Design of a minimum variance multiple input-multiple output neuro self-tuning proportional-integral-derivative controller for non-linear dynamic systems

In this study a minimum variance neuro self-tuning proportional-integral-derivative (PID) controller is designed for complex multiple input-multiple output (MIMO) dynamic systems. An approximation model is constructed, which consists of two functional blocks. The first block uses a linear submodel to approximate dominant system dynamics around a selected number of operating points. The second block is used as an error agent, implemented by a neural network, to accommodate the inaccuracy possibly introduced by the linear submodel approximation, various complexities/uncertainties, and complicated coupling effects frequently exhibited in non-linear MIMO dynamic systems. With the proposed model structure, controller design of an MIMO plant with n inputs and n outputs could be, for example, decomposed into n independent single input-single output (SISO) subsystem designs. The effectiveness of the controller design procedure is initially verified through simulations of industrial examples.

A neural network enhanced generalized minimum variance self-tuning proportional, integral and derivative control algorithm for complex dynamic systems

A neural network enhanced proportional, integral and derivative (PID) controller is presented that combines the attributes of neural network learning with a generalized minimum-variance self-tuning control (STC) strategy. The neuro PID controller is structured with plant model identification and PID parameter tuning. The plants to be controlled are approximated by an equivalent model composed of a simple linear submodel to approximate plant dynamics around operating points, plus an error agent to accommodate the errors induced by linear submodel inaccuracy due to non-linearities and other complexities. A generalized recursive least-squares algorithm is used to identify the linear submodel, and a layered neural network is used to detect the error agent in which the weights are updated on the basis of the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model, and therefore the error agent is naturally functioned within the control law. In this way the controller can deal not only with a wide range of linear dynamic plants but also with those complex plants characterized by severe non-linearity, uncertainties and non-minimum phase behaviours. Two simulation studies are provided to demonstrate the effectiveness of the controller design procedure.

Self-tuning proportional, integral and derivative controller based on genetic algorithm least squares

A self-tuning proportional, integral and derivative control scheme based on genetic algorithms (GAs) is proposed and applied to the control of a real industrial plant. This paper explores the improvement in the parameter estimator, which is an essential part of an adaptive controller, through the hybridization of recursive least-squares algorithms by making use of GAs and the possibility of the application of GAs to the control of industrial processes. Both the simulation results and the experiments on a real plant show that the proposed scheme can be applied effectively.

Autonomous intelligent cruise control using a novel multiple-controller framework incorporating fuzzy-logic-based switching and tuning

This paper presents a novel intelligent multiple-controller framework incorporating a fuzzy-logic-based switching and tuning supervisor along with a generalised learning model (GLM) for an autonomous cruise control application. The proposed methodology combines the benefits of a conventional proportional-integral-derivative (PID) controller, and a PID structure-based (simultaneous) zero and pole placement controller. The switching decision between the two nonlinear fixed structure controllers is made on the basis of the required performance measure using a fuzzy-logic-based supervisor, operating at the highest level of the system. The supervisor is also employed to adaptively tune the parameters of the multiple controllers in order to achieve the desired closed-loop system performance. The intelligent multiple-controller framework is applied to the autonomous cruise control problem in order to maintain a desired vehicle speed by controlling the throttle plate angle in an electronic throttle control (ETC) system. Sample simulation results using a validated nonlinear vehicle model are used to demonstrate the effectiveness of the multiple-controller with respect to adaptively tracking the desired vehicle speed changes and achieving the desired speed of response, whilst penalising excessive control action. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.

A genetic algorithm for the design of a fuzzy controller for active queue management

Active queue management (AQM) policies are those policies of router queue management that allow for the detection of network congestion, the notification of such occurrences to the hosts on the network borders, and the adoption of a suitable control policy. This paper proposes the adoption of a fuzzy proportional integral (FPI) controller as an active queue manager for Internet routers. The analytical design of the proposed FPI controller is carried out in analogy with a proportional integral (PI) controller, which recently has been proposed for AQM. A genetic algorithm is proposed for tuning of the FPI controller parameters with respect to optimal disturbance rejection. In the paper the FPI controller design metodology is described and the results of the comparison with random early detection (RED), tail drop, and PI controller are presented.

A fuzzy approach for the network congestion problem

In the recent years, the unpredictable growth of the Internet has moreover pointed out the congestion problem, one of the problems that historicallyha ve affected the network. This paper deals with the design and the evaluation of a congestion control algorithm which adopts a FuzzyCon troller. The analogyb etween Proportional Integral (PI) regulators and Fuzzycon trollers is discussed and a method to determine the scaling factors of the Fuzzycon troller is presented. It is shown that the Fuzzycon troller outperforms the PI under traffic conditions which are different from those related to the operating point considered in the design.

