Multiple-input Multiple-output Nonlinear Systems Research Articles

Reconstruction of multiple-input multiple-output non-linear differential equation models from the generalized frequency response function matrix

A new algorithm is introduced to identify differential equation models for linear and non-linear multiple-input multiple-output systems from frequency response data using a weighted complex orthogonal estimator. The estimation procedure is progressive beginning with the estimation of the linear terms and then sequentially adding higher-order non-linear terms to build up the model. Simulated examples are included to demonstrate the performance of the new algorithm.

Non-linear dynamic system identification: A multi-model approach

We are concerned with models which are able to describe multiple-input multiple-output (MIMO) non-linear dynamic systems. These models are represented in the form of rules and are known as Tagaki-Sugeno models. An identification algorithm for these models based on input and output data is presented. Parameter estimation is based on the calculation of model sensitivity functions with respect to their parameters. Some aspects of structure identification are also tackled, i.e. determination of local model orders and number of rules.

Decoupling of Multivariable Rule-Based Fuzzy Systems

Decoupling of interactions among variables in multiple-input, multiple-output (MIMO) rule-based systems is addressed. It is well known that by proper decoupling the design of a controller for a MIMO process can be substantially simplified. Also the computational costs are reduced which facilitates the real-time implementation of the control system. However, decoupling methods are well developed for linear systems only. No general approach seems to be available for nonlinear MIMO systems. It is shown in this article that if a nonlinear MIMO system is represented by a set of linguistic if-then rules, the decoupling can be accomplished in a systematic way. An algorithm for the design of a decoupler (pre-compensator) is presented and illustrated by an example.

Design of a General-Purpose MIMO Predictor with Neural Networks

A new multi-step predictor for multiple-input, multiple-output (MIMO) systems is proposed. The output prediction of such a system is represented as a mapping from its historical data and future inputs to future outputs. A neural network is designed to learn the mapping without re quiring a priori knowledge of the parameters and structure of the system. The major problem in de veloping such a predictor is how to train the neural network. In case of the back propagation algorithm, the network is trained by using the network's output error which is not known due to the unknown predicted future system outputs. To overcome this problem, the concept of updating, in stead of training, a neural network is introduced and verified with simulations. The predictor then uses only the system's historical data to update the configuration of the neural network and always works in a closed loop. If each node can only handle scalar operations, emulation of an MIMO mapping requires the neural network to be excessively large, and it is difficult to specify some known coupling effects of the predicted system. So, we propose a vector-structured, multilayer perceptron for the predictor design. MIMO linear, nonlinear, time-invariant, and time-varying systems are tested via simulation, and all showed very promising performances.

Internal Model Control for Nonlinear Systems: Application to an Induction Motor

An internal model control (IMC) technique for multiple-input multiple-output nonlinear systems is proposed. The IMC structure provides a practical approach to the design of robust controllers. A practical procedure is proposed to quantify the robust stability of the closed-loop system. This procedure has been applied, in simulation, to an induction motor.

Real-time dynamic simulation of non-linear mimo systems

A PC based real-time simulator of the dynamic behaviour of non-linear MIMO (Multiple Input, Multiple Output) systems is presented. The strategy is developed in the time domain. Virtually all processes represented mathematically by sets of non-linear algebraic-differential equations can be described by the simulator. Exceptions, not yet found in our practice, may be cases of large number of ill-conditioned equations where the numerical strategies employed, albeit tested and robust, may experience difficulties. The User defines in very simple terms his own process (algebraic-differential) equations, control inputs, loads, measured variables and process parameters. The latter can be changed on-line during the simulation. Protocols for input/output are included for A/D, D/A and RS232 communications. Studies employing this simulator have been effectively conducted on penicillin and baker's yeast fed-batch fermentation, on sugar crystallization and on multiple-effect evaporation, among other systems.

Robust design of MIMO feedback systems having an uncertain non-linear plant

An n × n non-linear multiple-input multiple-output system W is presented, known only to belong to a set {W}. W is embedded in a two-degree-of-freedom feedback structure, {r} is a set of possible command inputs, where for each r ∊ {r} there is a set {A r } of acceptable outputs. The two degrees of freedom have to be selected such that in response to each command input r, the plant's output y ∊ {Ar } for all W ∊ {W}, A design technique is presented for solving this problem, based on the Horowitz design method for MIMO linear time invariant feedback systems. Sufficient conditions are given under which a solution is guaranteed. A design example is provided.

Extended Luenberger observer for non-linear multivariable systems

For non-linear multiple-input multiple-output systems [xdot] = f(x, u), y = h(x, u), nonlinear observers are designed using a transformation into the non-linear observer canonical form and an extended linearization. The differential equation of observer error in canonical coordinates is linearized about the reconstructed trajectory, and dimensioned by eigenvalue assignment. With reference to the extended Kalman filter algorithm, this non-linear observer design is called the extended Luenberger observer. This observer design is possible for all sufficiently smooth and locally observable systems. In comparison with single-output systems, the non-linear observer design can be essentially simplified using the degrees of freedom available in the case of multiple outputs.