Nonlinear Single-input Single-output Research Articles

Performance Evaluation of an On-Line Self-Learning Fuzzy Logic Controller Applied to Non-Linear Processes

The generation of rule-bases in conventional fuzzy logic controllers can be a difficult and time consuming problem for implementation by process operators thus affecting their wider applicability. A Self-Learning Fuzzy Logic Control (SLFLC) offers a possible solution. A performance study is therefore presented to evaluate the performance of a proposed SLFLC by analysing its transient performance for a variety of on-line tests and examining its ability to generate a consistent set of rules, based on a predetermined criteria. The results presented show that even with a limited knowledge of the process, the self-learning procedure is able to develop a suitable set of rules and produce a satisfactory process performance with some degree of robustness and repeatability when applied to a non-linear single-input single-output (SISO) or multi-input multi-output (MIMO) laboratory liquid-level processes.

Control system design based on a nonlinear first-order plus time delay model

Abstract Most chemical processes are nonlinear in nature. When large set point changes or load disturbances occur frequently, nonlinear control systems are required. Instead of using the differential geometric method or nonlinear model predictive method, simple gain scheduling may be sufficient for many nonlinear single input-single output (SISO) processes. To design such simple control systems systematically, a nonlinear first-order plus time delay model is proposed for model-based control. A logarithmic transformation which is very useful for control of high purity distillation columns is shown to be effective in general. Several chemical process examples are also given.

The identification of nonlinear biological systems: Volterra kernel approaches.

Representation, identification, and modeling are investigated for nonlinear biomedical systems. We begin by considering the conditions under which a nonlinear system can be represented or accurately approximated by a Volterra series (or functional expansion). Next, we examine system identification through estimating the kernels in a Volterra functional expansion approximation for the system. A recent kernel estimation technique that has proved to be effective in a number of biomedical applications is investigated as to running time and demonstrated on both clean and noisy data records, then it is used to illustrate identification of cascades of alternating dynamic linear and static nonlinear systems, both single-input single-output and multivariable cascades. During the presentation, we critically examine some interesting biological applications of kernel estimation techniques.

Nonlinear control of dynamical systems from time series.

Feedback control of multidimensional, nonlinear single-input single-output systems is formulated in terms of an invariant hypersurface in the delayed state space of a system observable and a control parameter. The surface is created directly from the response of the system to random perturbations, providing a model-independent nonlinear control algorithm. The algorithm can be used to stabilize unstable states or to drive a system to any particular objective state in a minimum number of steps.

Nonlinear tracking and input disturbance rejection with application to pH control

This paper presents a nonlinear observer-based controller configuration for a class of nonlinear single-input single-output systems with certain observability and stability properties. Particular attention is paid to the effect of input disturbances typically present in chemical processes. It is pointed out that conventional feedback linearizing internal model controllers reject output disturbances linearly, but that they can experience significant performance degradation in the presence of input disturbances. This problem is shown to originate in the lack of the linear superposition property. It is proven that the proposed control architecture rejects constant input disturbances from the control signal and then recovers linear reference tracking. The convenient tuning and improved performance are illustrated for pH neutralization.

H/sup ∞/ tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach

A fuzzy logic controller equipped with a training (adaptive) algorithm is proposed in this work to achieve H/sup /spl infin// tracking performance for a class of uncertain (model free) nonlinear single-input single-output (SISO) systems with external disturbances. An attempt is also made to create a bridge between two important control design techniques, i.e., H/sup /spl infin// control design and fuzzy control design, so as to supply H/sup /spl infin// control design with more intelligence and fuzzy control design with better performance. The perfect matching of parameters in an adaptive fuzzy logic system is generally deemed impossible. Therefore, a desired tracking performance cannot be guaranteed in the conventional adaptive fuzzy control systems. In this study, the influence of both fuzzy logic approximation error and external disturbance on the tracking error is attenuated to a prescribed level. Both indirect and direct adaptive fuzzy controllers are employed to treat this H/sup /spl infin// tracking problem. The authors' results indicate that arbitrarily small attenuation level can be achieved via the proposed adaptive fuzzy control algorithm if a weighting factor of control variable is adequately chosen. The proposed design method is also useful for the robust tracking control design of the nonlinear systems with external disturbances and a large uncertainty or unknown variation in plant parameters and structures. Furthermore, only smooth control signals are needed via the proposed control designs. Two simulation examples are given finally to illustrate the performance of the proposed methods. Computer simulation results confirm that the effect of both the fuzzy approximation error and external disturbance on the tracking error can be attenuated efficiently by the proposed method.

