Integer Order Proportional Integral Derivative Controller Research Articles

Fractional Order Modeling and Control of an Articulated Robotic Arm

This paper presents a fractional order system modeling of a robotic arm and the development of a Fractional Order PID (FOPID) controller applied to the system. The controller technique originated from non-integer calculus, which improves the robotic arm's overall stability and positioning. The robotic arm system is modeled using the non-integer order technique in order to improve system accuracy. Thus, a non-integer order Proportional Integral Derivative (PID) control method is implemented to stabilize the plant positioning. Using MATLAB/Simulink the FOPID controller simulations were confirmed and compared to the Integer Order PID (IOPID) controller for tracking the robotic arm positioning. Simulation outcomes imply that the proposed non-integer controller increases the system stability and position with/without external disturbances being present in the environment.

Concurrent frequency–voltage stabilization for hybrid microgrid with virtual inertia support

AbstractThis paper presents a novel control scheme for combined frequency and voltage stabilization of an islanded multi‐generator hybrid microgrid (IHμG). The control concept incorporates an improved virtual inertia support scheme (IVIS) and the recently developed yellow saddle goatfish technique (YSGA) to obtain optimal control parameters. IHμG model consists of an AVR‐based voltage compensating loop for synchronous biodiesel generator, wind generator, wave generator, photon exchange membrane fuel cell (PEMFC), and controllable heat pump and freezer. An integer order proportional‐integral‐derivative (IOPID) controller is leveraged for frequency‐voltage stabilization. A comparative response assessment has been performed with/without IVIS. The utilization of YSGA has been justified by comparative assessment with particle swarm optimization, firefly, and sine‐cosine techniques. A meticulous performance evaluation of YSGA optimized IOPID control scheme in the IHμG has been conducted through several case studies. Furthermore, the rigorous sturdiness assessment of YSGA optimized IOPID controller was performed under different uncertainties such as: variation of amplifier gain, ±30% variation in demanded loading magnitude, moment of inertia and droop co‐efficient. Finally, real‐time hardware‐in‐the‐loop (HIL) simulation platform is utilized to validate the proposed control approach.

A Two-Degree-of-Freedom Controller Design Satisfying Separation Principle With Fractional-Order PD and Generalized ESO

This article proposes a two-degree-of-freedom fractional-order proportional derivative (FOPD) controller with a general extended state observer (GESO) to achieve both optimal set-speed tracking and disturbance rejection performance for a typical permanent magnet synchronous motor servo system. The GESO simplifies the control plant, estimates and actively rejects total disturbances. The FOPD controller achieves fast speed tracking with almost no overshoot. Furthermore, it is verified that the control system with the proposed FOPD-GESO controller design meets the separation principle through mathematical derivation and simulation illustration. It shows that the proposed controller breaks the inherent tradeoff on tracking performance and disturbance robustness of the typical traditional proportional–integral–derivative (PID) control. Meanwhile, a systematic scheme for designing the FOPD-GESO controller to satisfy both frequency-domain and time-domain specifications is proposed in this article. Simulation illustration and experimental validation are performed to demonstrate that the proposed FOPD-GESO controller is superior to the typical integer-order PID controller, integer-order active disturbance rejection control with a typical extended state observer, and fractional-order PID controller in terms of speed tracking, antiload disturbance, and robustness to internal uncertainties.

A novel application of ALO-based fractional order fuzzy PID controller for AGC of power system with diverse sources of generation

The operation and control of the modern power system has become complex and difficult due to the incessant penetration of nonconventional energy sources integrated to the power grid and the structural variation of power system with continuing escalation of power demand in recent years. This entails the implementation of intelligent control strategy for satisfactory operation of the power system. Hence, a fractional order fuzzy proportional integral derivative (FOFPID) controller is suggested in this article for automatic generation control of two unequal area interconnected power system with diverse generating units such as thermal, hydro, diesel and wind power plants. The dynamic performance of the system is investigated by using proportional integral derivative (PID), fractional order PID (FOPID), fuzzy PID (FPID) and fractional order fuzzy PID (FOFPID) controllers separately. The parameters of these controllers are optimised by using ant lion optimiser algorithm with integral time absolute error as the objective function. The supremacy of the proposed controller is established by contrasting the results with FPID, FOPID and PID controllers. It is also observed that FPID controller gives superior result than PID and FOPID controllers. Further it is found that the result of FOPID controller is better than the integer order PID controller. Finally robustness analysis is performed to confirm the robustness of the proposed controller against parametric variations and random loading of the system.

