Models For Multivariable Systems Research Articles

Dynamic Modeling and Control of Dual Wheeled Mobile Robots Compliantly Coupled to a Common Payload

Lagrange formalism is applied to derive a dynamic model, and design a nonlinear controller for two nonholonomic, differentially steered, wheeled mobile robots compliantly linked to a common payload. The resulting multivariable system model is of a large order and can be block decoupled by selective state feedback into five independent subsystems, two of which effectively represent the deviation dynamics of the individual robots from a prescribed path; two others represent their forward motion dynamics; while the fifth describes the payload dynamics. Controllers for each of the robot subsystems, including self-tuning adaptive controllers for the nonlinear deviation dynamics subsystems, are designed by the pole-placement technique. System performance is then evaluated via simulation for the case where each robot is undergoing curvilinear motion.

Identification of a multivariable interval dynamic model from measurements in the frequency domain

Frequently, manufacturing processes cannot be accurately described using a model with fixed parameters. Interval models for which the parameters are within certain intervals may be more effective in describing such processes. In this paper, an algorithm is proposed to identify interval models of multivariable systems from measurements in the frequency domain. The intervals are minimized with membership constraints. The numerical aspects for implementing the proposed algorithm are also addressed. Simulation examples are given to show the effectiveness of the proposed algorithm.

MULTIVARIABLE CONSTRAINED ADAPTIVE GPC: THEORY AND EXPERIMENTAL EVALUATION

This paper deals with on-line identification and constrained long-range predictive control of multivariable systems. It extends a recently proposed augmented upper diagonal factorization identification (AUDI) algorithm to identify input-output models of multivariable systems with distinct time delays. The multi-input, multi-output (MIMO AUDI) algorithm can simultaneously identify the process model order and process parameters. The MIMO AUDI algorithm is implemented by decomposing a MIMO system into as many multi-input, single-output (MISO) subsystems as the number of outputs and then identifying each MISO subsystem separately. The performance of the new MIMO AUDI algorithm is demonstrated by application to input-output data from a real process. The extension of this algorithm by incorporating a variable forgetting factor with a lower bound in its value is implemented on real plant data to demonstrate 'alertness' of the estimator. This paper evaluates the performance of the MIMO adaptive generalized predictive control algorithm with and without constraints by experimental application on a computer-interfaced, pilot-scale process. The MIMO adaptive GPC is shown to have good regulatory plus servo-tracking properties.

A 4SID-Based Change-Detection Algorithm

Recently, subspace based methods for state-space system identification (4SID) have attracted much attention. This interest is mainly due to the ability to provide non-iterative methods that accurately estimate state-space models for multivariable systems directly from input-output measurements. Typically, all 4SID methods include advanced numerical linear algebra which makes them hard to analyze. The close relationship to Kalman filtering theory has increased the understanding. Herein an algorithm for change-detection, based on 4SID concepts, is proposed. The algorithm reuses N4SID-quantities (Numerical algorithms for Subspace based State Space System Identification, pronounced 'enforce it'). These quantities are interpreted in terms of Kalman and Instrumental Variable theory and are used in order to generate approximate one-step ahead prediction errors. The prediction errors are then used in a statistical X2 change detection test.

Simplification of system model in time domain using continued fraction expansion in third Cauer form

An algorithm for determining the matrix continued fraction expansion in third Cauer form for a given state space model of a multivariable system directly, without the necessity for determining the corresponding transfer function matrix, is presented. This algorithm can be used for many applications such as determining the transfer function matrix from a state space model, system realisation, and simplification of a system model in the time domain. The procedure for simplification of a multivariable system model in the time domain has been outlined and an example has been given to illustrate the application.

Minimal realizations interpolating first- and second-order information

In this paper, we consider the problem of finding minimal realizations of multivariable linear stable discrete-time systems which interpolate the given first- and second-order information. We present the condition for the existence of a solution to this interpolation problem, the discriminant of its uniqueness and a parametrization of the class of all the solutions. The results may be applied to the design of digital filters, model reduction preserving stability, and the ARMA modelling of multivariable systems.

