Integer Order PID Controller Research Articles

Numerical Study of Modified Mathieu Equation with Time-Delayed Fractional-Order PIλDμ Controller using a Recursive Filter

Abstract In this paper, we have studied numerically free vibration of modified Mathieu Equation with quadratic damping using time-delayed FOPID (fractional-order Proportional-Integral-Derivative) controller focussed on displacement feedback. A special filter known as Oustaloup filter is employed to carry out the fractional order differetiation and integration numerically with the help of Matlab Simulink. The effect of time delayed FOPID with displacement feedback on control performance of the parametrically excited system based on modified Mathieu equation are studied by time response. The results show that the system becomes unstable when time delay increases. It also shows that the use of FOPID becomes quite advantageous over traditional integer order PID (IOPID) control only when the natural frequency is kept low. Equivalent damping of the system could be enhanced to increase the differential gain in order to stabilize the system. On increasing the proportional and integral gain, the system gets destabilized which is in good agreement with the classical integer-order PID control

Design and Implementation of Novel Fractional-Order Controllers for Stabilized Platforms

As a position servo system to isolate disturbance from its carrier, stabilized platform requires high-precision and high-adaptability control. However, conventional integer-order PID (IOPID) control fails to meet that requirement. In this paper, a new controller design scheme is proposed for stabilized platform based on fractional calculus. The designed controller is called fractional-order PID (FOPID) controller, which has two extra parameters compared to conventional PID controller. On one hand, it provides more degrees of freedom to design FOPID controller. On the other hand, its differential order and integral order provides more flexibility to tune the controller performance. Therefore, a design method of FOPID controller based on dynamic software modeling is presented. To obtain the ideal controller's parameters, the particle swarm optimization (PSO) bionic algorithm is used to optimize an objective function. In addition, software simulation platform and hardware experiment system are built to design and test the FOPID controller. Finally, the results of simulation and experiment are included to show the effectiveness of the new control method.

Implementation of Simplified Fractional-Order PID Controller Based on Modified Oustaloup’s Recursive Filter

The aim of this paper is to simplify the design of fractional-order PID controllers. Because the analytical expressions and operations of fractional-order systems are complex, numerical approximation tool is needed for the simulation analysis and engineering practice of fractional-order control systems. The key to numerical approximation tool is the exact approximation of the fractional calculus operator. A commonly used method is to approximate the fractional calculus operator with an improved Oustaloup’s recursive filter. Based on the modified Oustaloup’s recursive filter, a mathematical simplification method is proposed in this paper, and a simplified fractional-order PID controller (SFOC) is designed. The controller parameters are tuned by using genetic algorithm (GA). Effectiveness of the proposed control scheme is verified by simulation. The performance of SFOC has been compared with that of the integer-order PID controller and conventional fractional-order PID controller (CFOC). It is observed that SFOC requires smaller effort as compared with its integer and conventional fractional counterpart to achieve the same system performance.

Fractional-order PID controller for permanent magnet DC motor based on PSO algorithm

<span>This paper proposes the fractional-order proportional integral derivative (FOPID) controller, as a speed controller for permanent magnet direct current (PMDC) motor, instead of the traditional integer-order PID controller. The FOPID controller is the general form of the integer-order PID controllers, which found wide applications in all engineering fields. In this work a hybrid M-file and SIMULINK program is developed to simulate the overall system, the FOPID controller has five associated parameters. The optimum values of those parameters are found out by using particle swarm optimization technique. Simulation results show excellent command speeds tracking and superior dynamic response in conjunction with that of the integer-order PID controller. The proposed controller shows a high ability to overcome any external disturbance the system may be exposed; also, it performs a high degree of robustness to control the system in motoring and regenerative operating modes.</span>

Fractional Order PID Controller Design for Supply Manifold Pressure Control of Proton Exchange Membrane Fuel Cell

Abstract In this work, fractional order PIλDµ (FOPID) controller designed to enhance the dynamic performance of the Proton Exchange Membrane (PEM) fuel cell. The control objective is to regulate the supply manifold pressure on cathode side to maintain oxygen excess ratio of the PEM fuel cell. The higher order PEM fuel cell model is approximated to First order plus time delay (FOPTD) model for controller design and analysis. The proposed FOPID controller is designed based on minimization of Integral Absolute Error (IAE) with pre specified maximum sensitivity (Ms) as a constraint. Uncertainty and measurement noise analysis is carried out to verify the robustness of the designed controller. The simulation results of proposed FOPID controller is compared with other designing methods. Based on minimization of IAE value, the SP 1.4 FOPID controller produces IAE value of 0.255 where as AMIGO 1.4 tuning method and ZN based FOPID tuning methods produces 0.263 and 3.817 respectively for perfect case. Based on maximum sensitivity Ms is 1.4, the SP 1.4 FOPID controller produces Ms of 1.4 where as AMIGO 1.4 PID and ZN based FOPID tuning methods produces Ms of 1.5 and 1.25 respectively for perfect case, which indicates that the proposed SP 1.4 FOPID controller is robust. The proposed SP 1.4 FOPID provides better values (rise time of 0.331 sec, settling time of 0.692 sec and percentage of peak overshoot of 0.797 for perfect case) when compared with other methods. From simulation results, for the control of supply manifold pressure of PEM fuel cell, the proposed fractional-order PID controllers improves the closed loop performance in terms of rise time, settling time and percentage of peak overshoot when compared to the integer-order PID controllers.