Dynamic analysis of gear system under fractional-order PID control with the feedback of meshing error change rate

Based on the fractional-order proportional-integral-derivative (PID) control of the feedback of change rate of gear meshing error, the nonlinear dynamics problem of a spur gear pair is investigated. A model is established including backlash, time-varying stiffness, internal and external excitations and other factors, where the fractional-order PID control terms are also considered. The periodic solution is obtained based on the incremental harmonic balance method, and it is verified by the numerical solution. The effects of the coefficients and the orders of the fractional-order PID controller are analyzed in detail. The control performances of fractional-order PID controller and integer-order PID controller are compared. The results show that the fractional-order PID controller has good control performance for the gear meshing system. By changing the parameters of the controller, the resonance amplitude of the gear meshing system can be suppressed, and the resonance frequency of the gear meshing system can also be adjusted.

Fractional PID controller in an active image stabilization system for mitigating vibration effects in agricultural tractors

Recent demands in sophisticated agricultural machinery require passive or active image sensors to be mounted on vehicle frames. The impact produced by vertical displacements due to tire-soil interaction and mechanical engine vibration causes oscillations that reduce the data quality of any activity performed by equipment such as a camera, spectroradiometer, or scanner laser. This paper presents the modeling and simulation of an active system for stabilization of oscillations using a fractional order PID (Proportional-Integral-Derivative) controller. A method for tuning the fractional order PID is presented for a closed-loop dynamic system. Experiments based on simulations are carried out to compare the performance of the active stabilization system with fractional and integer order PID controllers. Common excitation functions are used to assess the performance of the active stabilization system, along with some common vibration disturbances acquired by a field experiment with a tractor-implement set. The results show that the active stabilization system presents better performance, mitigating vibration displacements and accelerations through a closed-loop system with a fractional PID controller. Additionally, numerical results confirm the superior capacity of the fractional controller based system for attenuating the vibration disturbance compared to the classical PID system for different machinery operational conditions such as forward speed and load.

An optimized fractional order PID controller for suppressing vibration of AC motor

Fractional order Proportional-Integral-Derivative (PID) controller is composed of a number of integer order PID controllers. It is more accurate to control the complex system than the traditional integer order PID controller. The values of parameters of the fractional order PID controller play a decisive role for the control effect. Because the fractional order PID controller added two adjustable parameters than the traditional PID controller, it is very difficult to tune parameters. So the Back Propagation (BP) neural network is selected to optimize the parameters of the fractional order PID controller in order to obtain the high performance. Then the optimized fractional order PID controller and the traditional PID controller are used to control AC motor speed governing system. And the vibration spectrum and stator current spectrum under different rotating speeds are compared and analyzed in detail. The results show that the optimized fractional order PID controller has better vibration suppression performance than the traditional PID controller. The reason is that the optimized fractional order PID controller changed the stator current component, and further changed the frequency components and the amplitude of the vibration signal of the motor.

Primary Resonance of Dry-Friction Oscillator With Fractional-Order Proportional-Integral-Derivative Controller of Velocity Feedback

The classical mass-on-moving-belt model describing friction-induced vibration is studied. The primary resonance of dry-friction oscillator with fractional-order PID (FOPID) controller of velocity feedback is investigated by Krylov–Bogoliubov–Mitropolsky (KBM) asymptotic method, and the approximately analytical solution is obtained. The effects of the parameters in FOPID controller on dynamical properties are characterized by five equivalent parameters. Those equivalent parameters could distinctly illustrate the effects of the parameters in FOPID controller on the dynamical response. The effects of dry friction on the dynamical properties are characterized in the form of the equivalent linear damping and nonlinear damping. The amplitude-frequency equation for steady-state solution associated with the stability condition is also studied. A comparison of the analytical solution with the numerical results is fulfilled, and their satisfactory agreement verifies the correctness of the approximately analytical results. Finally, the effects of the coefficients and orders in FOPID controller on the amplitude-frequency curves are analyzed, and the control performances of FOPID and traditional integer-order proportional-integral-derivative (PID) controllers are compared. The comparison results show that FOPID controller is better than traditional integer-order PID controller for controlling the primary resonance of dry-friction oscillator, when the coefficients of the two controllers are the same. This presents theoretical basis for scholars and engineers to design similar fractional-order controlled system.