On “order reduction of linear systems using an error minimization technique”

A method of obtaining reduced order models for multivariable systems is described. It is shown that the method has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. Irrespective of whether the original multivariable system is described in state space form or in the transfer matrix form, the proposed method yields the reduced order models in state space form. In this method the Routh approximation is used to formulate the common denominator polynomial of a reduced order model. This is used to describe the structure of Ar matrix. The matrices Br and Cr are chosen appropriately and some of the elements of Br/Cr matrices are specified in such a way that after matching time moments/Markov parameters, the resulting equations are linear in the unknown elements of Br and Cr matrices. The procedure is illustrated via a numerical example.

Cross-validation Ideas in Model Structure Selection for Multivariable Systems

Using cross-validation ideas, two procedures are proposed for making a choice between different model structures used for (approximate) modelling of multivariable systems. The procedures are derived under fairly general conditions: the ‘true’ system does not need to be contained in the model set; model structures do not need to be nested and different criteria may be used for model estimation and validation. The proposed structure selection rules are invariant to parameter scaling. Under certain conditions (essentially requiring that the system belongs to the model set and that the maximum likelihood method is used for parameter estimation) they are shown to be asymptotically equivalent to the (generalized) Akaike structure selection criteria

Model structure selection for multivariable systems by cross-validation methods

Using cross-validation ideas, two procedures are proposed for making a choice between different model structures used for (approximate) modelling of multivariable systems. The procedures are derived under fairly general conditions: the ‘true’ system does not need to be contained in the model set; model structures do not need to be nested and different criteria may be used for model estimation and validation. The proposed structure selection rules are shown to be invariant to parameter scaling. Under certain conditions (essentially requiring that the system belongs to the model set and that the maximum likelihood method is used for parameter estimation) they are shown to be asymptotically equivalent to the (generalized) Akaike structure selection criteria.

Decoupling precompensators for multivariable, equidimensional input-output models

In this paper multivariable system models having an equal number of inputs and outputs that are stable, linear, multivariable, and time invariant, expressed in the form of a transfer matrix in the Laplace variable, will be considered. The spectral form of the transfer matrix will be used to show that if the number of coupled right-hand plane zeros is less than or equal to the number of inputs to the system, then proper, stable, realizable decoupling precompensators for the system exist. Thereafter, algorithms that give the number of decoupling realizations in the set are derived, and demonstrations of the wide range of options afforded by these variations to the system designer are presented. To emphasize the flexibility and generality of the result, the decoupling precompensators for a simple multivariable system are computed together with the resulting noninteracting system/compensator combination. Selection of the “best” configuration is then made on the basis of the pole-zero pattern associated with each interfaced system. Finally, the design may be completed by way of the Nyquist array method using the preferred decoupling precompensator as a starting point in the search for a low-order realization, producing diagonal dominance rather than noninteracting characteristics.

パルス光によるサラダナ光合成速度の多変数システム同定

In our previous study, we identified the effect of the pulsed light illumination on the photosynthesis of Okayama Saradana with an one input-output system model and showed the possibility of saving electrical power by the application of the new artificial light source in the plant factory.Photosynthesis of plant is also affected by CO2concentration besides the pulsed light. So, the dynamic characteristics of the photosynthesis to CO2concentration is also important to the analysis of the cultivating processes in the plant factory.In this paper, we used a multivariable system model to estimate the effect of the pulsed light illumination on the photosynthesis of Okayama Saradana. Pulsed light illumination and CO2concentration were taken as two input signals and the net CO2uptake as the output signal. Impulse responses of net CO2uptake to the two inputs were estimated. From the simulation, we got the same result to that of the one input-output system model discussed in our previous study that the net CO2uptake of the plant under the illumination of low duty ratio of the pulsed light could be increased if CO2concentration of the environment is increased.Furthermore, we discussed the differences between the result from the one input-output system model and the multivariable system model. It seems that the one input-output system model could not give a reasonable result when CO2concentration had great change as to ±50 ppm, but the multivariable system identification could do.Plant and environments make up a very complicated system, in which many factors are included. We think that the multivariable system identification is a powerful method to analyse this system.