Design and Implementation of Real Time Integer Order PID Controller for Infrared Heater

A modified technique is introduced to understand the design of Integer order PID controller. Due to simple tuning rules, conventional PID controller has the great success with the automatic tuning feature and tables that simplify their design. The Integer order PID controller show better robustness performance with the comparison of PID control's experimental to Heating control system (HIL). In Integer order control, design of simulation model of system can be designed straight forwardly with design specification based on frequency analysis which can be change continuously. The simulation analysis and real time results shows that Integer order PID controller is more effective way to enhance the system control performance.

Efficient control of a 3-link planar rigid manipulator using self-regulated fractional-order fuzzy PID controller

A self-regulated fractional-order fuzzy proportional–integral–derivative (SRFOFPID) controller is proposed to control a highly non-linear, complex and coupled 3-link planar rigid robotic manipulator in a virtual industrial environment. Industrial environment was simulated by introducing different kind of disturbances in the system and sensor noise. Proposed SRFOFPID controller is a direct non-linear adaptive controller having self-regulating feature and has been realized using fractional-order operators i.e. integrator and differentiator in self-regulated integer-order fuzzy PID (SRIOFPID) controller. Gains of SRFOFPID and SRIOFPID controllers are optimized using Backtracking Search Algorithm by minimizing an amalgamation of integral absolute error signal and integral absolute change in control signal as cost function. Performance of SRFOFPID and SRIOFPID controllers are assessed and compared with reference path under virtually simulated industrial environment. Presented intensive simulation studies revealed that both the controllers offered decent reference trajectory tracking performance under nominal operating conditions while SRFOFPID controller offered exceptionally robust performance under industrial scenario and uncertainties. Finally, the stability analysis of overall closed loop system is performed using small gain theorem and necessary and sufficient bounded-input and bounded-output stability conditions are established.

Fractional-order self-tuned fuzzy PID controller for three-link robotic manipulator system

With increasing links in a manipulator system, efficacy and usefulness are enhanced along with the complexity. In this paper, a fractional-order self-tuned fuzzy PID (FOSTFPID) controller is investigated to control a highly nonlinear, coupled multi-input multi-output, three-link rigid robotic manipulator system. The performance of FOSTFPID controller is investigated for trajectory tracking, disturbance rejection, noise suppression and model uncertainty. The comparative analysis between the performances of FOSTFPID, fractional-order fuzzy PID and integer-order self-tuning fuzzy PID controllers, all tuned for minimum weighted sum of integral of absolute error and integral of absolute change in controller output using cuckoo search algorithm, revealed a clear superiority of FOSTFPID for trajectory tracking, disturbance rejection, noise suppression and model uncertainty.

Synthesis of a fractional-order PIλDμ-controller for a closed system of switched reluctance motor control

The relevance of creating high-quality control systems for electric drives with a switched reluctance motor (SRM) was substantiated. Using methods of mathematical modeling, transient characteristics of the process of turn-on of SRMs with various moments of inertia were obtained. Based on analysis of the obtained transient characteristics, features of the SRM turn-on process determined by dynamic change of parameters of the SRM during its turn-on were shown. Low accuracy of SRM identification using a fractionally rational function of rat34 class was shown. Regression coefficient of the resulting model was 85 %. Based on analysis of transient characteristics of the SRM turn-on process, a hypothesis was put forward about the possibility of identifying the SRM by means of a fractional-order transfer function. Using the methods of mathematical modeling, transient characteristics of the process of turning-on the SRMs with various moments of inertia were obtained. Using the FOMCON MATLAB Toolbox, identification of the SRM turn-on process with the help of a fractional-order transfer function of second order was performed. Regression coefficient of the resulting model was 93–96 %. For the obtained fractional-order transfer functions, a method of synthesis of a fractional-order PI λ D μ controller optimized in terms of minimum integral square error of the transition function of the closed system of fractional-order control of objects was implemented. The FOMCON MATLAB Toolbox was used for synthesis of the PI λ D μ controller. Comparative analysis of the SRM turn-on processes in both open and closed control systems with a classical integer-order PID controller and with a fractional-order PI λ D μ controller was made. Use of the fractional-order PI λ D μ controller in comparison with the classical integer-order regulator makes it possible to reduce overshoot from 13.3 % to 2.64 %, increase speed of the closed ACS, decrease regulation time from 1.48 s to 0.53 s while reducing variability of transient characteristics. The study results can be used to improve performance of closed systems for controlling angular velocity of the SRM