Research on vibration suppression method of alternating current motor based on fractional order control strategy

At present, the changing structure, material and increasing device are used to suppress the vibration of motor in general. These methods increase system complexity in the different degree. So a novel vibration suppression method based on fractional order Proportional-Integral-Derivative (PID) controller is proposed in this article. First, the digital realization process of fractional order PID controller is illustrated in detail. Then the integer order PID controller and fractional order PID controller are, respectively, used to adjust the input current of inverter to control the 1.5 kW alternating current motor. The vibration frequency spectrums and stator current frequency spectrums in low-frequency and carrier frequency band are, respectively, studied by using the comparison and analysis methods. At the same time, the vibration frequency spectrum and stator current frequency spectrum of 15 kW alternating current motor are compared and analyzed. And the frequency spectrums near the rotating frequency of stator current of 1.5 kW and 15 kW alternating current motors are amplified to deeply analyze spectrum characteristics. The experimental results show that the fractional order PID controller has the characteristics of multi-point control by comparing with the integer order PID controller. It changes the frequency components of stator current, and then the electromagnetic torque is more stable. So, the fractional order PID controller can better suppress the vibration of alternating current motor. The proposed method can provide a new idea for vibration suppression of rotating machinery.

Design of Fractional-order PID Controllers for Time Delay Systems Using Differential Evolution Algorithm

This paper aims to club on the scheme of Fractional-Order Proportional-Integral-Derivative (FOPID) controllers for time delay systems. The way is based on a composition of the DE algorithm and the Smith predictor control method to arrive meliorated control efficiency of the time delay process. Lately, Differential Evolution (DE) has been transpired as an ordinary but very powerful materiel for real parameter optimization. Parameters of FOPID controllers consisted proportionality constant, integral constant, derivative constant, derivative order and integral order, thus its scheme is more intricate than that of conventional integer-order Proportional-Integral-Derivative (PID) controller. Manufacturing of the controller portrayed here is based on user- specified peak overshoot and settling time and has been formulated as a single objective optimization issue. Finally, better simulation results and control performance of the Fractional-Order PID (FOPID) will be showed in these controllers in collation with those of the integer-order PID controllers.

Design of Fractional–order PID Controllers for Time Delay Systems using Differential Evolution Algorithm

This paper aims to club on the scheme of Fractional-Order Proportional-Integral-Derivative (FOPID) controllers for time delay systems. The way is based on a composition of the DE algorithm and the Smith predictor control method to arrive meliorated control efficiency of the time delay process. Lately, Differential Evolution (DE) has been transpired as an ordinary but very powerful materiel for real parameter optimization. Parameters of FOPID controllers consisted proportionality constant, integral constant, derivative constant, derivative order and integral order, thus its scheme is more intricate than that of conventional integer-order Proportional-Integral-Derivative (PID) controller. Manufacturing of the controller portrayed here is based on user- specified peak overshoot and settling time and has been formulated as a single objective optimization issue. Finally, better simulation results and control performance of the Fractional-Order PID (FOPID) will be showed in these controllers in collation with those of the integer-order PID controllers. Keywords: Differential Evolution, Fractional Order Controller, Smith Predictor Control, Time Delay System

Pitch Loop Control of a VTOL UAV Using Fractional Order Controller

Pitch loop control is the fundamental tuning step for vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs), and has significant impact on the flight. In this paper, a fractional order strategy is designed to control the pitch loop of a VTOL UAV. First, an auto-regressive with exogenous input (ARX) model is acquired and converted to a first-order plus time delay (FOPTD) model. Next, based on the FOPTD model, a fractional order [proportional integral] (FO[PI]) controller is designed. Then, an integer order PI controller based on the modified Ziegler-Nichols (MZNs) tuning rule and a general integer order proportional integral derivative (PID) controller are also designed for comparison following three design specifications. Simulation results have shown that the proposed fractional order controller outperforms both the MZNs PI controller and the integer order PID controller in terms of robustness and disturbance rejection. At last, ARX model based system identification of AggieAir VTOL platform is achieved with experimental flight data.

Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems

For all the stable first order plus time delay (FOPTD) systems, a fractional order proportional integral (FOPI) or a traditional integer order proportional integral derivative (IOPID) controller can be designed to fulfill a flat phase constraint and two design specifications simultaneously: gain crossover frequency and phase margin. In this paper, a guideline for choosing two feasible or achievable specifications, and a new FOPI/IOPID controller synthesis are proposed for all the stable FOPTD systems. Using this synthesis scheme, the complete feasible region of two specifications can be obtained and visualized in the plane. With this region as the prior knowledge, all combinations of two specifications can be verified before the controller design. Especially, it is interesting to compare the areas of these two feasible regions for the IOPID and FOPI controllers. This area comparison reveals, for the first time, the potential advantages of one controller over the other in terms of achievable performances. A simulation illustration is presented to show the effectiveness and the performance of the designed FOPI controller compared with the optimized integer order PI controller and the IOPID controller designed following the same synthesis for the FOPI in this paper.

