Model predictive control using dynamic integrated system optimisation and parameter estimation (DISOPE)

DISOPE is a technique for solving optimal control problems where there are differences in structure and parameter values between reality and the model employed in the computations. The model reality differences can also allow for deliberate simplification of model characteristics and performance indices in order to facilitate the solution of the optimal control problem. The technique was developed originally in continuous time and later extended to discrete time. The main property of the procedure is that by iterating on appropriately modified model based problems the correct optimal solution is achieved in spite of the model-reality differences. Algorithms have been developed in both continuous and discrete time for a general nonlinear optimal control problem with terminal weighting, bounded controls and terminal constraints. The aim of this paper is to show how the DISOPE technique can aid receding horizon optimal control computation in nonlinear model predictive control.

Bifurcation Analysis of Eigenstructure Assignment Control in a Simple Nonlinear Aircraft Model

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled � ight. The construction of a robust closed-loop control that extends the stable and decoupled � ight envelope as far as possible is pursued. For the study of these systems, nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and to investigate control effects on dynamic behavior. Linear feedback control designs constructed by eigenstructure assignment methods at a � xed � ight condition are investigated for a simple nonlinear aircraft model. Bifurcation analysis, in conjunction with linear control design methods, is shown to aid control law design for the nonlinear system.

Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part I: Ideal energy source

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

An Optimal Linear Control Design for Nonlinear Systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimal linear and nonlinear control design for chaotic systems

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rössler system and the Duffing oscillator are provided to show the effectiveness of this method. Copyright © 2005 by ASME.

Swarm control designs applied to a micro-electro-mechanical gyroscope system (MEMS)

This paper analyzes the non-linear dynamics of a MEMS Gyroscope system, modeled with a proof mass constrained to move in a plane with two resonant modes, which are nominally orthogonal. The two modes are ideally coupled only by the rotation of the gyro about the plane's normal vector. We demonstrated that this model has an unstable behavior. Control problems consist of attempts to stabilize a system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. We also developed a particle swarm optimization technique for reducing the oscillatory movement of the nonlinear system to a periodic orbit. © 2010 Springer-Verlag.

On nonlinear dynamics and control of a robotic arm with chaos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Chaos control and sensitivity analysis of a double pendulum arm excited by an RLC circuit based nonlinear shaker

In this paper the dynamical interactions of a double pendulum arm and an electromechanical shaker is investigated. The double pendulum is a three degree of freedom system coupled to an RLC circuit based nonlinear shaker through a magnetic field, and the capacitor voltage is a nonlinear function of the instantaneous electric charge. Numerical simulations show the existence of chaotic behavior for some regions in the parameter space and this behaviour is characterized by power spectral density and Lyapunov exponents. The bifurcation diagram is constructed to explore the qualitative behaviour of the system. This kind of electromechanical system is frequently found in robotic systems, and in order to suppress the chaotic motion, the State-Dependent Riccati Equation (SDRE) control and the Nonlinear Saturation control (NSC) techniques are analyzed. The robustness of these two controllers is tested by a sensitivity analysis to parametric uncertainties.

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

Nonlinear control of heart rate variability in human infants.

Nonlinear analyses of infant heart rhythms reveal a marked rise in the complexity of the electrocardiogram with maturation. We find that normal mature infants (gestation greater than or equal to 35 weeks) have complex and distinctly nonlinear heart rhythms (consistent with recent reports for healthy adults) but that such nonlinearity is lacking in preterm infants (gestation > or = to 27 weeks) where parasympathetic-sympathetic interaction and function are presumed to be less well developed. Our study further shows that infants with clinical brain death and those treated with atropine exhibit a similar lack of nonlinear feedback control. These three lines of evidence support the hypothesis championed by Goldberger et al. [Goldberger, A.L., Rigney, D.R. & West, B.J. (1990) Sci. Am. 262, 43-49] that autonomic nervous system control underlies the nonlinearity and possible chaos of normal heart rhythms. This report demonstrates the acquisition of nonlinear heart rate dynamics and possible chaos in developing human infants and its loss in brain death and with the administration of atropine. It parallels earlier work documenting changes in the variability of heart rhythms in each of these cases and suggests that nonlinearity may provide additional power in characterizing physiological states.