Parallel genetic algorithms for the tuning of a fuzzy AQM controller

This paper presents the results of the application of a parallel Genetic Algorithm (GA) in order to design a Fuzzy Proportional Integral (FPI) controller for active queue management on Internet routers. The Active Queue Management (AQM) policies are those policies of router queue management that allow the detection of network congestion, the notification of such occurrences to the hosts on the network borders, and the adoption of a suitable control policy. Two different parallel implementations of the genetic algorithm are adopted to determine an optimal configuration of the FPI controller parameters. Finally, the results of several experiments carried out on a forty nodes cluster of workstations are presented.

Regularization of descriptor systems by output feedback

Conditions are given under which a descriptor, or generalized state-space system can be regularized by output feedback. It is shown that under these conditions, proportional and derivative output feedback controls can be constructed such that the closed-loop system is regular and has index at most one. This property ensures the solvability of the resulting system of dynamic-algebraic equations. A reduced form is given that allows the system properties as well as the feedback to be determined. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way.

Feedback design for regularizing descriptor systems

This paper surveys numerical techniques for the regularization of descriptor (generalized state-space) systems by proportional and derivative feedback. We review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the Weierstraß canonical form. Three condensed forms display the controllability and observability properties of a descriptor system. The condensed forms are obtained through orthogonal equivalence transformations and rank decisions, so they may be computed by numerically stable algorithms. In addition, the condensed forms display whether a descriptor system is regularizable, i.e., when the system pencil can be made to be regular by derivative and/or proportional output feedback, and, if so, what index can be achieved. Also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback.

Minimum norm regularization of descriptor systems by mixed output feedback

We study the regularization problem for linear, constant coefficient descriptor systems Ex' = Ax+Bu, y1 = Cx, y2 = Γx' by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and E+BGΓ has a desired rank, i.e., there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedback gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.

Regularization of Descriptor Systems by Derivative and Proportional State Feedback

For linear multivariable time-invariant continuous or discrete-time singular systems it is customary to use a proportional feedback control in order to achieve a desired closed loop behaviour. Derivative feedback is rarely considered. This paper examines how derivative feedback in descriptor systems can be used to alter the structure of the system pencil under various controllability conditions. It is shown that derivative and proportional feedback controls can be constructed such that the closed loop system has a given form and is also regular and has index at most 1. This property ensures the solvability of the resulting system of dynamic-algebraic equations. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way. The problem of pole placement with derivative feedback alone and in combination with proportional state feedback is also investigated. A computational algorithm for improving the “conditioning” of the regularized closed loop system is derived.

A well-posed integral equation formulation for three-dimensional rough surface scattering

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space L-2 (Gamma) when the scattering surface G does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, kappa, for kappa > 0, if the coupling parameter h is chosen proportional to the wave number. In the case when G is a plane, we show that the choice eta = kappa/2 is nearly optimal in terms of minimizing the condition number.

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

Field evaluation of systemic inducing resistance chemicals at different growth stages for the control of apple (Venturia inaequalis) and pear (Venturia pirina) scab

Two field trials were conducted using established apple (Malus cv. Golden Delicious) and pear (Pyrus communis 'Williams' Bon Chretien') to assess the efficacy of three commercially available systemic inducing resistance (SIR) products, Messenger (a.i. Harpin protein), Phoenix (a.i. Potassium phosphite) and Rigel (a.i. Salicylic acid derivative) applied at four different growth stages of tree development (bud break, green cluster, 90% petal fall, early fruitlet) against the foliar pathogens Venturia inaequalis and Venturia pirina which cause apple and pear scab respectively. A conventional synthetic fungicide (penconazole) used within the UK for apple and pear scab control was included for comparison. Little efficacy as scab protectants was demonstrated when each SIR product and penconazole was applied at only two growth stages (bud break, green cluster). However when the above compounds were applied at three or more growth stages efficacy as scab protectants was confirmed. The synthetic fungicide penconazole provided greatest protection against apple and pear scab in both the 2006 and 2007 field trials. There was little difference in the magnitude of scab protection conferred by each SIR agent. Results suggest application of at least three sprays during bud break to early fruitlet formation with an appropriate SIR agent may provide a useful addition to existing methods of apple and pear scab management under field conditions. (C) 2009 Published by Elsevier Ltd.