Tuning Of Fractional Order Controller Research Articles

Experimentally validated analytical single parametric FOTID control for time-delayed fractional order processes

In current studies, non-integer order (NIO) plants with dead time have gained the significant attention of many researchers in the area of control theory. However, the design methods for fractional order controller tuning suffer from a lack of direct systematic tuning strategies due to a higher number of tuneable parameters. Most of the works on such design are optimisation-based whereas the analytical solutions are achieved with assumptions and approximations leading to compromised closed-loop robustness. This paper proposes a simple analytical design of a fractional-order tilt-integral-derivative (FOTID) controller for time-delayed NIO processes with a single tuneable parameter. Explicit tuning rules in terms of plant parameters are derived with user-defined stability margins. To prove the efficiency of the proposed control law, simulation comparisons with recently developed tuning rules are included. Lastly, the proposed control law is tested through experiments in a two-tank level loop for real-time validation.

A Novel Toolbox for Automatic Design of Fractional Order PI Controllers Based on Automatic System Identification from Step Response Data

This paper describes a novel automatic control toolbox, designed for non-experienced practitioners. Fractional order (FO) controllers are easily tuned with the main purpose of easy practical implementation. Experimental step data are required for the automatic FO controller tuning. An embedded system identification algorithm uses the step data to obtain a process model as a second order plus dead-time (SOPDT) system. Finally, the FO controller is computed based on the previously estimated SOPDT model in order to fulfil a set of user-imposed frequency domain performance specifications: phase margin, gain crossover frequency and gain margin maximization. Experimental step response data from a strongly nonlinear vertical take-off and landing unit have been used to design an FO controller using the toolbox. The experimental closed loop results validate the proposed toolbox. The end result is a user-friendly automatic fractional order controller tuning with endless possibilities of real-world applicability.

Optimal Tuning of Fractional Order Controllers for Dual Active Bridge-Based DC Microgrid Including Voltage Stability Assessment

In this article, three evolutionary search algorithms: particle swarm optimization (PSO), simulated annealing (SA) and genetic algorithms (GA), have been employed to determine the optimal parameter values of the fractional-order (FO)-PI controllers implemented in the dual active bridge-based (DAB) DC microgrid. The optimum strategy to obtain the parameters of these FO-PI controllers is still a major challenge for many power systems applications. The FO-PI controllers implemented in the DAB are used to control the DC link voltage to the desired value and limit the current flowing through the converter. Accordingly, the investigated control system has six parameters to be tuned simultaneously; Kp1, Ki1, λ1 for FO-PI voltage controller and Kp2, Ki2, λ2 for FO-PI current controller. Crucially, this tuning optimization process has been developed to enhance the voltage stability of a DC microgrid. By observing the frequency-domain analysis of the closed-loop and the results of the subsequent time-domain simulations, it has been demonstrated that the evolutionary algorithms have provided optimal controller gains, which ensures the voltage stability of the DC microgrid. The main contribution of the article can be considered in the successful application of evolutionary search algorithms to tune the parameters of FO-based dual loop controllers of a DC microgrid scheme whose power conditioner is a DAB topology.

High-Level Renewable Energy Integrated System Frequency Control with SMES-Based Optimized Fractional Order Controller

The high-level penetration of renewable energy sources (RESs) is the main reason for shifting the conventional centralized power system control paradigm into distributed power system control. This massive integration of RESs faces two main problems: complex controller structure and reduced inertia. Since the system frequency stability is directly linked to the system’s total inertia, the renewable integrated system frequency control is badly affected. Thus, a fractional order controller (FOC)-based superconducting magnetic energy storage (SMES) is proposed in this work. The detailed modeling of SMES, FOC, wind, and solar systems, along with the power network, is introduced to facilitate analysis. The FOC-based SMES virtually augments the inertia to stabilize the system frequency in generation and load mismatches. Since the tuning of FOC and SMES controller parameters is challenging due to nonlinearities, the whale optimization algorithm (WOA) is used to optimize the parameters. The optimized FOC-based SMES is tested under fluctuating wind and solar powers. The extensive simulations are carried out using MATLAB Simulink environment considering different scenarios, such as light and high load profile variations, multiple load profile variations, and reduced system inertia. It is observed that the proposed FOC-based SMES improves several performance indices, such as settling time, overshoot, undershoot compared to the conventional technique.

