Traditional Integer Order PID Research Articles

A hybrid SCSO-QNN approach based load frequency control of three area power system with renewable sources using FOPID controller

ABSTRACT This research proposes a hybrid SCSO-QNN method for designing a FOPID controller in a three-area power system to regulate load frequency. The proposed hybrid approach combines quantum neural networks with sand cat swarm optimization, and it is commonly named as the SCSO-QNN method. The proposed method’s primary goal is to overcome load disturbances and attain the intended output of the interconnected system. The SCSO generates controller parameters tuned by the FOPID controller, providing a significant improvement in performance, while the QNN is employed to forecast the optimal control signal of the converter. Reducing steady-state errors and improving system stability are areas where the FOPID performs better than a traditional integer-order PID controller. Moreover, SCSO-QNN optimization technique exhibits excellent convergence properties, resulting in improved control performance. The proposed method ensures system frequency control by controlling frequency deviation and power fluctuations in the connect line during load disturbances. The proposed method is executed on the MATLAB platform and contrasted with current techniques. The proposed technique outperforms all current techniques, including ABC-FOPID, Genetic Algorithm, and Artificial Bee Colony PID. The proposed method Area control error is 1.8%, which is less than other existing methods.

Nondimensional analysis and experimental assessment of the PII1/2DD1/2 position control of a rotary axis

Fractional Order controllers, based on derivatives and integrals of non-integer order, represent a propitious and promising research area since they can improve the performance of mechatronic systems compared to traditional Integer Order PID controllers without requiring hardware upgrades, but only using their higher tuning flexibility. Nevertheless, Fractional Order controllers are still rarely applied in real automation tasks, since their tuning is more complex and in general requires a model-based optimization for full exploitation of their capabilities. Recently, the PII1/2DD1/2 controller has been proposed, extending the classical PID by introducing a half-integral and a half-derivative term. A Bode plot-based tuning method has been presented for this controller, deriving the PII1/2DD1/2 parameters from a given set of PID gains. This method enables a significant reduction in tracking error for position control of a mechatronic axis without the need for complex model-based optimizations. In this paper, the previous results of this PII1/2DD1/2 tuning methodology have been generalized by employing a nondimensional approach. This approach highlights the conditions under which the benefits of this Fractional Order controller over the PID are most significant. The findings have been validated through experimental tests on a rotary axis, confirming the correctness and usefulness of the method.

Combined frequency and voltage regulation in multi-area system using an equilibrium optimiser based non-integer controller with penetration of electric vehicles

The frequency and terminal voltages in power systems are the two critical operating points that balance active and reactive powers, which must be maintained within predefined limits through automatic generation control (AGC) and automatic voltage regulator (AVR) control loops. To address this issue, in this manuscript, the problem of a combined AGC and AVR is solved using a non-integer order PID controller. Its parameters are adjusted using the recently proposed equilibrium optimiser (EO) technique. Along with conventional sources, renewable energy sources such as geothermal power plants and electric vehicles are considered. The EO-tuned non-integer order PID controller outperformed the traditional integer order PI and PID controllers in view of peak overshoots, undershoots and settling times. The performance of EO is evaluated and found superior against widely used particle swarm optimisation and firefly algorithms in the presence of non-integer order PID controller. Different case studies such as random load disturbance, the effect of nonlinearities, the impact of communication time delay and sensitivity analysis have been performed, which also test the heftiness of the non-integer order PID controller. The obtained results are verified using the real-time digital simulator OPAL-RT (OP4510) for nominal conditions.

Auto-Tuning Parameters of Fractional PID Controller Design for Air-Conditioning Fan Coil Unit

The traditional integer order PID controller manipulates the air-conditioning fan coil unit (FCU) that offers cooling and heating loads to each air-conditioning room in summer and winter, respectively. In order to maintain a steady indoor temperature in summer and winter, the control quality cannot meet the related requirements of air-conditioning automation, such as large overshoot, large steady state error, long regulating time, etc. In view of these factors, this paper develops a fractional order PID controller to deal with such problem associated with FCU. Then, by varying mutation factor and crossover rate of basic differential evolution algorithm adaptively, a modified differential evolution algorithm (MDEA) is designed to tune the satisfactory values of five parameters of indoor temperature fractional order PID controller. This fractional order PID control system is configured and the corresponding numerical simulation is conducted by means of MATLAB software. The results indicate that the proposed fractional order PID control system and MDEA are reliable and the related control performance indexes meet with the related requirements of comfortable air-conditioning design and control criteria.

