Control Of Nonlinear Multivariable Systems Research Articles

Model Reference Adaptive Control of Non-linear Multivariable Systems using an Interactor Structure Estimation

This paper concerns the model reference adaptive control of non-linear multivariable systems. For this purpous, we make use of the interactor structure estimation and the adaptive control technique for linear systems.

Robust controller design for multivariable nonlinear systems via multi-model H2/ H∞ synthesis

Input/output (I/O) linearization via state feedback provides a convenient framework for designing controllers for multivariable nonlinear systems. However this approach does not account for parametric uncertainty which may lead to loss of stability and performance degradation. In this paper, a multi-model H 2/ H ∞ approach is utilized to design a robust controller for minimum phase multivariable nonlinear systems that are subject to parametric uncertainty. It is first shown that a state feedback (inner loop) based on nominal parameters introduces nonlinear perturbations to the linear sub-system and results in loss of decoupling. The uncertain system is characterized in a form that provides a framework for robust controller design. Recent results from linear robust control theory are utilized to design an outer-loop controller to account for the parametric uncertainty. This methodology is illustrated via simulation of a regulation problem in a continuous stirred tank reactor.

Neural Network Application To Optimal Control Of Nonlinear Systems

This paper presents the derivation of the numerical algorithm for optimal control of nonlinear multivariable systems with control and state vectors constraints. The algorithm derivation is based on the backpropagationthrough-time (BPTT) algorithm which is used as a learning algorithm for recurrent neural networks. This approach is not based on Lagrange multiplier techniques and the calculus of variations. The derived algorithm is used for the control of the cooperative work of two robots with two degrees of freedom. The main problem is the determination of the control vectors of robots for the transfer of rigid load from the initial state to the final one in a fixed time while maintaining constant distance between robot hands and avoiding the cross-section of the robot hands.

Constrained nonlinear multivariable control of a fluid catalytic cracking process

Abstract In this paper, a nonlinear constrained optimization strategy is proposed and applied to the reactor-regenerator section of a fluid catalytic cracking (FCC) unit. A nonlinear dynamic model of the fluid catalytic cracking process was used for the dynamic analysis of the plant and nonlinear multivariable control system. The model realistically simulates the riser-reactor and the one stage regenerator by assembling the mass and energy balances on the system of reactions. The model results were tested in a real-time application and the results were used to provide the initial values for the nonlinear control system design. A dynamic parameter update algorithm was used to reduce the effect of large modelling errors by regularly updating the model parameters. The constrained nonlinear optimization algorithm and strategies were tested in real-time on the fluid catalytic cracking reactor-regenerator. The results compared favourably to those from a linear multivariable controller.

Stable adaptive control for nonlinear multivariable systems with a triangular control structure

A stable adaptive controller is developed for a class of nonlinear multivariable systems using nonlinearly parametrized function approximators. By utilizing the system triangular property, integral-type Lyapunov functions are introduced for deriving the control structure and adaptive laws without the need of estimating the "decoupling matrix" of the multivariable nonlinear system. It is shown that stability of the adaptive closed-loop system is guaranteed, and transient performance is analytically quantized by mean square and L/sub /spl infin// tracking error bound criteria.

A fuzzy basis function vector-based multivariable adaptive controller for nonlinear systems

In this paper, a new fuzzy basis function vector (FBFV) approach for the adaptive control of multivariable nonlinear systems is presented. With this method, the nonlinear plant is first linearized. The linearized bias and uncertainties as well as disturbances are assumed to be included in the model structure and their upper bound will be adaptively learned by the FBFV method. The output of the FBFV is used as the parameters of the robust controller in the sense that both the robustness and the asymptotic error convergence can be obtained for the multivariable nonlinear system. The effectiveness of the proposed analysis and design method is illustrated with a simulated example.

An Approach for Synthesis of Robust Neural Network Controller for Multivariable Non-Linear Systems with Stochastic Parameters

In this paper, an approach is proposed to synthesize robust neural network controller for multi-input multi-output non-linear systems with uncertain parameters. The approach is based on the capability of neural networks to approximate arbitrary non-linear mappings. The case of known probability distributions of the uncertain parameters is considered. The control problem is to maintain the system on the required steady state despite of changes of the system parameters. The overall controller structure includes two neural network controllers: a global neural controller which transfers the system near steady state by minimizing the mathematical expectation of the optimality criterion and a local neural controller which generates the correct steady state values of the control variables based on the system response achieved with the global controller.

Tracking Control of General Nonlinear Systems by Direct Gradient Descent Method

This paper is concerned with tracking control of nonlinear multivariable systems whose relative degree is more than one. The control method is based on a direct steepest descent method using the gradient of a performance index such as the squared error from a desired equilibrium. Several simulation results demonstrate the usefulness of the proposed method.

