Parametric models of linear multivariable systems for adaptive control

This paper presents a parametrization method for direct adaptive control of linear multivariable systems with strictly proper discrete-time or continuous-time transfer functions. The necessary a priori information is shown to be a diagonal matrix with the noninvertible zeros of the Smith form and appropriate polynomial degrees.     

Immersion and invariance adaptive control of linear multivariable systems

We show in this paper that it is possible to globally adaptively stabilize linear multivariable systems with reduced prior knowledge of the high-frequency gain. In particular, we relax the restrictive (nongeneric) symmetry condition usually required to solve this problem. Instrumental for the establishment of our result is the use of the new immersion and invariance approach to adaptive control recently proposed in the literature. The controllers obtained with this technique are not certainty equivalent—though smooth and without projections or overparameterizations—and the resulting Lyapunov functions contain cross-terms between the plant states and the parameter errors.     

Arbitrary adaptive pole placement for linear multivariable systems

This paper presents a methodology for adaptively assigning the closed-loop poles of either continuous or discrete time linear mnltivariable systems. The scheme is direct in nature in that no parametrized model of the unknown plant needs to be explicitely identified. Rather the control parameters, and an "equivalent" plant parameterization are simultaneously estimated from input-output data using linear parameter estimation procedures. Implementation of the scheme requires only knowledge of the system controllability indexes, and an upper bound on the observabilily index.     

An improved adaptive identifier for discrete multivariable linear systems

It is shown that the Kudva-Narendra method for recursive identiffication of discrete-time linear multivariable systems may be modified to allow possibly improved convergence during the initial stages, finite convergence, or the use of a priori information about the parameter estimates. The modification entails orthogonal projection of the vector of system states and inputs used for excitation of the adaptation equations and does not impair the stability of the original identifier. Examples illustrating various aspects of the modification are given.     

Parameter adaptive control of multivariable systems

Model reference adaptive controllers for multivariable plants are designed using only input and output signals rather than the complete state vector. The design is based on Liapunov's direct method, and the Meyer-Kalman-Yacubovich lemma. State variable filters are employed to avoid differentiating output signals. Augmented error signals are used in deriving stable adaptive control laws which assure that the normally used response error signals approach zero asymptotically.     

A synthesis procedure for parameter adaptive control systems

Given a plant with differential equations characterized by a parameter vector ω which is unknown and slowly varying with time and given a corresponding feedback controller with equations characterized by an adjustable parameter vector γ, a synthesis procedure is presented which leads to a closed-loop adaptive control system for adjusting γ in the face of drift variations in ω. The steps in the synthesis procedure involve 1) the structuring of the basic control system such that model matching is possible for an optimal choice in γ corresponding to every ω,gamma^{ast} = gamma^{ast}(omega), 2) the selection of a performance indexrho(gamma, gamma^{ast})which has the properties of a metric function on every adjustment interval, and 3) the derivation of a modified gradient for updating the value of γ which can be implemented on-line during the normal course of system operation. An example of a pitch-rate orientational control system is used to illustrate the synthesis procedure, and the results of a computer simulation study of the overall adaptive system are discussed which include the effects of nonlinearities, disturbance and measurement noises, as well as time variations in the unknown ω-parameters.     

Decentralized control of linear multivariable systems

This paper studies the effect of decentralized feedback on the closed-loop properties of jointly controllable, jointly observablek-channel linear systems. Channel interactions within such systems are described by means of suitably defined directed graphs. The concept of a complete system is introduced. Complete systems prove to be precisely those systems which can be made both controllable and observable through a single channel by applying nondynamic decentralized feedback to all channels. Explicit conditions are derived for determining when the closed-loop spectrum of ak-channel linear system can be freely assigned or stabilized with decentralized control.     

Adaptive dynamic surface control for linear multivariable systems

In this paper, an output-feedback adaptive control is presented for linear time-invariant multivariable plants. By using the dynamic surface control technique, it is shown that the explosion of complexity problem in multivariable backstepping design can be eliminated. The proposed scheme has the following features: (1) The L_∞ performance of the system’s tracking error can be guaranteed, (2) it has least number of updated parameters in comparison with other multivariable adaptive schemes, and (3) the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.     

Direct adaptive decoupling control for general stochastic multivariable systems

This paper presents a novel adaptive decoupling controller for general stochastic multivariable systems with arbitrary time delay structure. The decoupling controller is constructed using a diagonal dynamic precompensator to diagonalize the system interactor matrix and then combining the feedforward control strategy and the generalized minimum variance approach. It cannot only control unstable and'or non-minimum phase processes but also decouple the closed-loop systems both dynamically and in the static state. It is adaptively implemented in direct form. The global convergence properties and parameter estimate consistency for this adaptive decoupling algorithm are also discussed. It is shown that this adaptive controller not only has globally convergent properties but also generates strongly consistent parameter estimates. The results of simulations and an application are proposed to demonstrate the effectiveness of the algorithm.     

Non-linear tracking control for multivariable constrained input linear systems

This paper extends the non-linear tracking methodology of Lin et al. to high-order and multivariable linear systems. The results provide a method of synthesizing controllers which asymptotically track a constant set-point. As with the original scheme, allowances for control limits are handled directly in the design phase, and no a posteriori compensation is required. The resulting control law consists of both linear and non-linear parts; the non-linear term being added with a view to improving the response of the system, without reducing the size of its basin of attraction. The proposed technique is demonstrated on two aerospace examples which indicate promising results.     

