Linear Multivariable Plants Research Articles

Multivariable Binary MRAC with Guaranteed Transient Performance Using Non-homogeneous Robust Exact Differentiators

In this paper, we propose an extension of the binary model reference adaptive control (BMRAC) for uncertain multivariable linear plants with non-uniform arbitrary relative degree. The BMRAC is a robust adaptive strategy which has good transient properties and robustness of sliding mode control with the important advantage of having a continuous control signal free of chattering. The relative degree obstacle is circumvented using a multivariable version of a hybrid estimation scheme, named global robust exact differentiator (GRED). The hybrid estimator switches between robust exact differentiators (RED) based on higher-order sliding modes and lead filters in a way that the exact derivatives are globally obtained in finite time. To improve the robustness and the transient performance of the GRED, we propose a modification of the switching scheme replacing the conventional RED with a non-homogeneous one. Global exact output tracking is obtained with robustness and guaranteed transient performance without requiring stringent symmetry assumptions on the plant high-frequency-gain matrix.

A direct MRAC based multivariable multiple-model switching control scheme

In this paper a direct model reference adaptive control (MRAC) based multiple-model switching control scheme is developed for linear multivariable plants. Such a scheme is capable of ensuring desired system performance, avoiding control singularity and possible persistent control switching. A plant signal identity is used to derive a bank of parameter estimators which are initialized from different parameter subregions. A bank of adaptive controllers are constructed, whose parameters are directly updated from the estimators with globally stable adaptive laws for desired parameter adaptation without control gain matrix inversion to avoid control singularity. A control switching mechanism is designed with performance indexes formed from estimation errors which are directly used in the controller parameter update laws and are closely related to the tracking error, together with the use of a lower threshold switching parameter to ensure the eventual settle-down of the control switching. Closed-loop stability and output tracking are analyzed, and some extensions of the multiple-model design are given. Simulation results are presented to show the desired system performance, especially, improved system transient responses.

Building Temperature Control Based on Population Dynamics

Temperature control in buildings is a dynamic resource allocation problem, which can be approached using nonlinear methods based on population dynamics (i.e., replicator dynamics). A mathematical model of the proposed control technique is shown, including a stability analysis using passivity concepts for an interconnection of a linear multivariable plant driven by a nonlinear control system. In order to illustrate our control strategy, some simulations are performed, and we compare our proposed technique with other control strategies in a model with a fixed structure. Finally, experimental results are shown in order to observe the performance of some of these strategies in a multizone temperature testbed.

Multivariable adaptive dynamic surface control based on norm estimation of unknown parameter matrices

In this article, a novel output-feedback adaptive dynamic surface control scheme is proposed for linear time-invariant multivariable plants based on the norm estimation of unknown parameter matrices. Besides avoiding the explosion of complexity problem in traditional multivariable backstepping design, the proposed scheme has the following features: (1) only one parameter needs to be updated on-line regardless of the plant order and input–output dimension, (2) only the Hurwitz condition is required for the high-frequency gain matrix and (3) the ℒ∞ performance of the tracking error can be guaranteed. It is shown that all signals of the closed-loop system are semi-globally uniformly bounded. Simulation results are given to illustrate the effectiveness of the proposed scheme.

Multivariable Adaptive Backstepping Control: A Norm Estimation Approach

In this note, a novel output-feedback adaptive backstepping control is proposed for linear time-invariant multivariable plants under a mild assumption that the Hurwitz condition for high-frequency gain matrix is satisfied. By estimating the norm of those unknown parameter matrices instead of their elements, it is shown that only one parameter needs to be updated online and therefore, the computational burden can be greatly reduced compared with any current multivariable adaptive control scheme.

Control of Handling Stability in Four-Wheel Steering Vehicles Based on Individual Channel Design

This paper presents a new steering control structure for vehicles equipped with four-wheel steering system. A linear model of the lateral dynamics is used in this paper. This control structure is based on a simplified linear model of the lateral dynamics of such vehicles and aims to decouple the control of sideslip from the control of yaw rate. The control design is based on a linear multivariable plant and the front and rear steering angles, According to the Individual Channel Design paradigm. The proposed control structure has been applied to design sideslip and yaw rate controllers using a more accurate model of the lateral dynamics of four-wheel steering vehicles. Simulations are used to illustrate the performance and robustness of the designed controllers.

Decentralized Control Structure for Linear Stable and Unstable Plants based on the Output Controllability Analysis

AbstractIn this paper a new input-output pairing method for linear multivariable plants based on the output controllability analysis is presented. All control configuration selection methodologies which use the state space model of plant to pairing analysis are applicable only to stable multivariable plants. Here, by using of output controllability analysis, we introduce a new input-output pairing strategy which is applicable to all linear stable and unstable multivariable plants and considers the plant dynamical behavior in pairing analysis.

Global Exact Tracking for Uncertain Multivariable Systems by Switching Adaptation

AbstractIn this paper, we propose an output feedback sliding mode controller to solve the problem of global exact output tracking for uncertain multivariable linear plants with non-uniform arbitrary relative degree. The controller is based on a hybrid estimation scheme, which adapts the relative degree compensation through switching between a high-gain observer and a set of locally exact differentiators. As a result, uniform global exponential practical stability and exact tracking are achieved with peaking free control signal.