Delta Parallel Robotic Manipulator Tracking Control using Fractional Order Controllers

Tracking control of robotic manipulators presents many challenges on the controller design due to the system nonlinear behavior. This paper presents the design of a tracking control for a parallel robotic manipulator using a fractional order PID controller with the feedback linearization technique. The kinematic and dynamic models of the manipulator are obtained, and a parametric identification of the dynamic model is performed using the recursive least squares algorithms. A MSC-ADAMS/MATLAB co-simulation model of the manipulator is built to perform the identification and control tasks. The inverse dynamics method gives a linearized and uncoupled model of the robotic system, which is employed to design the fractional order PID controller. The fractional order PID controller is contrasted with an integer order PID controller on performing tracking tasks. A quantitative performance analysis of the controllers is made calculating the performance indices for different tracking tasks. Obtained results show that the fractional order PID controller has a better performance on tracking tasks than the integer order PID controller.

Fractional-Order PID Motion Control for AUV Using Cloud-Model-Based Quantum Genetic Algorithm

Aiming to improve the performance of motion for autonomous underwater vehicle (AUV), a fractional-order PID strategy is proposed. It is a more generalized form for the conventional integer-order PID controller, keeping its simplicity and utilizing the generalized derivative and integral control actions. The fractional-order PID controller has been successfully applied to heading control, diving control and path-following system of AUV on sea trial. In addition, the fractional-order closed-loop system has proven to be stable. By comparing simulations and experiments, the satisfactory performance, such as overshoot, settling time and steady-state error, has been achieved. The cloud-model-based quantum genetic algorithm (CQGA) is employed to tune coefficients of fractional-order PID controller. The quantum bits and quantum superposition states avoid the pressure of selection and maintain the diversity of population in chromosome coding. Due to the randomness and stability tendency of cloud droplets, the cloud crossover operator and the cloud mutation operator can effectively overcome the shortcomings of premature and slow searching speed. Numerical simulations show that the CQGA is more efficient to find the optimal coefficients of fractional-order PID controller than GA.

Fractional-Order Water Level Control Based on PLC: Hardware-In-The-Loop Simulation and Experimental Validation

An industrial-oriented water tank level control system with PLC- and Simulink-based fractional-order controller realizations is presented. The discrete fractional-order and integer-order PID implementations are realized via the PLC and Simulink simulator. The benefits of the fractional-order PID compared to the integer-order PID control are confirmed by the hardware-in-the-loop (HIL) simulations and experiments. HIL simulations are realized using real-time communication between PLC and Simulink. The fractional-order controller is obtained for a desired phase/gain margin and validated via HIL simulations and experimental measurements.

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

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.

PLC-based Discrete Fractional-order Control Design for an Industrial-Oriented Water Tank Volume System with Input Delay

Abstract We present PLC-based fractional-order controller design for an industrial-oriented water tank volume control application. The system comprises input delay which is a typified characteristic in such industrial process control applications. The particular contribution of this work is on discrete fractional-order PID implementation via PLC and its application to the aforementioned realistic water tank test bed. Stability and robustness properties of fractional-order discrete PID feedback-loops for different approximation methods and orders are also shown. Fractional-order controllers are obtained for a variety of stability margin choices, and benefits of the non-integer-order controllers compared to the integer-order PID control are illustrated via simulation and experimental runs on a realistic test-bed.

Tracking Control for Robotic Manipulators using Fractional Order Controllers with Computed Torque Control

This paper presents the tracking tasks control for a robotic manipulator employing a fractional order PID controller with the computed torque control strategy. The proposed control strategy is contrasted with an integer order PID controller with the computed torque control strategy. The robotic system is a two degree of freedom manipulator simulated using a MSCADAMS/MATLAB cosimulation model. The manipulator dynamic model is identified employing the recursive least squares algorithm. The fractional order PID controller is tuned using optimization techniques. Controllers robustness is evaluated against the presence of external disturbances in the joints torques, random noise in the feedback loop and payload variations. Obtained results show that the fractional order PID controller with the computed torque control strategy has better performance and robust stability against the presence of the analyzed external disturbances for tracking tasks.