Dynamical discontinuous feedback strategies in the regulation of nonlinear chemical processes

In this article, a unified approach is proposed for the design of dynamical discontinuous feedback controllers leading to the chattering-free stabilization of nonlinear single-input single-output systems describing chemical processes. The adopted framework is that of a generalized state representation form of the given nonlinear plant. Use is made of the associated generalized observability canonical form of such representation. Unification of discontinuous feedback policies is achieved by zeroing of an input-dependent auxiliary output function using simple discontinuous feedback control paradigms of various kinds. The zeroing of such scaler stabilizing function induces asymptotically stable controlled dynamics on the given nonlinear minimum-phase plant. Pulse-frequency-modulation, pulse-width-modulation and sampled sliding mode control strategies are considered from this unified viewpoint. Examples are provided including simulations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Real-Time Neural Network Control - An IMC Approach

An internal model control (IMC) structure provides a practical framework to nonlinear control design. Current nonlinear IMC design procedures are restricted to open-loop stable systems with stable inverse. In this paper, a novel IMC design method is presented for time-discrete, nonlinear single-input single-output systems. The design method is based on a nonlinear parametric optimal control law which is realized by a perceptron network. The parameters of the network are obtained by minimizing the cost function by the recursive prediction error method (RPEM).Also, a parameter projection is employed to restrict the parameters of the controller into the stable region of the parameter space. This procedure relaxes the assumption about the stability of the model inverse. The properties of the resulting controller are studied in real-time experiments with a laboratory heating process. The results demonstrate that the proposed design method yields good performance characteristics and robust control

On the dynamical sliding mode control of nonlinear systems

The consequences of the differential algebraic approach in the sliding mode control of nonlinear single-input single-output systems are reviewed in tutorial fashion. Input-dependent sliding surfaces, possibly including time derivatives of the input signal, are shown to arise naturally from elementary differential algebraic results pertaining to the Fliess's Generalized Controller Canonical Forms of nonlinear systems. This class of switching surfaces generally leads to chattering-free dynamically synthesized sliding regimes, in which the highest time derivative of the input signal undergoes all the bang-bang type discontinuities. Examples illustrating the obtained results are also included.

Dynamical pulse width modulation control of nonlinear systems

The design of dynamical stabilizing pulse-width-modulated controllers is addressed in full generality for the class of analytical nonlinear single-input single-output systems expressible in Fliess' local generalized observability canonical form.

Zero dynamics of regularly perturbed systems may be singularly perturbed

In this paper we present new results on the structure of the zeros of linear and nonlinear systems under perturbation. In particular, we show that when state space descriptions of linear or nonlinear single-input single-output systems with relative degree ≥ 2 are regularly perturbed, then their zero dynamics may be singularly perturbed and show a separation of time scales. In the SISO case, we give asymptotic formulas for the new high frequency zero dynamics arising from the regular perturbation.

Almost disturbance decoupling for single-input single-output nonlinear systems

The almost disturbance decoupling problem for nonlinear single-input single-output systems is addressed by using singular perturbation methods and high-gain feedback. Sufficient conditions and the explicit high-gain nonlinear state feedback in solvable cases are given. They generalize both previous almost results for linear systems and exact ones for nonlinear systems. The necessity of the conditions is discussed; in particular, an example is given where the main structural condition is not satisfied and the high-gain control designed on the basis of linear approximations fails to achieve almost disturbance decoupling for the original system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The extended Luenberger observer for nonlinear systems

For nonlinear single-input single-output systems dot x = f(x, u), y = h(x, u) , the relationships for a state transformation into the nonlinear observer canonical form are developed. It is possible to dimension a nonlinear observer by an eigenvalue assignment without solving the nonlinear partial differential equations for the transformation, if the transformed nonlinearities are linearized about the reconstructed state. With reference to the extended Kalman filter algorithm, this nonlinear observer design is called the extended Luenberger observer.

New aspects on linear and non-linear single-input single-output systems

Abstract By means of a new state description of single-input-single-output systems whose statement is given in the paper, we propose a global study of linear time-invariant systems. By use of a stability criterion together with this description a study of a class of non-linear systems is presented. Throughout the paper there is no formal distinction between continuous and discrete-time processes.