A robust adaptive dynamic surface control for linear systems

In this article, a robust output-feedback adaptive dynamic surface control (DSC) is proposed for linear time-invariant single-input single-output plants with unmodelled dynamics and unmeasurable output disturbance. With the proposed adaptive DSC scheme, the ‘explosion of terms’ problem inherent in backstepping control is eliminated and the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. More importantly, it is proved that with an initialisation technique, the ?_∞ performance of the tracking error can be guaranteed even with unmodelled dynamics, bounded output disturbance exists and the plant high-frequency gain is unknown.     

Design of multivariable adaptive model following control systems

The results for the problems of “perfect model following” and “hyperstability of model reference adaptive systems” are integrated in order to develop a general design technique for multivariable adaptive model following control systems. Two types of adaptation are involved: adaptation of the parameters of the control loop and signal synthesis adaptation for model following control systems with a fixed structure. The design and the implementation of the adaptation mechanism based on the use of a hyperstable adaptation algorithm are discussed. The feasibility and the advantages of the procedure are illustrated by applying it to a non trivial aircraft control problem.     

An adaptive disturbance rejection control scheme for multivariable nonlinear systems

An adaptive disturbance rejection control scheme is developed for uncertain multi-input multi-output nonlinear systems in the presence of unmatched input disturbances. The nominal output rejection scheme is first developed, for which the relative degree characterisation of the control and disturbance system models from multivariable nonlinear systems is specified as a key design condition for this disturbance output rejection design. The adaptive disturbance rejection control design is then completed by deriving an error model in terms of parameter errors and tracking error, and constructing adaptive parameter-updated laws and adaptive parameter projection algorithms. All closed-loop signals are guaranteed to be bounded and the plant output tracks a given reference output asymptotically despite the uncertainties of system and disturbance parameters. The developed adaptive disturbance rejection scheme is applied to turbulence compensation for aircraft fight control. Simulation results from a benchmark aircraft model verify the desired system performance.     

A model reference adaptive control system for discrete multivariable systems with time delays

This paper presents a new method for designing a model reference adaptive control system for multivariable plants with time delays in the input and output variables. An adaptive algorithm guarantees the asymptotic stability of the error between the plant output and the reference sequence using no anticipative value of the plant output and unknown plant parameter. The validity of the theoretical result is illustrated by a numerical example.     

An adaptive control algorithm for linear systems

A modified gradient procedure is presented for adjusting parameters in a linear control system in the absence of complete knowledge of the plant dynamic characteristics. The algorithm operates to make discrete-time changes in the adjustable parameters during the normal course of system operation and incorporates the best available information on the unknown quantities. Sufficient conditions for the error corrective properties of the algorithm are derived, and the results of a simulation study are discussed.     

The feedforward control of linear multivariable time-invariant systems

Necessary and sufficient conditions are derived for a stable feedforward control system to exist for a multivariable linear time-invariant system so that: (1) any measurable disturbances occurring in the system are asymptotically rejected, and (2) the outputs of the system asymptotically become equal to preassigned functions of a given class of outputs. The result may be interpretated as being a generalization of the single-input, single-output feedforward servo problem to multivariable systems or as being a solution to the asymptotic decoupling problem. Some numerical examples varying from 2nd to 9th order are included to illustrate the result.     

Synthesis of output-feedback control laws for linear multivariable continuous-time systems

It is known (Porter and Bradshaw 1978 a) that, in the case of self-conjugate distinct eigenvalue spectra, the closed-loop eigenstructure assignable by output feedback is constrained by the requirement that the eigenvectors and reciprocal eigenvectors lie in well-defined subspaces. In this paper a technique is presented which can be used to select the eigenvectors and reciprocal eigenvectors from these subspaces in the case of appropriately augmented (Kimura 1975) controllable and observable continuous-time systems. Thin technique is ideally suited to digital-computer implementation and therefore greatly facilitates the synthesis of both static (Porter and Bradshaw 1978 a) and dynamic (Porter and Bradshaw 1978 b) output-feedback controllers.     

The systematic design of control systems for large multivariable linear time-invariant systems

A systematic design procedure for determining realistic feedforward-feedback control systems for large multivariable linear constant systems is outlined in this paper. A numerical example of a boiler system and a distillation column is included and a comparison of the simulated response of the controlled systems obtained by the proposed method is made with the corresponding conventional control systems. The new control systems obtained are relatively simple, are realistic to implement, and appear to be a significant improvement over the conventional ones.     

Chattering-free fuzzy variable structure control for multivariable nonlinear systems

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) with guaranteed stability for multivariable systems is presented. It is aimed at obtaining an improved performance of nonlinear multivariable systems. The main contribution of this work is firstly developing a generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, with a special attention to non-zero final state. Secondly, ensuring the global stability of the controlled system. The multivariable nonlinear system is represented by T-S fuzzy model. The identification of the T-S model parameters has been improved using the well known weighting parameters approach to optimize local and global approximation and modeling capability of T-S fuzzy model. The main problem encountered is that T-S identification method cannot be applied when the membership functions (MFs) are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. In order to overcome the chattering problem a switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules together with the state variables. A two-link robot system and a mixing thermal system are chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of proposed FLC-VSC method.     

A robust adaptive feedforward control in repetitive control design for linear systems

This paper proposes a new adaptive feedforward cancellation (AFC) control that achieves periodic tracking and/or periodic disturbance rejection. The new control design is a direct scheme in the sense that it adaptively updates the desired control without estimating the unknown disturbance. The proposed new control has several advantages. First, its adaptation gain can be arbitrarily chosen without upsetting the system stability if given the exact system model. Second, it can be applied to not only minimum-phase systems, but also non-minimum phase systems. Third, the new control law is independent of where the disturbance enters the system. Finally, a robustness analysis is made to show that the proposed control is robust with respect to un-modelled dynamics.