Robust controller design: Recent emerging concepts for control of mechatronic systems

The recent industrial revolution puts competitive requirements on most manufacturing and mechatronic processes. Some of these are economic driven, but most of them have an intrinsic projection on the loop performance achieved in most of closed loops across the various process layers. It turns out that successful operation in a globalization context can only be ensured by robust tuning of controller parameter as an effective way to deal with continuously changing end-user specs and raw product properties. Still, ease of communication in non-specialised process engineering vocabulary must be ensured at all times and ease of implementation on already existing platforms is preferred. Specifications as settling time, overshoot and robustness have a direct meaning in terms of process output and remain most popular amongst process engineers. An intuitive tuning procedure for robustness is based on linear system tools such as frequency response and bandlimited specifications thereof. Loop shaping remains a mature and easy to use methodology, although its tools such as Hinf remain in the shadow of classical PID control for industrial applications. Recently, next to these popular loop shaping methods, new tools have emerged, i.e. fractional order controller tuning rules. The key feature of the latter group is an intrinsic robustness to variations in the gain, time delay and time constant values, hence ideally suited for loop shaping purpose. In this paper, both methods are sketched and discussed in terms of their advantages and disadvantages. A real life control application used in mechatronic applications illustrates the proposed claims. The results support the claim that fractional order controllers outperform in terms of versatility the Hinf control, without losing the generality of conclusions. The paper pleads towards the use of the emerging tools as they are now ready for broader use, while providing the reader with a good perspective of their potential.

Design of fractional order controllers using constrained optimization and reference tracking method

In recent times, fractional order controllers are gaining more interest. There are several fractional order controllers are available in literature. Still, tuning of these controllers is one of the main issues which the control community is facing. In this paper, online tuning of five dierent fractional order controllers is discussed viz. tilted proportional-integral-derivative (T-PID) controller, fractional order proportional-integral (FO-PI) controller, fractional order proportional-derivative (FO-PD) controller, fractional order proportional-integral-derivative (FO-PID) controller. A reference tracking method is proposed for tuning of fractional order controllers. First order with dead time (FOWDT) system is used to check feasibility of the control strategy.

A new fractional order controller tuning method based on Bode’s ideal transfer function

A new tuning method for Fractional Order Controllers (FOC) based on Bode’s ideal transfer function as a reference model is proposed in this paper. The proposed fractional order controller parameters are obtained by a simple tuning technique in two steps. In the first step, the open loop reference fractional integrator is designed according to the desired performances, and then approximated by a rational transfer function using Charef’s or Oustaloup’s approximation method. In the second step, a standard pole placement technique is used to align each pole of the plant transfer function with the nearest one of the Rational Function Approximation (RFA). The FOC transfer function is then obtained by gathering the remained poles and zeros of the RFA. The most innovative character of the proposed method is its simplicity and its remarkable performances in terms of robustness towards the variation of the static gain. Simulation of some illustrative examples confirms and validates the proposed method.

Simplified Fractional Order Controller Design Algorithm

Classical fractional order controller tuning techniques usually establish the parameters of the controller by solving a system of nonlinear equations resulted from the frequency domain specifications like phase margin, gain crossover frequency, iso-damping property, robustness to uncertainty, etc. In the present paper a novel fractional order generalized optimum method for controller design using frequency domain is presented. The tuning rules are inspired from the symmetrical optimum principles of Kessler. In the first part of the paper are presented the generalized tuning rules of this method. Introducing the fractional order, one more degree of freedom is obtained in design, offering solution for practically any desired closed-loop performance measures. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, using simple tuning-friendly equations. It can be applied to a wide range of process models, from integer order models to fractional order models. Simulation results are given to highlight these advantages.

Experimental Validation of a Novel Auto-Tuning Method for a Fractional Order PI Controller on an UR10 Robot

Classical fractional order controller tuning techniques usually consider the frequency domain specifications (phase margin, gain crossover frequency, iso-damping) and are based on knowledge of a process model, as well as solving a system of nonlinear equations to determine the controller parameters. In this paper, a novel auto-tuning method is used to tune a fractional order PI controller. The advantages of the proposed auto-tuning method are two-fold: There is no need for a process model, neither to solve the system of nonlinear equations. The tuning is based on defining a forbidden region in the Nyquist plane using the phase margin requirement and determining the parameters of the fractional order controller such that the loop frequency response remains out of the forbidden region. Additionally, the final controller parameters are those that minimize the difference between the slope of the loop frequency response and the slope of the forbidden region border, to ensure the iso-damping property. To validate the proposed method, a case study has been used consisting of a pick and place movement of an UR10 robot. The experimental results, considering two different robot configurations, demonstrate that the designed fractional order PI controller is indeed robust.