Building Temperature Control Based on Replicator Dynamics

Temperature control in buildings is a dynamic resource allocation problem, which can be approached using nonlinear methods based on population dynamics (i.e., replicator dynamics). A mathematical model of the proposed control technique is shown, including a stability analysis using passivity concepts for an interconnection of a linear multivariable plant driven by a nonlinear control system. In order to illustrate our control strategy, some simulations are performed, and we compare our proposed technique with another control strategy (conventional PI) in a model with a fixed structure.

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.

On Limitations to the Achievable Path Following Performance for Linear Multivariable Plants

In this paper, we consider a problem termed ldquopath followingrdquo. This differs from the common problem of reference tracking, in that here we can adjust the speed at which we traverse the reference trajectory. We are interested in ascertaining the degree to which we can track a given trajectory, and in characterizing the class of paths for which we can generate an appropriate temporal specification so that the path can be tracked arbitrarily well in an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> sense. We give various bounds on the achievable performance, as well as tight results in special cases. In addition, we give a numerical procedure based on convex optimization for computing the achievable performance. The results demonstrate that there are situations where arbitrarily good <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance may be achieved even though the origin is not in the convex hull of the positive limit set of the path to be followed.

Input–output pairing analysis for uncertain multivariable processes

Decentralized control structure is widely employed in many industrial multivariable processes. In this approach, control structure design and in particular input–output pairing is a vital stage in the design procedure. There are several powerful methods to select the appropriate input–output pair in linear multivariable plants. However, in the face of plant uncertainties, the input–output pairs can change. Input–output pairing problem, in the presence of uncertainties, and its consequences on the pairing problem have not been widely addressed. In this paper, Hankel interaction index array is used to choose the appropriate input–output pair and a new method is proposed to compute Hankel interaction index array, which reduces the computational load. Also, a theorem will be presented to show the effect of additive uncertainties on input–output pairing of the process. An upper bound on the element variations of Hankel interaction index array of the additive uncertainties in state space framework is given to show the possible change in input–output pairing. Finally, two typical processes are employed to show the main points of the proposed methodology.

A New Approach to Compute the Cross-Gramian Matrix and its Application in Input-Output Pairing of Linear Multivariable Plants

A New Approach to Compute the Cross-Gramian Matrix and its Application in Input-Output Pairing of Linear Multivariable Plants

Design of robust H ∞-controllers of multivariable systems based on the given stability degree

For the linear multivariable plants whose physical parameters are subject to deviations from the rated values, the measurable output-based controllers were designed providing the given degree of stability of the closed-loop system which defines the desired time of control. This approach relies on the "technique of opening the plant-controller system" for the investigated physical parameters and comes to a standard problem of H ?-optimization. An example was presented.

Strong stabilization with infinite multivariable gain margin through linear periodic control

The problem of the strong stabilization with infinite gain margin, with the additional requirement of a prescribed rate of convergence of the free responses, is addressed for linear time-invariant discrete-time multivariable plants in the case when unknown different scalar gains act either on the inputs or on the outputs. Necessary and sufficient conditions for the solvability of the problem by means of a stable linear periodic discrete-time output feedback dynamic controller are derived. Algorithmic procedures are given for designing the proposed periodic controllers.

A New Method for Singular Value Loop Shaping in Design of Multiple-Channel Controllers

In this note, simple symmetric interval bounds on the singular values of a matrix based on its Gershgorin disks are proposed. This allows the Gershgorin theorem to be used not only to provide information about the location of the eigenvalues of a matrix but also its singular values. This is utilized for the proposition of a new design technique for singular value loop shaping based on the diagonal dominance methodology for design of linear multivariable plants. In return, this allows multiple-channel simply structured controllers to be designed with a view to robustness and to meet constraints and specifications on the behavior of its singular values. A design example is given demonstrating the effectiveness of this approach.

Selection of variables for stabilizing control using pole vectors

For a linear multivariable plant, it is known from earlier work that the easy computable pole vectors provide useful information about in which input channel (actuator) a given mode is controllable and in which output channel (sensor) it is observable. In this note, we provide a rigorous theoretical basis for the use of pole vectors, by providing a link to previous results on performance limitations for unstable plants.

Evolutionary achievement of diagonal dominance in linear multivariable plants

Adaptive evolution strategies without crossover are used to design pre-compensators for linear multivariable plants. Such compensators are required to achieve diagonal-dominant plant transfer function matrices in order to reduce plant interactions as much as possible. The effectiveness of the evolutionary design technique is illustrated by synthesising a multivariable pre-compensator for the Rolls-Royce Spey jet engine.

Decoupling precompensation and optimal decoupling

We study decoupling control under a unity‐feedback configuration for linear multivariable plants. We parametrize the set of all admissible decoupling precompensators. With the parametrization, it is shown that decoupling controller design is equivalent to a set of SISO controller designs. The parametrization is also used to establish a necessary and sufficient condition for the existence of a stable decoupling controller. Optimal decoupling controller design is proposed and the cost of decoupling is discussed.

BLOCK DECOUPLING CONTROL OF LINEAR MULTIVARIABLE SYSTEMS

This paper gives parameterizations of block decoupling controllers and achievable block‐diagonal I/O maps for linear multivariable plants under unity‐feedback configuration. The parameterizations, based on coprime factorizations and a special generalized Bezout identity, do not require the computation of Smith McMillan forms and, thus, can be reliably computed. It is also shown that through the construction of an admissible block decoupling precompensator, block decoupling controller design reduces to a set of controller designs for the block channels which are smaller in dimension.