On the sliding mode control of multivariable nonlinear systems

Sliding mode control of multivariable nonlinear systems is addressed, from the perspective of linear differential algebra, for a special but large class of linearizable systems known as differentially flat systems. Essential orders and differential flatness are shown to be, a relevant concept and a sensible requirement respectively, associated with the possibilities of designing static or dynamical sliding mode multivariable feedback regulators for nonlinear systems.

RECURRENT NEURAL NETWORKS IN DECOUPLING CONTROL OF MULTIVARIABLE NONLINEAR SYSTEMS

In this work we focus on the synergy between modeling with RNNs, and nonlinear controller design for decoupling control. The thesis of the paper is that recurrent neural networks (RNNs) can be conveniently used in an integrated black-box modeling and controller design methodology for decoupling control of multivariable nonlinear systems. A simulation example on a multivariable continuous-stirred-tank-reactor (CSTR) is provided to elucidate related issues. The effects of modeling uncertainty and state reconstruction on decoupling performance are specifically discussed.

Adaptive control of nonlinear multivariable systems using neural networks

Most practical systems have multiple inputs and multiple outputs, and the applicability of neural networks as practical adaptive controllers will eventually be judged by their success in multivariable problems. The representation, identification, and control of nonlinear multivariable systems are rendered difficult by the coupling as well as the delays that exist between the inputs and outputs. In the first part of the paper, theoretical questions related to system representation and existence of a desired control input are discussed. The second part of the paper develops a design methodology using neural networks. It is shown that under appropriate conditions, it may be possible to design efficient neural controllers for nonlinear multivariable systems for which linear controllers are inadequate.

Transformations of a class of non-linear multivariable control systems to block companion forms and their applications

The problem of transforming a class of multivariable non-linear systems to the controller and observer block companion forms is considered for pole assignment and observer design. Solving non-linear partial differential equations is needed for finding the transformations and the conditions for the existence of such transforms are stated.

Control of multivariable non-linear systems by the sliding mode method

Sliding mode control is a technique that has been successfully used for SISO nonlinear systems in controllable canonical form and for some particular multivariable system structures. It is the purpose of this paper to generalize the sliding mode approach to a larger class of multivariable systems and to illustrate the relationship between I/O linearization and the sliding mode approach when the error dynamics on the sliding surfaces are chosen to be linear and time-invariant. The developed technique is applied to a multivariable non-linear example.

CAD of Control Systems with Transients Limited by the Admissible Region

In [1] was defined the generalized criterium for the quality of control. According to it, the output of control system must belong to the admissible region, defined by upper limits for: settling time, overshoot and statical error.In [2], an approach for the solution of the synthesis problem for linear systems satisfying this criterium was described. This approach was based on concepts of: inequalities, desired transient and frequency response.In this paper the algorithm and program package for computer aided design (parametric synthesis) of multivariable nonlinear control systems for more general and advanced statement of the aforementioned problem is given.

Steady-state stability of an HVDC system using frequency-response methods

An HVDC scheme is an amalgamation of both AC and DC components, the behaviour of which is often difficult to describe because of the interdependence of many of the parameters. The response of the DC system is dependent on the AC system and vice versa. The basic scheme controls also include both rectifier and inverter controls, which are basically separate but interdependent. The complete scheme could be described as a nonlinear multivariable control system which is sensitive to external disturbances. The paper describes the analysis of such an HVDC scheme using a simulator model and frequency-response techniques. The results described constitute a sensitivity analysis of the system to the principal parameters which affect the steady-state stability, such as the inverter short-circuit ratio and AC-system damping, as well as the sensitivity to control parameter changes.

Invertibility of affine nonlinear control systems: a geometric approach

The paper deals with the invertibility of multivariable non-linear control systems. By using the recently developed theory on controlled invariant and controllability distributions necessary and sufficient conditions for invertibility are derived.

Generalized functional reproducibility condition for nonlinear systems

A new sufficient condition for the existence of control to generate a given real analytic function as the output of a large class of multivariable nonlinear control system is derived. Furthermore, a prefilter (right-inverse system) is constructed to generate the required control.

Functional reproducibility of multivariable nonlinear systems

Based on the algorithm of Hirschorn [1] for the construction of inverses, a sufficient condition for the existence of control to generate a given real analytic function as the output of a multivariable nonlinear control system is derived. Furthermore, a prefilter (right-inverse system) is constructed to generate the required control.

Self-tuning control of a class of multivariable non-linear systems

Self-tuning is applied to the minimum variance control of non-linear multivariable systems which can be characterized by a ‘ multivariable Hammerstein model ’. It is also shown that such systems are not amenable to self-tuning control if control costing is to be included in the performance criterion.

Necessary conditions for absolute stability of nonlinear multivariable regulators

Simple necessary conditions involving the fundamental frequency-domain concept of transmission zeros are established for the absolute stability of nonlinear multivariable regulators. These results significantly complement the sufficient conditions provided by the matrix Popov criterion in the analysis and synthesis of nonlinear multivariable control systems.