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

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>

Analysis of Actuator Rate Limit Effects on First-Order Plus Time-Delay Systems under Fractional-Order Proportional-Integral Control

Actuator rate limit deteriorates control performance, and may even lead to system instability in precision process control. In this paper, a first-order plus time-delay (FOPTD) system class with actuator rate limit is considered. The describing function (DF) of the rate limiter is derived to obtain the describing functions of the closed-loop and open-loop systems, and the onset frequency in the Nichols chart is used to analyze the rate limit effects in frequency domain. A fractional-order proportional-integral (FOPI) controller is first designed based on the flat phase constraint, crossover frequency, and phase margin specifications. Then a traditional integer-order PID (IOPID) controller is designed based on the same specifications to compare with the FOPI controller in the presence of actuator rate saturation. A careful simulation study is presented to validate all the conclusions.

Fractional order PIλDμ controller design for satisfying time and frequency domain specifications simultaneously

In order to achieve a desired control performance characterized by satisfying specifications in both frequency-domain and time-domain simultaneously, an optimal fractional order proportional integral derivative (PIλDμ) controller design strategy is proposed based on analytical calculation and Differential Evolution algorithm for a permanent magnet synchronous motor (PMSM) servo system in this paper. In this controller design, the frequency-domain specifications can guarantee the system stability with both gain margin and phase margin, and also the system robustness to loop gain variations. The time-domain specifications can ensure the desired step response performance with rapid rising curve, constrained overshoot, and proper power consuming. Compared with the PIλ controller and the traditional PID controller, PIλDμ controller can get obvious benefits from two more degrees of freedom of the fractional orders λ and μ on satisfying multiple constraints simultaneously and achieving better servo tracking performance for the PMSM servo system. PMSM speed tracking simulations and experiments are demonstrated to show the significant advantages of using the proposed optimal PIλDμ controller over the optimal fractional order PIλ controller and traditional integer order PID controller.

Optimization design on fractional order PID controller based on adaptive particle swarm optimization algorithm

Compared with traditional integer-order PID controller, fractional order PID controller can expand the range of its parameters and control controlled objects more flexibly. It has become one of the research focuses in control field in recent years. Directing at the problem that it is not easy for model parameters of nonlinear fractional order PID controller to be determined, this paper presents a new adaptive particle swarm optimization algorithm which is named YLPSO and can conduct automatic setting of parameters for fractional order PID controller. This algorithm, mainly adopting strategies of adaptive dynamic weight and asynchronization adjustment of learning factors, realizes ability in intensifying algorithm convergence to global optimum by balancing global searching performance and local searching performance of PSO algorithm. Simulation results show that, compared with differential evolution algorithm and standard particle swarm optimization algorithm, YLPSO can control parameter optimizing effect better. Algorithm put forward in this paper provides a new reference for combination of intelligent optimization algorithm and nonlinear fractional order controller.

Robust Fractional Order Proportional Integral Control for Large Time-Delay System

In this paper, a new control method for large time delay system is proposed. Firstly, the decreasing time delay controller is used to remodel large delay time plant into small delay time plant. Then, a fractional robust proportional-integral controller (FOPI) is designed, using the phase margin and cut-off frequency at a specified point in the Bode plot of flat robust conditions, to guarantee the desired control performance and the robustness of the high order system to the gain order system. For comparison between the fractional order proportional integral controller and the traditional integer order PID (IOPID) controller, the IOPID controller is also designed following the same proposed tuning specifications. The simulation results indicates that the both designed controllers work efficiently. Furthermore, the FOPI controller makes the large time-delay system get better control effect, the system has high robustness, adaptive ability and anti-jamming ability.

