On an Optimal Linear Control Applied to a Non-Ideal Load Transportation System, Modeled with Periodic Coefficients

In this paper, a load transportation system in platforms or suspended by cables is considered. It is a monorail device and is modelled as an inverted pendulum built on a car driven by a DC motor. The governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the DC motor and the dynamical system, that is, we have a so-called non-ideal periodic problem. The problem is analysed and we also developed an optimal linear control design to stabilize the problem.

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

An insulin infusion advisory system for type 1 diabetes patients based on non-linear model predictive control methods

In this paper, an Insulin Infusion Advisory System (IIAS) for Type 1 diabetes patients, which use insulin pumps for the Continuous Subcutaneous Insulin Infusion (CSII) is presented. The purpose of the system is to estimate the appropriate insulin infusion rates. The system is based on a Non-Linear Model Predictive Controller (NMPC) which uses a hybrid model. The model comprises a Compartmental Model (CM), which simulates the absorption of the glucose to the blood due to meal intakes, and a Neural Network (NN), which simulates the glucose-insulin kinetics. The NN is a Recurrent NN (RNN) trained with the Real Time Recurrent Learning (RTRL) algorithm. The output of the model consists of short term glucose predictions and provides input to the NMPC, in order for the latter to estimate the optimum insulin infusion rates. For the development and the evaluation of the IIAS, data generated from a Mathematical Model (MM) of a Type 1 diabetes patient have been used. The proposed control strategy is evaluated at multiple meal disturbances, various noise levels and additional time delays. The results indicate that the implemented IIAS is capable of handling multiple meals, which correspond to realistic meal profiles, large noise levels and time delays.

Optimal control of non-linear systems through hybrid cell-mapping/artificial-neural-networks techniques

In this paper, a real-time optimal control technique for non-linear plants is proposed. The control system makes use of the cell-mapping (CM) techniques, widely used for the global analysis of highly non-linear systems. The CM framework is employed for designing approximate optimal controllers via a control variable discretization. Furthermore, CM-based designs can be improved by the use of supervised feedforward artificial neural networks (ANNs), which have proved to be universal and efficient tools for function approximation, providing also very fast responses. The quantitative nature of the approximate CM solutions fits very well with ANNs characteristics. Here, we propose several control architectures which combine, in a different manner, supervised neural networks and CM control algorithms. On the one hand, different CM control laws computed for various target objectives can be employed for training a neural network, explicitly including the target information in the input vectors. This way, tracking problems, in addition to regulation ones, can be addressed in a fast and unified manner, obtaining smooth, averaged and global feedback control laws. On the other hand, adjoining CM and ANNs are also combined into a hybrid architecture to address problems where accuracy and real-time response are critical. Finally, some optimal control problems are solved with the proposed CM, neural and hybrid techniques, illustrating their good performance.

Control of Structures with Cubic and Quadratic Non-Linearities with Time Delay Consideration

This paper studies the effect of time delay on the active non-linear control of dynamically loaded flexible structures. The behavior of non-linear systems under state feedback control, considering a fixed time delay for the control force, is investigated. A control method based on non-linear optimal control, using a tensorial formulation and state feedback control is used. The state equations and the control forces are expressed in polynomial form and a performance index, quadratic in both state vector and control forces, is used. General polynomial representations of the non-linear control law are obtained and implemented for control algorithms up to the fifth order. This methodology is applied to systems with quadratic and cubic non-linearities. Strongly non-linear systems are tested and the effectiveness of the control system including a delay for the application of control forces is discussed. Numerical results indicate that the adopted control algorithm can be efficient for non-linear systems, chiefly in the presence of strong non-linearities but increasing time delay reduces the efficiency of the control system. Numerical results emphasize the importance of considering time delay in the project of active structural control systems.

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 critique of neural networks for discrete-time linear control

This paper discusses the use of multi-layer perceptron networks for linear or linearizable, adaptive feedback.control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parametrization. A comparison is made with standard, non-perceptron algorithms, e.g. self-tuning control, and it is shown how gross over-parametrization can occur in the neural network case. Because of the resultant heavy computational burden and poor controller convergence, a strong case is made against the use of neural networks for discrete-time linear control.

Non-linear dynamics of a tower orchard sprayer based on an inverted pendulum model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On non-linear and non-ideal interactions in two vibrating problems

In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power, as that provided by a DC motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a non-ideal problem. In this work, we considerer two non-ideal problems analyzed by using numerical simulations. The existence of the Sommerfeld effect was verified, that is, the effect of getting stuck at resonance (energy imparted to the DC motor being used to excite large amplitude motions of the supporting structure). We considered two kinds of non-ideal problem: one related to the transverse vibrations of a shaft carrying two disks and another to a piezoceramic bar transducer powered by a vacuum tube generated by a non-ideal source Copyright © 2007 by ASME.

Optimal linear control to parametric uncertainties in a micro electro mechanical system

This paper, a micro-electro-mechanical systems (MEMS) with parametric uncertainties is considered. The non-linear dynamics in MEMS system is demonstrated with a chaotic behavior. We present the linear optimal control technique for reducing the chaotic movement of the micro-electromechanical system with parametric uncertainties to a small periodic orbit. The simulation results show the identification by linear optimal control is very effective. © 2013 Academic Publications, Ltd.

Vibration Control Applied in a Semi-Active Suspension using Magneto Rheological Damper and Optimal Linear Control Design

In this paper we study the behavior of a semi-active suspension witch external vibrations. The mathematical model is proposed coupled to a magneto rheological (MR) damper. The goal of this work is stabilize of the external vibration that affect the comfort and durability an vehicle, to control these vibrations we propose the combination of two control strategies, the optimal linear control and the magneto rheological (MR) damper. The optimal linear control is a linear feedback control problem for nonlinear systems, under the optimal control theory viewpoint We also developed the optimal linear control design with the scope in to reducing the external vibrating of the nonlinear systems in a stable point. Here, we discuss the conditions that allow us to the linear optimal control for this kind of non-linear system.