Linear Multivariable Plants Research Articles

Adaptive backstepping control design for linear multivariable plants

A nonlinear backstepping scheme is developed for adaptive control of linear plants with multiple inputs and multiple outputs. Solutions to plant parametrization, state observer, and adaptive control law for the multivariable backstepping design are proposed. The developed adaptive controller has the desired properties for ensuring closed-loop signal boundedness and asymptotical tracking.

H∞-Control Using Polynomial Matrices and Interval Arithmetic

A design method for H∞-compensators is presented for linear multivariable plants. The advantages of a compensator with two degrees of freedom are applied, and the intuitive method using transfer and polynomial matrices is pursued. With the introduction of an interval arithmetic, the numerical obstacles are avoided, and a numerical stable design tool is offered. The tool was then tested on a single engine VISTA F-16 supersonic test vehicle.

Controller design for partial decoupling of linear multivariable systems

In the design of feedback control systems for linear multivariable plants, insisting on the elimination of coupling in closed-loop is often achieved at the expense of an increase in the multiplicity of infinite and non-minimum phase zeros beyond those of the plant plant. This behaviour is known as the ‘cost of decoupling’ since these additional zeros are manifested in the time domain by increased rise times and undershoots in step responses. Using partially decoupling controllers, however, it is always possible to obtain closed-loop systems with precisely the same number of infinite and non-minimum phase zeros as the plant, albeit at the expense of a restricted form of transient coupling. This paper uses a generalization of the interactor matrix to generate a class of partially decoupling controllers for square, stable plants in which diagonal decoupling arises as a special case, thereby permitting the designer to trade off speed of response versus the severity of transient interaction.

Controller Reduction with Consideration of Closed-Loop Performance and Stability.

In this paper we consider controller reduction preserving both performance and stability of the closed-loop system. First, a quadratic cost is introduced which represents the performance of the closed-loop system formed by a linear multivariable plant and high-dimensional dynamic controller. Then the controller reduction problem is formulated as the problem of finding a fixed low-dimensional dynamic controller preserving stability and value of the quadratic cost. Secondly, by using the Lyapunov equation, the problem is converted into the convex optimization problem with constraint described by a linear matrix inequality (LMI), and the sufficient condition for the existence of such an optimal reduced controller is shown. Finally, an example illustrates the methodology.

Generalized characterization of tracking systems and linear multivariable plants

In order to design tracking systems incorporating linear multivariable plants with more controlled outputs than manipulated inputs, it is shown that a more'general tracking concept than set-point tracking is necessary. The inclusion of inequalities in tracking conditions facilitates the characterization of tracking systems and linear multivariable plants. It is shown that the possibility of undertracking (i.e. tracking with non-negative errors) is characterized by the separation theorem of convex analysis, that linear multivariable plants can be classified into Class I and Class II plants based upon their steady-state transfer-function matrices, and that, in the case of Class I plants, undertracking is possible for any set-point commands. Furthermore, the necessary and/or sufficient conditions for Class I plants are given. Finally, it is shown that, in the case of Class 1 plants, undertracking is also possible for any set-point commands and any constant disturbances.

Synthesis of limit-tracking systems incorporating linear multivariable plants

The steady states of tracking systems incorporating self-selecting controllers and linear multivariable plants exhibit limit tracking when none of the plant outputs exceeds its corresponding set point (i.e. its limit value) and the number of pairs of equal plant outputs and set points is not less than the rank of the plant steady-state transfer-function matrix. The condition for the feasibility of limit tracking is given. An approach to the synthesis of limit-tracking systems is proposed that utilizes an order-reduction technique to reduce the number of separate set-point tracking controllers from pCm to p − m + 1 in the case of m-input/p-output plants while guaranteeing the existence of the steady states of such tracking systems.

H(infinity) robust control design for linear feedback systems

This paper deals with the problem of designing, for a linear time-invariant multivariable plant, a feedback controller that minimizes the H°° norm of a quadratic combination of the sensitivity and complementary sensitivity functions. With the parameterization of the controller and quadratic cost, a design procedure based on a gain equalization test for computing the optimal controller is described in detail. A design algorithm, which is implementable in computers, is presented. The pitch-axis controller design for a digitized version of the Grumman F-14 aircraft is given. The performance robustness under the external disturbances and large aircraft parameter variations are shown to demonstrate the effectiveness of this approach.

Digital iterative learning control of compensated linear multivariable plants

It is shown that digital iterative learning controllers can be designed for irregular linear multivariable plants by introducing appropriate digital compensators. This demonstration is effected by proving a fundamental theorem which establishes precise sufficient conditions under which iterative learning control is achieved by such digital controllers and compensators in the case of first-order irregular plants. These general results are illustrated by the presentation of numerical results for the digital iterative learning control of a third-order partially irregular plant with two inputs and two outputs. The extension of the results to higher-order irregular plants is discussed.

Learning rates in the digital iterative learning control of linear multivariable plants

Abstract The learning rates achievable in the digital iterative learning control of linear multi-variable plants are investigated. It is shown that the irregularity and stability characteristics of the plants under control impose severe constraints on the achievable learning rates. These results are not only significant in their own right but also strongly motivate the introduction of compensators to increase the learning rates achievable in irregular plants. These general results are illustrated by the presentation of numerical results for the iterative learning digital control of an uncompensated fourth-order completely irregular plant with two inputs and two outputs

Digital iterative learning control of linear multivariable plants

Abstract It is shown that digital iterative learning controllers can be designed for linear multivariable plants using only the step-response matrices of such plants. This demonstration is effected by proving a fundamental theorem which establishes precise sufficient conditions under which iterative learning control is achieved by such digital controllers. These general results are illustrated by the presentation of numerical results for the digital iterative learning control of a third-order linear multivariable plant with two inputs and two outputs.

