Fractional Differential Equations

In this paper, atom search optimization (ASO) algorithm and a novel chaotic version of it [chaotic ASO (ChASO)] are proposed to determine the optimal parameters of the fractional-order proportional+integral+derivative (FOPID) controller for dc motor speed control. The ASO algorithm is simple and easy to implement, which mathematically models and mimics the atomic motion model in nature, and is developed to address a diverse set of optimization problems. The proposed ChASO algorithm, on the other hand, is based on logistic map chaotic sequences, which makes the original algorithm be able to escape from local minima stagnation and improve its convergence rate and resulting precision. First, the proposed ChASO algorithm is applied to six unimodal and multimodal benchmark optimization problems and the results are compared with other algorithms. Second, the proposed ChASO-FOPID, ASO-FOPID, and ASO-PID controllers are compared with GWO-FOPID, GWO-PID, IWO-PID, and SFS-PID controllers using the integral of time multiplied absolute error (ITAE) objective function for a fair comparison. Comparisons were also made for the integral of time multiplied squared error (ITSE) and Zwe-Lee Gaing's (ZLG) objective function as the most commonly used objective functions in the literature. Transient response analysis, frequency response (Bode) analysis, and robustness analysis were all carried out. The simulation results are promising and validate the effectiveness of the proposed approaches. The numerical simulations of the proposed ChASO-FOPID and ASO-FOPID controllers for the dc motor speed control system demonstrated the superior performance of both the chaotic ASO and the original ASO, respectively.

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Optimal Tuning of Fractional Order PID Controller for DC Motor Speed Control via Chaotic Atom Search Optimization Algorithm

Linear fractional order controllers; A survey in the frequency domain

Converter-driven direct current (dc) motors exhibit various advantages in industry, but impose several challenges to higher precision speed regulation in the presence of parametric uncertainties and exogenous, time-varying load torque disturbances. In this paper, the robust predictive speed regulation problem of a generic dc–dc buck converter-driven permanent magnet dc motors is addressed by using an output feedback discrete-time model predictive control algorithm. A new discrete-time reduced-order generalized proportional-integral observer (GPIO) is proposed to reconstruct the virtual system states as well as the lumped disturbances. The estimates of GPIO are then collected for output speed prediction. An optimized duty ratio law of the converter is obtained by solving a constrained receding horizon optimization problem, where the operational constraint on control input is explicitly taken into account. Finally, the effectiveness of the proposed new algorithm is demonstrated by various experimental testing results.

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Robust Predictive Speed Regulation of Converter-Driven DC Motors via a Discrete-Time Reduced-Order GPIO

Physical servo systems are affected by disturbances, uncertainties, and resource restrictions. In this paper, an event-triggered active disturbance rejection control approach is proposed to achieve position tracking of dc torque motors. An event-based sampler together with an extended state observer is introduced, which allows the joint observation of the system state, and the total disturbance induced by model uncertainty and intermittent sampling. Based on the observation results, closed-loop control is achieved with guaranteed stable tracking performance. To quantify the effect of event-based sampling, a quantitative relationship between the asymptotic upper bound of tracking error and the parameters in the event-based sampler is developed. The control strategy is applied to a dc torque motor system, and comparative experimental results indicate that for different reference signals, the proposed event-based control strategy can achieve satisfactory tracking performance with reduced sampling cost.

Event-Triggered Active Disturbance Rejection Control of DC Torque Motors

The aim of this paper is to employ fractional order proportional integral derivative &#x0028 FO-PID &#x0029 controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system &#x0028 MLS &#x0029, which is inherently nonlinear and unstable system. The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller. An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored. The controller parameters are tuned using dynamic particle swarm optimization &#x0028 dPSO &#x0029 technique. Effectiveness of the proposed control scheme is verified by simulation and experimental results. The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers. It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.

Design and implementation of digital fractional order PID controller using optimal pole-zero approximation method for magnetic levitation system

The aim of paper is to employ digital fractional order proportional integral derivative (FO-PID) controller for speed control of buck converter fed DC motor. Optimal pole-zero approximation method in discrete form is proposed for realization of digital fractional order controller. The stand-alone controller is implemented on embedded platform using digital signal processor TMS320F28027. The five tuning parameters of controller enhance the performance of control scheme. For tuning of the controller parameters, dynamic particle swarm optimization technique is employed. The proposed control scheme is simulated on MATLAB and verified by experimental results. Performance comparison shows better speed control of separately excited DC motor with the realized digital FO-PID controller than that of the integer order PID controller.

Design and Realization of Stand-Alone Digital Fractional Order PID Controller for Buck Converter Fed DC Motor

In industrial drives applications, fractional order controllers can exhibit phenomenal impact due to realization through digital implementation. Digital fractional order controllers have created wide scope as it possess the inherent advantages like robustness against the plant parameter variation. This paper provides brief design procedure of fractional order proportional-integral-derivative (FO-PID) controller through the indirect approach of approximation using constant phase technique. The new modified dynamic particle swarm optimization (IdPSO) technique is proposed to find controller parameters. The FO-PID controller is implemented using floating point digital signal processor. The building blocks are designed and assembled with all peripheral components for the 1.5 kW industrial DC motor drive. The robust operation for parametric variation is ascertained by testing the controller with two separately excited DC motors with the same rating but different parameters.

Demonstrative fractional order - PID controller based DC motor drive on digital platform.

This paper deals speed control of a Permanent Magnet Brushless Direct Current (PMBLDC) Motor using Fractional Order PID (FO-PID) controller tuned with different algorithms for PMBLDC motor. The inherent advantages of the FO-PID over conventional are its added fractions variables. The FO-PID controller is a generalized form of PID controller in which order of integration (I) and differentiation is any real number. It is shown that the proposed controller, which has five independent parameters (Kp, Ki, Kd, λ, μ) to tune, provides a powerful framework to control PMBLDC motor. The gain of PID controller is obtained by conventional methods of Ziegler-Nicholas (ZN), Cohen Coon (CC) and Amstron-Hagglund (AH). The Oustaloup's method is used to approximate the fractional order. Integration (s-λ) and differentiation (sμ) order is tuned using Nelder-Mead (NM), Interior point (IP) and Active set (AS) algorithm. The controller analysis is presented with the plant to ascertain the performance of the PMBLDC motor. Improvement in transient performance of the system using FO-PID controller is observed in the comparative results.

Design and tuning of fractional order PID controller for speed control of permanent magnet brushless DC motor

The speed control of the DC motor fed through buck-converter is generally employed with conventional integer order PID. The closed loop speed control of these drives are prone to deteriorate in their performance over a period of time. This paper proposes the fractional order (FO) PID speed controller with DC motor. The feasibility of more tuning parameters enhances the performance. Oustaloup's approximation method is used to approximate the fractional order differentiator and integrator. This controller performances are tested in the simulation mode.

Amit S. Chopade

Papers

Design and implementation of digital fractional order PID controller using optimal pole-zero approximation method for magnetic levitation system

Design and Realization of Stand-Alone Digital Fractional Order PID Controller for Buck Converter Fed DC Motor

Demonstrative fractional order - PID controller based DC motor drive on digital platform.

Design and tuning of fractional order PID controller for speed control of permanent magnet brushless DC motor

Fractional order speed controller for buck-converter fed DC motor