Juri Belikov

Design and implementation of fractional-order PID controllers for a fluid tank system

In this paper, we investigate the practical problems of design and digital implementation of fractional-order PID controllers used for fluid level control in a system of coupled tanks. We present a method for obtaining the PIλDμ controller parameters and describe the steps necessary to obtain a digital implementation of the controller. A real laboratory plant is used for the experiments, and a hardware realization of the controller fit for use in embedded applications is proposed and studied. The majority of tasks is carried out by means of the FOMCON (“Fractional-order Modeling and Control”) toolbox running in the MATLAB computing environment.

Fractional-order controller design and digital implementation using FOMCON toolbox for MATLAB

In this paper, we present the suite of tools of the FOMCON (“Fractional-order Modeling and Control”) toolbox for MATLAB that are used to carry out fractional-order PID controller design and hardware realization. An overview of the toolbox, its structure and particular modules, is presented with appropriate comments. We use a laboratory object designed to conduct temperature control experiments to illustrate the methods employed in FOMCON to derive suitable parameters for the controller and arrive at a digital implementation thereof on an 8-bit AVR microprocessor. The laboratory object is working under a real-time simulation platform with Simulink, Real-Time Windows Target toolbox and necessary drivers as its software backbone. Experimental results are provided which support the effectiveness of the proposed software solution.

Incorporation of fractional-order dynamics into an existing PI/PID DC motor control loop.

The problem of changing the dynamics of an existing DC motor control system without the need of making internal changes is considered in the paper. In particular, this paper presents a method for incorporating fractional-order dynamics in an existing DC motor control system with internal PI or PID controller, through the addition of an external controller into the system and by tapping its original input and output signals. Experimental results based on the control of a real test plant from MATLAB/Simulink environment are presented, indicating the validity of the proposed approach.

Recognition of the Surgeon's Motions During Endoscopic Operation by Statistics Based Algorithm and Neural Networks Based ANARX Models

Abstract The problem of recognition and short time prediction of the surgeons hand motions during surgical endoscopic operation are approached in the present contribution using neural network based nonlinear modeling techniques and statistics based segmentation of the operating room. It is shown that proposed technique provide precise recognition of surgeons motions.

A novel taylor series based approach for control computation in NN-ANARX structure based control of nonlinear systems

This paper presents an alternative approach for control computation in a closed loop of discrete-time nonlinear system and NN-ANARX based dynamic output feedback. Proposed technique is based on an application of Taylor series expansion for computation of control directly from neural network based model. Two modifications of the algorithm are proposed for both single-input single-output and multi-input multi-output nonlinear systems. The effectiveness of the proposed approach is demonstrated on numerical examples.

Realization of nonlinear MIMO system on homogeneous time scales

Abstract The paper addresses a state space realization problem of a set of higher order delta-differential input–output equations, defined on a homogeneous time scale. The algebraic framework of differential one-forms is applied to formulate necessary and sufficient solvability conditions. This approach applies the total differential operator to analytic system equations to obtain the infinitesimal system description in terms of one-forms. This representation can be converted into polynomial system description by interpreting the polynomial indeterminate as the delta derivative acting on one-forms. The system description in terms of two matrices over skew polynomial ring is then used to derive explicit formulas for the differentials of state coordinates that significantly simplify the calculations. The formulas are found from the left quotients computed by the left Euclidean division algorithm.

State-space control of nonlinear systems identified by ANARX and Neural Network based SANARX models

A state-space technique for control of nonlinear SISO systems identified by an Additive Nonlinear Autoregressive eXogenous (ANARX) model is presented. Two cases are shown. In the first case system model is given explicitly in the form of ANARX structure. In the second case controlled system is identified by Neural Network based Simplified Additive NARX (NN-SANARX) model linearized by dynamic feedback. The neural network based model is represented in the discrete-time state-space form. The effectiveness of the approach proposed in the paper is demonstrated on numerical examples with SISO and MIMO systems.

Adjoint Polynomial Formulas for Nonlinear State-Space Realization

This paper focuses on computational aspects of the realization of nonlinear multi-input multi-output systems. Instead of the algorithmic solutions, provided in earlier works, the explicit formulas are presented, which enable to compute the differentials of the state coordinates directly from the polynomial description of the nonlinear system. The solution is based on the concept of adjoint polynomials and requires a minimal amount of computations. The formulas are implemented in computer algebra system Mathematica and made available online via web Mathematica tools.

APPLICATION OF NEURAL NETWORKS BASED ANARX STRUCTURE TO BACKING UP CONTROL OF A TRUCK-TRAILER

Abstract Combination of NN-based modelling and dynamic feedback linearization is proposed in present paper as a solution for the problem of backing up control of a truck-trailer. Backing up truck-trailer is modelled by NN based Additive Nonlinear Autoregressive Exogenous model which is linearized by dynamic output feedback.

Calculation of the control signal in MIMO NN-based ANARX models: Analytical approach

In this paper, an application of Neural Networks based Additive Nonlinear AutoRegressive eXogenous (NN-ANARX) structure is investigated for modeling and control of nonlinear multi-input-multi-output (MIMO) systems. A novel analytical technique for calculation of control signal is proposed. After that the ANARX-based dynamic output feedback linearization control algorithm is applied for control of nonlinear MIMO systems. The effectiveness of the proposed technique is demonstrated on numerical examples.