Fractional Order PIλ Controller Research Articles

Design of PIλ-PDμ controller for high-order systems based on model order reduction using BB-BC and time moment matching

In this paper, a practical fractional proportional–integral and proportional–derivative (PIλ-PDμ) controller tuning method and a model reduction method are proposed for high-order systems with or without time delay. First, the Big Bang–Big Crunch (BB-BC) algorithm and the time moment matching method are used to reduce the order of the high-order system function, and the approximate low-order system function is obtained. Second, the parameter region of fractional-order PIλ-PDμ controller is obtained according to the D partition method, and the improved weighted geometric center (WGC) method is introduced to select the special points in the stable region as the control parameters. Then, the fractional-order PIλ controller is discretized by Muir method, and the fractional-order PDμ controller is discretized by continued fraction expansion (CFE). Finally, the BB-BC algorithm is used to optimize the control parameters, and the parameters with better control performance are obtained. The simulation results show that the fractional PIλ-PDμ parameter setting method based on BB-BC algorithm can improve the control performance of the system, and the model reduction scheme based on the combination of moment matching method and BB-BC algorithm is effective in both time domain and frequency domain analysis.

An enhanced whale optimized fractional order piλ controller based power quality improvement for sensorless brushless dc motor under dynamic operating conditions

This paper presents an Enhanced Whale Optimization Algorithm (EWO) approach for tuning to perfection of Fractional Order Proportional Integral and integral order Controller (FOPI λ) is used to sensorless speed control of permanent magnet Brushless DC (PMBLDC) motor under the operating dynamic condition such as (i) speed change by set speed command signal (ii) varying load conditions, (iii) integrated conditions and (iv) controller parameters uncertainty. On the other hand, it deals with a reduced THD (Total Harmonic Distortion) under dynamic operating conditions to improve the power quality for the above control system. Here present are three optimization techniques, namely (i) Enhanced Whale Optimization (EWO), (ii) Invasive Weed Optimization (IWO), and (iii) Social Spider Optimization (SSO) for fine-tuning of the FOPI λ controller parameters with reduction of THD. The proposed optimization algorithm optimized FOPI λ controller are compared under various BLDC motor operating conditions. Based on the results of MATLAB/Simulink models, the proposed algorithms are evaluated. Here, both the simulation and the results of the experiments are validated for the proposed controller technique. It demonstrates that the effectiveness of the proposed controllers is completely validated by comparing the three intelligent optimization techniques mentioned above. The EWO optimized FOPI λ controller for speed control of sensorless PMBLDC motor clearly outperforms the other two intelligent controllers by minimizing the time domain parameters, THD, performance Indices error, convergence time, control efforts, cost function, mean and standard deviation.

Ractional PI Stabilization of Delay Systems: Application to a Thermal System

In this paper, an application of fractional-order PIλ controller is given as an alternative to solve some control problems that can arise. It aims to apply the analytical tuning procedure to control the heat flow systems. This system, modeled by first-order system involving time delay, is one with open loop characteristic equations are fractional order quasi-polynomials. Using the proposed method, the entire stability region of PI λ controllers is obtained and visualized in the plane (Kp,Ki, λ ). The simulation was carried out on thermal systems and the results demonstrate the effectiveness of the proposed type of controllers and the tuning rule.

Fractional-order composite control for the transient creep of a piezoelectric actuator

In this study, a fractional-order composite controller is proposed to decrease the settling time and narrow the range of the transient creep of a piezoelectric actuator. The controller is composed of backlash modules and a fractional-order PIλ controller. The backlash modules reduce the effect of the transient creep and the hysteresis, while the fractional-order controller decreases the settling time. Experiments show that the settling time is decreased from 11 ms to 6 ms. The controller exhibits good performance on step creep and hysteresis when the input signal is discretised into steps, whether 10, 20, 40 or 80 steps. All standard deviations are suppressed to levels 39.3% lower than that of a standard PI controller and the range of the transient creep is reduced to 19.46%.

A Fractional-Order Noise-Shaping Integrator for Sigma-Delta Modulator

A novel fractional-order Sigma-Delta modulator, which can improve the signal to noise ratio (SNR) and is of robust stability of a high order Sigma-Delta modulator, is presented in the paper. Traditional Sigma-Delta modulator mainly focused on forming an integer high order integrator to improve the SNR, whereas the paper presents a fractional-order integrator instead to obtain higher SNR and better stability. Specifically, a 4th order digital integrator and a fractional-order PIλ controller are inserted between the AFE and the quantizer. The 4th order digital integrator increases overall loop order to produce much higher SNR for Sigma-Delta modulator and the fractional-order PIλ controller allows fine tuning accuracy in seeking the coefficients for Sigma-Delta modulator and provides stability in the placement of poles and zeros for compensating the phase delays caused by system nonlinearity. The parameters of PIλ controller are optimized by using swarm intelligent optimization algorithm. The stability of the proposed fractional-order Sigma-Delta modulator is analyzed and the robustness of the proposed fractional-order Sigma-Delta modulator is demonstrated. Further simulation from the fractional-order Sigma-Delta modulator, results of SNR>145dB and the noise floor under -190dB are obtained in frequency range of [5-150Hz].