Anti-windup Fractional Order $$\textit{PI}^\lambda -\textit{PD}^\mu $$ PI λ - PD μ Controller Design for Unstable Process: A Magnetic Levitation Study Case Under Actuator Saturation

Many studies have been conducted by researchers globally in the recent past on the control scheme to stabilize the levitated object of magnetic levitation system (MLS) at the unstable equilibrium point though very small amount of work has been reported regarding the design and tuning of fractional order controller for unstable process, especially in the presence of actuator saturation. In this paper, a novel methodology of fractional order \(PI^\lambda -PD^\mu \) controller for MLS is proposed for both stabilizing the system and removing the actuator saturation. Fractional order control facilitates an extra degree of freedom to change the order of integrator, arise a new concept to diminish the error windup during actuator saturation. The tuning of gain parameter of PID controller is done using the conventional pole placement technique, while a simple tuning method is proposed here to tune fractional parameter using stability margin and sensitivity function. Stability of the proposed controller scheme employed to MLS is analyzed on the basis of Riemann sheets concept in w-plane. To compensate for saturation due to integral term, back-calculation anti-windup scheme is used here. Experimental demonstration of proposed scheme on magnetic levitation confirms the ability of the controller to reject the external random perturbations as well as its robustness against the variation of system parameters.

Fractional order control of unstable processes: the magnetic levitation study case

Although a considerable amount of research has been carried out in the field of fractional order controllers, the majority of the results deal with stable processes. Very little research has been reported regarding the design, analysis, and tuning of fractional order controllers for unstable processes. This paper proposes a methodology for designing and tuning fractional order controllers for a class of unstable second-order processes. The design is carried out using the stability analysis of fractional order systems, by means of Riemann surfaces and a proper mapping in the \(w{\text {-}}\hbox {plane}\). The resulting fractional order controllers are implemented using graphical programming on industrial equipment and are validated experimentally using a laboratory scale magnetic levitation unit.

Tuning of <i>PI</i> <sup>λ</sup> Controllers Based on Gain and Phase Margins and its Application in Water Tank

This paper discusses the parameters tuning of fractional-order controller satisfying the desired gain-margin and phase-margin specifications in terms of a stability equation method applicable to fractional-delay systems. The tuning procedure is then applied to the level control of double water tank, which is modeled as a second-order transfer function with time-delay. The Matlab simulations and the experiments on the water tank device show the effectiveness of the tuning and the benefits of using fractional-order controllers.

A Hybrid Differential Artificial Bee Colony Algorithm based tuning of fractional order controller for Permanent Magnet Synchronous Motor drive

In this paper a novel Hybrid Differential Artificial Bee Colony Algorithm (HDABCA) has been proposed for designing a fractional order proportional-integral (FO-PI) speed controller in a Permanent Magnet Synchronous Motor (PMSM) drive. FO-PI controllers’ parameters involve proportionality constant, integral constant and integral order, and hence its design is more complex than that of the usual Integral-order proportional-integral controller. To overcome this complexity in designing, we had used the proposed hybrid algorithm, such that all the design specifications of the motor are satisfied. In order to digitally realize the FO-PI controller, an Oustaloup approximation method has been used. Simulations and comparisons of proposed HDABCA with conventional methods and also other state-of-art methods demonstrate the competence of the proposed approach, especially for actuating fractional order controller for integer order plants.

Time Domain Tuning of Fractional Order Controllers Combined With a Smith Predictor for Automation of Water Distribution in Irrigation Main Channel Pools

AbstractThis paper proposes a new technique for designing fractional order controllers applied to the automation of main canal pools of a water irrigation system. As large variation of all the plant parameters is present in such systems, a fractional order family of controllers combined with a Smith Predictor is designed using time domain specifications. The designed controllers are compared with the standard combination of a Smith Predictor with a proportional‐integral (PI) controller. All these controllers are tuned to fulfil the same time specifications in the case of canal nominal dynamics. In some canals the plant parameters may experience large changes that deteriorate the time response, and can even unstabilize the closed‐loop system. The fractional controllers are therefore designed to minimize the loss of performance of the system to variations in these parameters. Simulated results show the performance improvements achieved with these controllers compared with a conventional PI controller.