Fractional Order PID Control of Railway Rescue Crane Leveling System

Aiming at the overshoot problem of electro-hydraulic position servo system used in the process of railway rescue crane hydraulic automatic leveling, and based on its characteristics such as big output power, high control accuracy, quick response speed, et al, this paper established the linear mathematical model of railway rescue crane electro-hydraulic automatic leveling system, besides, the fractional order PID control method was proposed based on the oustaloup digital filter algorithm and the working principle of fractional order PID control method was given, and then the fractional order PID controller was designed. In order to verify the effectiveness of the proposed control strategy, the MATLAB/Simulink simulation software was used. The simulation results show that the fractional order PID controller improved the speed of electro-hydraulic servo system unit step response and the capacity of resisting disturbance compared to traditional integer order PID controller, besides it can ensure the response without overshoot at the same time, so it meets the requirements for rapidity and no overshoot of railway rescue crane hydraulic automatic leveling system very well.

The Frequency Research of Fractional Order PIλDμ Controller

Since most of the control systems in real industrial production are fractional，there is necessery to propose fractional order PIλDμ controller, which extend the traditional integer-order PID controller to fractional order, it has increased two free degree: Integral-order λ and differential-order μ, to more accurately control those complex systems. At the same time analysis the performance of fractional order PIλDμ controller in frequency domain. Especially,the two degrees’ effect to controller.

Automated design of fractional PI QFT controller using interval constraint satisfaction technique (ICST)

In this paper, a fractional-order proportional-integral (FOPI) controller is proposed and designed for a class of nonlinear integer-order (IO) systems. For fair comparison, the proposed FOPI and the traditional integer-order PID (IOPID) controllers are designed following the same set of imposed tuning constraints, which can guarantee the desired control performance and the robustness of the designed controllers to the loop gain variations. This proposed design scheme offers a practical and systematic way of controller design for the nonlinear IO plant. We also propose a new and efficient method for automated synthesis of a fixed structure Quantitative Feedback Theory (QFT) FO controller. This is achieved by solving QFT quadratic inequalities of robust stability and performance specifications. The controller synthesis problem is posed as interval constraint satisfying problem (ICSP) and solved with interval constraint solver. The main feature of this method is that it guarantees to find all feasible controllers of given structure in the specified search domain. The designed FOPI and the traditional IOPID controllers are tested on the experimental setup designed by Educational Control Product (ECP) Magnetic Levitation Setup ECP 730. From the experimental results presented, it is observed that the designed FO controllers work more efficiently, with improved performance compared with the designed stabilizing IOPID controller.

Tuning fractional order proportional integral controllers for fractional order systems

In this paper, two fractional order proportional integral controllers are proposed and designed for a class of fractional order systems. For fair comparison, the proposed fractional order proportional integral (FOPI), fractional order [proportional integral] (FO[PI]) and the traditional integer order PID (IOPID) controllers are all designed following the same set of the imposed tuning constraints, which can guarantee the desired control performance and the robustness of the designed controllers to the loop gain variations. This proposed design scheme offers a practical and systematic way of the controllers design for the considered class of fractional order plants. From the simulation and experimental results presented, both of the two designed fractional order controllers work efficiently, with improved performance comparing with the designed stabilizing integer order PID controller by the observation. Moreover, it is interesting to observe that the designed FO[PI] controller outperforms the designed FOPI controller following the proposed design schemes for the class of fractional order systems considered.

Fractional order [proportional derivative] controller for a class of fractional order systems

Recently, fractional order systems (FOS) have attracted more and more attention in various fields. But the control design techniques available for the FOS suffer from the lack of direct systematic approaches. In this paper, we focus on a given type of simple model of FOS. A fractional order [proportional derivative] (FO-[PD]) controller is proposed for this class of FOS, and a practical and systematic tuning procedure has been developed for the proposed FO-[PD] controller synthesis. The fairness issue in comparing with other controllers such as the traditional integer order PID (IO-PID) controller and the fractional order proportional derivative (FO-PD) controller has been addressed under the same number of design parameters and the same specifications. Fair comparisons of the three controllers (i.e., IO-PID, FO-PD and FO-[PD]) via the simulation tests illustrate that, the IO-PID controller designed may not always be stabilizing to achieve flat-phase specification while both FO-PD and FO-[PD] controllers designed are always stabilizing. Furthermore, the proposed FO-[PD] controller outperforms FO-PD controller for the class of fractional order systems.