Model reduction of diagonally dominant systems

Model reduction methods based on open-loop considerations often fail to preserve the closed-loop interaction characteristics of the original system they represent and therefore lead to unreliable controller design. A method is presented that addresses the interaction aspects of multivariable-system model reduction and provides insight into the reasons for the failure of previous methods. The method results in models with satisfactory responses both in the open-loop configuration and in the closed-loop configuration with prespecified controller structure.

MODEL REDUCTION OF LINEAR MULTIVARIABLE SYSTEMS

Reduced order models of multivariable systems obtained by available model reduction techniques often fail to preserve the interaction properties of the original systems they represent, and therefore lead to unreliable con-trol systems. A. method is presented which addresses the interaction aspects of multivariable system model reduction and provides insight into thereasons of failure of previous methods.

CASAM — an interactive package for computer aided system analysis and modelling

This paper presents an interactive package — CASAM, for the computer aided analysis and modelling of multivariable systems described either by state equations or by transfer-matrices. CASAM is based on several powerful, portable Fortran subroutine packages (BIMASC, BIMAS, EISPACK, LINPACK, ODEPACK) which implement the latest advances in numerical algorithms. All functions are performed by the means of a command language. The CASAM package is implemented on the Romanian family of minicomputers INDEPENDENT and CORAL, as well as on the DEC PDP-11 systems.

Tests for Determining the Order of Canonical Models of Multivariable Systems

If the physical relations between the input and output signals of a multi-input, multi-output system are described by discrete transfer functions Gij, their orders nij must be known. They are determined by a theoretical analysis or they can be estimated and verified by various tests for determining the model order. Eight of those methods to determine the orders of single-input, single-output systems are compared as regards their applicability and their ability to identify multivariable systems. Canonical models are used to describe the behaviour of these systems so that a systematical system identification and parameter identification is possible. The results are shown by a representative example.

Model reduction for linear multivariable systems

A method has been proposed for obtaining reduced-order models for multivariable systems. Termed nonminimal partial realization, this method is shown to encompass the methods of aggregation (or eigenvalue preservation) and moments matching (Padé-type approximation about more than one point). In particular, a promising subclass of reduced models, called aggregated partial realizations, is discussed in detail and appears to combine the good points of the aggregation as well as the moments matching methods.

Identification of MIMO systems with partially decoupled parameters

Physical models for multivariable systems generally exhibit a partial decoupling with respect to the parameters characterizing the system. The computational advantages of such decoupling are explored using a recently developed least squares-equation error technique which applies to a class of nonlinear differential systems with input-output data given over a fixed finite-time interval. It is shown how the partially decoupled parameterized differential operator equations can be used as a basis for formulating a finite sequence of lower dimensional function minimizations in lieu of a single high-dimensional parameter minimization problem. Simulation results are summarized for a helicopter example which illustrate the advantages of carrying out the finite sequence of lower dimensional function minimizations.

Modelling multivariable systems with industrial specifications

A method is presented in the frequency domain for constructing standard models of multivariable systems by using industrial or commonly used control system specifications. By means of a matrix continued fraction, an algebraic method is established for determination of the minimal realizations of the standard model in the time domain.

Two methods for simplifying multivariable systems with various numbers of inputs and outputs

Two methods arc presented in the frequency domain for obtaining reduced models of multivariable systems with various numbers of inputs and outputs. The method of matrix continued fraction and the mixed method are extended to obtain the reduced models. When the ratio of the rank and the dimension of a transfer-function matrix is not an integer or the ratio is an integer but there exist numerically ill-conditioned elements in the matrix, a technique is proposed to deal with these cases.

Linear modelling of multivariable systems with pseudo-random binary input signals

Properties and methods of generation of pseudo-random binary signals are discussed. A theory of linear modelling is developed for multivariable systems in which these signals form the inputs. Modelling with delay operators and exponential weighting function operators is considered. Experimental results are presented to illustrate the theory.