Aleksei Tepljakov

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.

Implementation and real-time simulation of a fractional-order controller using a MATLAB based prototyping platform

Design and implementation of fractional-order controllers are important problems in contemporary control design practice. In this paper, we discuss issues associated with hardware implementation and real-time simulation of a particular fractional-order controller. The simulation is performed in MATLAB, which is interfaced with the controller by means of a data acquisition board. We provide design steps necessary to obtain a digital implementation of a fractional-order lead-lag compensator as well as the description of the used controller and data acquisition board. An example, illustrating the use of the prototyping platform, is provided.

Design of retuning fractional PID controllers for a closed-loop magnetic levitation control system

In this paper, we study the problem of fractional-order PID controller design for an unstable plant-a laboratory model of a magnetic levitation system. To this end, we apply model based control design. A model of the magnetic lévitation system is obtained by means of a closed-loop experiment. Several stable fractional-order controllers are identified and optimized by considering isolated stability regions. Finally, a nonintrusive controller retuning method is used to incorporate fractional-order dynamics into the existing control loop, thereby enhancing its performance. Experimental results confirm the effectiveness of the proposed approach. Control design methods offered in this paper are general enough to be applicable to a variety of control problems.

Closed-loop identification of fractional-order models using FOMCON toolbox for MATLAB

Closed-loop identification methods attract significant interest because they grant the possibility to obtain industrial process models without the need to perform separate open-loop experiments thus avoiding potential production losses. In this paper, we study the problem of identifying a fractional-order process model of a plant working in a closed control loop. We consider both the direct and the indirect identification approaches. Identification is performed offline by means of minimizing the model output error and is based on data collected in the time domain. We provide the description of the software implementation of the proposed identification procedure. All necessary computations are performed in FOMCON toolbox for MATLAB. An exemplary closed-loop system is studied. It comprises a real-life fractional-order PID controller prototype, and a simulated model of a plant running on a personal computer based real-time prototyping platform. Experimental results are provided with relevant discussion.

Robust FOPI and FOPID controller design for FFOPDT plants in embedded control applications using frequency-domain analysis

In this paper, we address the problem of fractional-order PID (FOPID) controller design for a fractional first-order plus dead time (FFOPDT) plant, the characteristics of which are studied. All the equations involved in the computation of control system robustness criteria in the frequency domain are derived, and an algorithm based on the Newton-Raphson method is proposed to obtain the solutions thereof. The performance criteria are considered as the basis for optimizing the parameters of the FOPID controller. The initial gains of the controller are obtained using well established conventional PID tuning rules. For optimization a simple parameter sweep method is used, as well as the Nelder-Mead simplex search method. An illustrative example of the controller design procedure is provided. The results are partially carried over to a FOPID controller prototype. The results of this work can be applied to embedded control and are useful in solving automatic controller tuning problems.

Application of MPC to industrial water boiler control system in district heat plant

The main goal of this paper is to identify an industrial water boiler model and design a model predictive controller (MPC). The boiler model was identified from the real process data collected during a heating season. Controller was designed and tested in virtual environment and its performance was compared with performance of classical PI control algorithm that is currently used to control a boiler system. Use of the designed controller leads to significant improvement of accumulated output error.

Gain and order scheduled fractional-order PID control of fluid level in a multi-tank system

Gain scheduling is widely regarded as an effective nonlinear control technique, and its extension to fractional-order control is a natural step. In this paper, we investigate a particular method based on a gain and order scheduling approach for fractional-order PID controllers. The method is applied to the control of a real-life laboratory model of an industrial multi-tank system. Gain and order scheduling is realized by means of a control law comprising two static PID controllers and an appropriate control blending rule providing this way means for stability analysis of the control system. The design of controllers for level control in the first tank is carried out by considering linear fractional-order approximations of the nonlinear model of the process with locally applicable frequency-domain robustness specifications. The controller for the second tank is obtained using time-domain optimization of the transient response. In addition, an extended Kalman filter is designed to reduce measurement noise propagation into the control law thereby enhancing the performance of the pump. The majority of necessary computations, including those related to controller design, are performed numerically in the FOMCON toolbox for MATLAB.

FOMCON: Fractional-Order Modeling and Control Toolbox

In the following chapter, FOMCON toolbox for MATLAB/Simulink is described. The chapter has the following structure. First, an overview of the toolbox is provided in Sect. 6.1. Next, the identification, control, and implementation modules comprising the toolbox are described in Sects. 6.2–6.4, respectively. Illustrative examples are provided for the most important tools available in each module. Finally, in Sect. 6.5 conclusions are drawn.