On mimo optimal preview tracking control for known trajectory models

AbstractA class of discrete time feedforward tracking controllers is presented for linear multivariable plants subjected to time‐varying exogenous inputs with known models. The controller design is based on linear quadratic optimization techniques and the augmented system approach. The optimal controllers use state feedback for regulation purposes. For the tracking objective the future set‐points along the reference trajectory vector are used. Necessary and sufficient conditions for the existence of an optimal feedforward solution are presented in terms of the relationships between the eigenvalues of the closed‐loop system and those of the trajectory models. For illustration a numerical example is included which is based on a dual‐stage positioning carriage modelled as a linear multivariable plant.

Iterative learning control of partially irregular multivariable plants with initial impulsive action

Iterative learning controllers with initial impulsive action are characterized for /th-order partially irregular linear time-invariant multivariable plants, i.e. plants with rank-defective first, second, …, /lth Markov parameters but full-rank (l + 1)th Markov parameters (l=1.2.3, …) These general results ate illustrated by the presentation of results for the Iterative learning of a typical first-order partially irregular liner multivariable plant

Iterative learning control of partially irregular multivariable plants with initial impulsive action

Iterative learning controllers with initial impulsive action are characterized for /th-order partially irregular linear time-invariant multivariable plants, i.e. plants with rank-defective first, second, …, /lth Markov parameters but full-rank (l + 1)th Markov parameters (l=1.2.3, …) These general results ate illustrated by the presentation of results for the Iterative learning of a typical first-order partially irregular liner multivariable plant

Design of tunable digital set-point tracking controllers for linear multivariable type-one plants

Since many industrial processes are essentially linear multivariable type-one plants (i.e. linear multivariable plants with unbounded step-response matrices but with bounded impulse-response matrices), the methodologies of Porter and Jones (1986) for linear multivariable type-zero plants are extended to embrace such linear multivariable type-one plants. It is shown that the proportional and derivative controller matrices in the resulting PD controllers can be directly determined from open-loop impulse-response tests performed on linear multivariable type-one plants. The disturbance-rejection properties of these controllers are fully developed by modifying the digital PD controller by the inclusion of an outer PID loop. The robustness propertcs of these PD-PID controllers are assessed by characterizing, in terms of the steady-state impulse-response matrices of nominal and actual plants, the admissible plant perturbations that can be tolerated. The effectiveness of this design methodology is illustrated by ...

Robustness properties of tunable digital set-point tracking PID controllers for linear multivariable plants

Abstract The robustness properties of tunable digital set-point tracking PID controllers are assessed. This assessment is effected by characterizing, in terms of the steady-state transfer function matrices of nominal and actual plants, the admissible plant perturbations that can be tolerated by such tunable digital PID controllers. The resulting robustness theorem is illustrated by designing an autopilot for a missile in the form of a tunable digital set-point tracking PID controller.

Robustness properties of tunable digital set-point tracking PID controllers for linear multivariable plants

Robustness properties of tunable digital set-point tracking PID controllers for linear multivariable plants

Two stable MRAC algorithms for linear discrete-time multivariable plants

Two stable MRAC algorithms for unknown linear discrete-time multivariable plants are presented, under the assumption that the state information is available. Proofs of stability are given and some simulations are carried out to show the applicability of the proposed algorithm.

Design of Set-point Tracking Systems Incorporating Fast-sampling Error-actuated Digital Controllers for Linear Multivariable Plants Using Step-response Matrices

Abstract Singular perturbation methods are used to exhibit the asymptotic structure of the transfer function matrices of discrete-time set-point tracking systems incorporating regular linear multivariable plants (ie, plants with full-rank first Markov parameters) which are amenable to fast-sampling error-actuated digital control but for which mathematical models are unavailable for design purposes. These general results are illustrated by designing a fast-sampling error-actuated digital process controller for a chemical reactor, using only the open-loop step-response matrix of the plant. It is indicated that similar general results are also available for discrete-time set-point tracking systems incorporating irregular linear multivariable plants (ie, plants with rank-defective first Markov parameters).

On-line frequency-and time-domain identification of a linear multivariable system

Abstract A method for the on-line identification of a linear multivariable plant subject to both deterministic and stochastic disturbances is proposed. The identification scheme rests on the use of a sum of sinusoids of distinct frequencies as probing-signal inputs and on the employment of linear time-varying filters to filter the plant inputs and the plant outputs. The time-varying filters are essentially banks of narrow-band filters tuned to the probing-signal frequencies. The filtered plant inputs and the filtered plant outputs yield an estimate of the plant transfer function matrix at the probing-signal frequencies. The filtered data are further processed using a recursive least-squares algorithm and a time-domain model estimate is obtained in terms of the coefficients of the difference equation relating each input-output pair. The identification algorithm is decoupled in the sense that the estimate of the transfer function or difference equation between the ith input and jth output is unaffected by other inputs or outputs. Simulation results on the performance of the time-varying filter and the identification scheme are given.

Time-domain identification of transmission zero locations of linear multivariable plants

In the case of asymptotically stable multivariable plants, the location in the complex plane of the transmission zeros is identified on the basis of the initial and ultimate time-domain behavior of the step-response matrix.