An algorithm for computerized automatic tuning of power system stabilizers

The main objective of this paper is to relieve the power system engineers from the burden of the complex and time-consuming process of power system stabilizer (PSS) tuning. To achieve this goal, the paper proposes an automatic process for computerized tuning of PSSs, which is based on an iterative process that uses a linear matrix inequality (LMI) solver to find the PSS parameters. It is shown in the paper that PSS tuning can be written as a search problem over a non-convex feasible set. The proposed algorithm solves this feasibility problem using an iterative LMI approach and a suitable initial condition, corresponding to a PSS designed for nominal operating conditions only (which is a quite simple task, since the required phase compensation is uniquely defined). Some knowledge about the PSS tuning is also incorporated in the algorithm through the specification of bounds defining the allowable PSS parameters. The application of the proposed algorithm to a benchmark test system and the nonlinear simulation of the resulting closed-loop models demonstrate the efficiency of this algorithm. (C) 2009 Elsevier Ltd. All rights reserved.

Intelligent behavior in a Cyber-Ambient training system for control center operators

This paper deals with the application of an intelligent tutoring approach to delivery training in diagnosis procedures of a Power System. In particular, the mechanisms implemented by the training tool to support the trainees are detailed. This tool is part of an architecture conceived to integrate Power Systems tools in a Power System Control Centre, based on an Ambient Intelligent paradigm. The present work is integrated in the CITOPSY project which main goal is to achieve a better integration between operators and control room applications, considering the needs of people, customizing requirements and forecasting behaviors.

Optimal fuzzy PID control tuned with genetic algorithms

Fuzzy logic controllers (FLC) are intelligent systems, based on heuristic knowledge, that have been largely applied in numerous areas of everyday life. They can be used to describe a linear or nonlinear system and are suitable when a real system is not known or too difficult to find their model. FLC provide a formal methodology for representing, manipulating and implementing a human heuristic knowledge on how to control a system. These controllers can be seen as artificial decision makers that operate in a closed-loop system, in real time. The main aim of this work was to develop a single optimal fuzzy controller, easily adaptable to a wide range of systems – simple to complex, linear to nonlinear – and able to control all these systems. Due to their efficiency in searching and finding optimal solution for high complexity problems, GAs were used to perform the FLC tuning by finding the best parameters to obtain the best responses. The work was performed using the MATLAB/SIMULINK software. This is a very useful tool that provides an easy way to test and analyse the FLC, the PID and the GAs in the same environment. Therefore, it was proposed a Fuzzy PID controller (FL-PID) type namely, the Fuzzy PD+I. For that, the controller was compared with the classical PID controller tuned with, the heuristic Ziegler-Nichols tuning method, the optimal Zhuang-Atherton tuning method and the GA method itself. The IAE, ISE, ITAE and ITSE criteria, used as the GA fitness functions, were applied to compare the controllers performance used in this work. Overall, and for most systems, the FL-PID results tuned with GAs were very satisfactory. Moreover, in some cases the results were substantially better than for the other PID controllers. The best system responses were obtained with the IAE and ITAE criteria used to tune the FL-PID and PID controllers.

On the Analysis and Control of a Linear Synchronous Servomotor with a Flexible Load

Industry's growing need for higher productivity is placing new demands on mechanisms connected with electrical motors, because these can easily lead to vibration problems due to fast dynamics. Furthermore, the nonlinear effects caused by a motor frequently reduce servo stability, which diminishes the controller's ability to predict and maintain speed. Hence, the flexibility of a mechanism and its control has become an important area of research. The basic approach in control system engineering is to assume that the mechanism connected to a motor is rigid, so that vibrations in the tool mechanism, reel, gripper or any apparatus connected to the motor are not taken into account. This might reduce the ability of the machine system to carry out its assignment and shorten the lifetime of the equipment. Nonetheless, it is usually more important to know how the mechanism, or in other words the load on the motor, behaves. A nonlinear load control method for a permanent magnet linear synchronous motor is developed and implemented in the thesis. The purpose of the controller is to track a flexible load to the desired velocity reference as fast as possible and without awkward oscillations. The control method is based on an adaptive backstepping algorithm with its stability ensured by the Lyapunov stability theorem. As a reference controller for the backstepping method, a hybrid neural controller is introduced in which the linear motor itself is controlled by a conventional PI velocity controller and the vibration of the associated flexible mechanism is suppressed from an outer control loop using a compensation signal from a multilayer perceptron network. To avoid the local minimum problem entailed in neural networks, the initial weights are searched for offline by means of a differential evolution algorithm. The states of a mechanical system for controllers are estimated using the Kalman filter. The theoretical results obtained from the control design are validated with the lumped mass model for a mechanism. Generalization of the mechanism allows the methods derived here to be widely implemented in machine automation. The control algorithms are first designed in a specially introduced nonlinear simulation model and then implemented in the physical linear motor using a DSP (Digital Signal Processor) application. The measurements prove that both controllers are capable of suppressing vibration, but that the backstepping method is superior to others due to its accuracy of response and stability properties.