A conformal mapping based fractional order approach for sub-optimal tuning of PID controllers with guaranteed dominant pole placement

A novel conformal mapping based fractional order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PIλDμ) controller have been approximated in this paper vis-à-vis a LQR tuned conventional integer order PID controller, to achieve equivalent integer order PID control system. This approach eases the implementation of analog/digital realization of a FOPID controller with its integer order counterpart along with the advantages of fractional order controller preserved. It is shown here in the paper that decrease in the integro-differential operators of the FOPID/PIλDμ controller pushes the open loop zeros of the equivalent PID controller towards greater damping regions which gives a trajectory of the controller zeros and dominant closed loop poles. This trajectory is termed as “M-curve”. This phenomena is used to design a two-stage tuning algorithm which reduces the existing PID controller’s effort in a significant manner compared to that with a single stage LQR based pole placement method at a desired closed loop damping and frequency.

Lateral directional fractional order (PI)α control of a small fixed-wing unmanned aerial vehicles: controller designs and flight tests

In this study, a fractional order (PI)λ controller is developed and implemented to improve the flight control performance and robustness of a small fixed-wing unmanned aerial vehicle (UAV). The decoupled roll-channel control is realised under certain conditions and tested using the designed controllers in this study. The inner closed-loop system of the roll-channel is approximately identified as a first-order plus time delay model using the flight test data. For comparison purpose, an integer-order PI controller is designed following the modified Ziegler–Nichols (MZNs) tuning rule, based on this identified roll-channel control model. According to three design pre-specifications, the integer-order proportional integral derivative (PID), fractional-order PIλ and (PI)λ controllers are designed for the roll-channel flight control system of a small fixed-wing UAV. These three designed controllers share the same gain crossover frequency and phase margin settings for fair comparisons. From both simulation and real flight experiments, the two designed fractionalorder controllers outperform the MZNs PI and the designed integer-order PID controllers. The designed (PI)λ controller can achieve even better performance than the designed PIλ controller.

Fractional Order Control of Fractional Diffusion Systems Subject to Input Hysteresis

This paper concerns the control of a time fractional diffusion system defined in the Riemann–Liouville sense. It is assumed that the system is subject to hysteresis nonlinearity at its input, where the hysteresis is mathematically modeled with the Duhem operator. To compensate the effects of hysteresis nonlinearity, a fractional order Proportional+Integral+Derivative (PID) controller is designed by minimizing integral square error. For numerical computation, the Riemann–Liouville fractional derivative is approximated by the Grünwald–Letnikov approach. A set of algebraic equations arises from this approximation, which can be solved numerically. Performance of the fractional order PID controllers are analyzed in comparison with integer order PID controllers by simulation results, and it is shown that the fractional order controllers are more advantageous than the integer ones.

Hardware-in-the-loop experimental study on a fractional order networked control system testbed

Networked Control Systems (NCS) are of great interest in many industries because of their convenience in data sharing and manipulation remotely. However, there are several problems along with NCS itself due to the uncertainties in network communication. One issue inherent to NCS is the network-induced delays which may deteriorate the performance and may even cause instability of the system. Therefore a controller which can make the plant stable at large values of delay is always desirable in NCS systems. Our past work on Optimal Fractional Order Proportional Integral (OFOPI) controller showed that fractional order PI controllers have larger jitter margin (maximum value of delay for which system is stable) for lag-dominated systems when compared to traditional Proportional Integral Derivative (PID) controllers, whereas integer order PID controllers have larger jitter margin for delay-dominated systems. This paper aims at the design process of a tele-presence controller based on OFOPI tuning rules. To illustrate this, an extensive experimental study on the real-time Smart Wheel networked speed control system is performed using hardware-in-the-loop control. The real-time random delay in the world wide network is collected by pinging different locations, and is considered as the delay in our simulation and experimental systems. Comparisons are made with existing integer order PID controller. It is found that the proposed OFOPI controller is a promising controller and has faster response time than the traditional integer order PID controllers. Since the plant into consideration viz. the Smart Wheel is a delay-dominated system, it is verified that PID achieves larger jitter margin as compared to OFOPI tuning rules. Simulation results and real-time experiments showing comparisons between OFOPI and OPID tuning rules prove the significance of this method in NCS.