Fractional order PID for tracking control of a parallel robotic manipulator type delta

This paper presents the tracking control for a robotic manipulator type delta employing fractional order PID controllers with computed torque control strategy. It is contrasted with an integer order PID controller with computed torque control strategy. The mechanical structure, kinematics and dynamic models of the delta robot are descripted. A SOLIDWORKS/MSC-ADAMS/MATLAB cosimulation model of the delta robot is built and employed for the stages of identification, design, and validation of control strategies. Identification of the dynamic model of the robot is performed using the least squares algorithm. A linearized model of the robotic system is obtained employing the computed torque control strategy resulting in a decoupled double integrating system. From the linearized model of the delta robot, fractional order PID and integer order PID controllers are designed, analyzing the dynamical behavior for many evaluation trajectories. Controllers robustness is evaluated against external disturbances employing performance indexes for the joint and spatial error, applied torque in the joints and trajectory tracking. Results show that fractional order PID with the computed torque control strategy has a robust performance and active disturbance rejection when it is applied to parallel robotic manipulators on tracking tasks.

Optimal PI$^{{\lambda}}$ D$^{{\mu}}$ Controller Design for Two Wheeled Inverted Pendulum

Fractional order controllers have a growing popularity in last years and they give more flexibility to researchers for designing a controller. In this paper, a fractional order PID controller is designed for the position control of a two wheeled inverted pendulum. The pendulum is modeled with DC electrical motors to obtain a more realistic model. Integer order PID controller is also designed to make a comparison with fractional order controller and all controllers are optimized by swarm algorithms to be sure obtained the best performance for each controller. A fractional order PID controller has two extra parameters ( $\lambda $ and $\mu$ ) and totally five parameters to be optimized. Optimization algorithms are powerful tools for designing a controller, and guarantee finding an optimum result. However, each optimization algorithm has a different performance not only because of the structure of the algorithm but also depending on the optimization problem. Because of this, four popular optimization algorithms (artificial bee colony, particle swarm optimization, grey wolf optimizer, and cuckoo search algorithm) are used to tune controller parameters, and compared regard with the optimized system performance. The results show that the best performance is obtained by the fractional order PID controller, which optimized by artificial bee colony algorithm. The fractional order PID controllers have also better performance than integer order PIDs when used the same optimization algorithm for tuning.

Novel Optimum Magnitude Based Fractional Order Controller Design Method

Due to adding the extra degree of freedom, the fractional order PID controllers can achieve better control performance than the integer order PID controllers. The present paper proposes a novel fractional order controller design method, inspired by the Kessler’s optimum magnitude method. The explicit tuning rules are accessible even to less experienced users in fractional calculus, taking only the advantages of the controller and not the disadvantage of complex mathematical background. The advantages of the method are demonstrated by a case study.

Real Time Implementation of Optimized I-PD Controller for the Magnetic Levitation System using Jaya Algorithm

Designing a suitable controller for a nonlinear and unstable plant is always very challenging to the control system practitioners. In this article, Integral - Proportional Derivative (I-PD) controller has been designed and implemented in simulation and real time for the Magnetic levitation (Maglev) system which is both nonlinear and unstable in nature. The nonlinear Maglev plant has been linearized around the equilibrium point to obtain the linearized model transfer function. The objective function, which has been formulated by taking the modulus of the characteristic polynomial of the plant along with the controller at dominant pole location, has been minimized using the recently evolved Jaya algorithm. The performance of the I-PD controller has been compared with that of the 1-DOF and 2-DOF Integer Order (IO) and Fractional Order (FO) PID controller (Swain et al., 2017). The result of comparison reveals that the I-PD controller optimized using Jaya algorithm outperforms the other controllers in terms of time domain and frequency domain specifications except the phase margin criteria. The robustness analysis has also been incorporated in this study to show the robust behaviour of the I-PD controller.

Optimal Design of Fuzzy Fractional Order PIλDµ Controller for Redundant Robot

The aim of this paper is to compare the performances of new fuzzy fractional order (FO) PID (fuzzy PIλDµ) controller with integer order fuzzy PID and PID controllers for controlling redundant robotic system for trajectory tracking problems. A five-degree of freedom (5-DOF) redundant manipulator is an MIMO, and extremely non-linear system. The performances of the controlled system are poorly affected by the presence model uncertainties and external disturbances. Thus, controller design for redundant robot system is difficult job for controller designer. The tuning of each controller’s parameters is completed with artificial bee colony (ABC) optimization techniques. For investigating the effectiveness, the robustness testing is also investigated for model uncertainties and disturbance rejection. After many numerical simulations and comparison with conventional controller i.e. fuzzy PID and PID controllers, it is found that fuzzy PIλDµ controller can not only promise best trajectory tracking but also meliorate the plant robustness for model uncertainties and disturbance rejection.