Fractional order [formula omitted] controller synthesis for steam turbine speed governing systems

The current state of the art of fractional order stability theory is hardly to build connection between the time domain analysis and frequency domain synthesis. The existing tuning methodologies for fractional order PIλDμ are not always satisfy the given gain crossover frequency and phase margin simultaneously. To overcome the drawbacks in the existing synthesis of fractional order controller, the synthesis of optimal fractional order PIλ controller for higher-order process is proposed. According to the specified phase margin, the corresponding upper boundary of gain crossover frequency and stability surface in parameter space are obtained. Sweeping the order parameter over λ∈(0,2), the complete set of stabilizing controller which guarantees both pre-specifying phase frequency characteristic can be collected. Whereafter, the optimal fractional order PIλ controller is applied to the speed governing systems of steam turbine generation units. The numerical simulation and hardware-in-the-loop simulation demonstrate the effectiveness and satisfactory closed-loop performance of obtained fractional order PIλ controller.

Fractional Order PIλ Controller Application for Limited Memory System

Bu çalışmada, asenkron motorun hız kontrolünde kesirli PI λ yöntemi, sınırlı hafızaya sahip olan bir dsPIC mikrodenetleyicisi kullanılarak gerçekleştirilmiştir. Kesirli integralin hesaplanması işleminde kullanılan hata fonksiyonu ve ağırlık fonksiyonu veri setleri sadece son 50 veriyi kullanacak şekilde sınırlandırılmıştır. Bu sınırlandırma işlemi kesirli kontrolörün dsPIC mikrodenetleyicisinde kullanılabilmesini sağlamıştır. Farklı k p , k i ve λ değerleri için hız kontrolü deneyleri gerçekleştirilmiştir. Sonuçlar tablolarda ve şekillerde sunulmuştur.

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.

A Study on Parameter Tuning of Fractional Order PI<sup>λ</sup>-PD<sup>μ</sup> Controller

Aiming at a kind of special object with fractional characteristics,a new kind of fractional order PIλ-PDμ controller is put forward in this paper,In this control system, the forward channel of system contains a fractional order PIλ controller,while the feedback loop adopts PDμ controller.The control structure in this fractional order system can achieve a good performance of the closed loop control.Moreover,the impacts on system dynamic performance and static performance are compared when the parameters in the controller are changed.The results show that when these parameters are in the reasonable range,the system can achieve better control performance.

Application of Fractional-Order PI<sup>λ</sup> Controller for PMSM Speed Control

Permanent Magnet Synchronous Motor(PMSM) is a multivariable, nonlinear system with strong couple. It’s sensitive to the parameters and load variations. To improve the system static, dynamic performance and robustness, the fractional-order PIλ control strategy is proposed. Compared with integer-order PI controller, the fractional-order PIλ controller achieves better control performance due to an extra adjustable knob λ. The simulation results show that the fractional-order PIλ controller can track the given speed quickly and accurately, and has better anti-interference with load variation.

Real Time Implementation of Third Generation CRONE Control Strategy for DC Motor Speed Control System

This work focuses on real time implementation of third generation CRONE control strategy for the speed control of DC motor. The dynamic second order transfer function model is analytically derived for the speed control system based on real time data. An attempt has been made to compare third generation CRONE controller with Fractional order (FO) PIλ controller. The real time run of both the controller results are recorded and reported in time domain and integral time performance indices. The real time result shows that the third generation CRONE controller may be more effective and gives superior performance over the FO PIλ controller

Robust fractional controller for interval first order system with time delay

In this paper, a new method is proposed to define the parameters of fractional order PIλ controller that stabilise an uncertain first order system with time delay. In fact, based on an extension version of Hermite-Biehler theorem and Pontryagin theorem the complete set stabilising PIλ parameters (KP, Ki, λ) is determined. The closed-loop characteristic equation of the system is a fractional order quasi-polynomial with interval uncertainty structure which is decomposed into several vertex. In the complex plane the value set of the vertex is a convex polygon. Simulation results are given to show the effectiveness of the proposed method.

Robust stability region of fractional order PIλ controller for fractional order interval plant

In this article, by using the fractional order PIλ controller, we propose a simple and effective method to compute the robust stability region for the fractional order linear time-invariant plant with interval type uncertainties in both fractional orders and relevant coefficients. The presented method is based on decomposing the fractional order interval plant into several vertex plants using the lower and upper bounds of the fractional orders and relevant coefficients and then constructing the characteristic quasi-polynomial of each vertex plant, in which the value set of vertex characteristic quasi-polynomial in the complex plane is a polygon. The D-decomposition method is used to characterise the stability boundaries of each vertex characteristic quasi-polynomial in the space of controller parameters, which can obtain the stability region by varying λ orders in the range (0, 2). These regions of each vertex plant are computed by using three stability boundaries: real root boundary (RRB), complex root boundary (CRB) and infinite root boundary (IRB). The method gives the explicit formulae corresponding to these boundaries in terms of fractional order PIλ controller parameters. Thus, the robust stability region for fractional order interval plant can be obtained by intersecting stability region of each vertex plant. The robustness of stability region is tested by the value set approach and zero exclusion principle. Our presented technique does not require sweeping over the parameters and also does not need linear programming to solve a set of inequalities. It also offers several advantages over existing results obtained in this direction. The method in this article is useful for analysing and designing the fractional order PIλ controller for the fractional order interval plant. An example is given to illustrate this method.