Systems

This paper presents a systematic study of the gain margins (GM) of adaptive control systems: the specification of the parameter range of a control gain matrix in a designed adaptive control system for maintaining the desired closed-loop signal boundedness and asymptotic tracking performance. It is proved that the GM is infinity for continuous-time direct model reference adaptive control (MRAC) schemes applied to multi-input, multi-output (MIMO) linear time-invariant (LTI) systems, while it is finite with an upper bound for the discrete-time case. The derived GM results are applicable to systems with adaptive nonlinear or pole placement control designs. Analytical GM result is also obtained for some indirect multivariable MRAC systems; in particular, the GM is infinity but with a lower bound for such systems. Methods for enlarging the GM by proper choices of design parameters are presented. Moreover, the effect of sample time on the GM of sampled-data adaptive control systems is studied, which establishes the relationship between the continuous-time and discrete-time GM results. A simulation example is provided to illustrate some of the theoretical results.

A Construction of Multivariate MRACS with Unknown Interactor Matrix Based on Coprime Factorization Approach

In this paper, a design method of multivariable MRACS (Model Reference Adaptive Control System) with unknown interactor matrix based on coprimc factorization approach over proper stable rational functions is proposed. The interactor matrix is a priori information in the standard multivariable MRACS problem. But since the interactor matrix is difficult to obtain in advance it is strongly required to construct multivariable MRACS with unknown interactor matrix. In this paper, it is shown that the problem can be solved by including fixed compensator, and designing it properly. The proposed system is considered to be the multivariable MRAPP(Modrl Reference Pole Placement), but the extension to the multivariable case can be achieved by using fixed compensator.

A Design Method for Multivariable Model Reference Adaptive Control Systems Including Fixed Compensator with Two-Degree-of-Freedom Structure

A multivariable model reference adaptive control system (MRACS) including a fixed compensator is proposed. First, an exact model matching (EMM) system with two-degree-of-freedom structure is derived. Using this structure, a multivariable MRACS including fixed compensator is constructed. Since the proposed method is based on the EMM system with two-degree-of-freedom structure, the fixed compensator is chosen independently of specifications for responses to reference commands. The boundedness of all signals in the closed-loop system and the convergence of the output error are proved. A design method of the fixed compensator for MRACS with low sensitivity is also given. Finally, numerical examples are illustrated in order to show the effectiveness of the proposed method.

On the design of multivariable model-reference adaptive control systems

Abstract An algorithm previously suggested for the design of multivariable model-reference adaptive control systems based on the Liapunov synthesis technique is reviewed. It is found to be a very attractive method both from a stability and performance viewpoint. However, it is only applicable to the class of systems in which the controllable elements of the plant and control matrices can be adjusted individually. In this paper a general design algorithm is derived which avoids the above restriction and hence caters for a wider class of systems. Simulation studies of an example are presented to illustrate the applicability and performance of such a design.

MODEL REFERENCE ADAPTIVE CONTROL BASED ON LIAPUNOV'S DIRECT METHOD Part I: Theory and Control System Design†

Abstract The Liapunov design approach for model reference adaptive control (MRAC) is extended to include adaptive integral and setpoint control modes. The feasibility of the Liapunov approach is illustrated by designing a multi-variable MRAC system based on a fifth-order state space model of a pilot scale, double-effect evaporator. Simulation results are presented to demonstrate that the MRAC approach gives satisfactory control for a wide range of adaptive loop gains and despite very poor initial control policies.