Vector-based tuning and experimental validation of fractional-order PI/PD controllers

The presence of disturbances in practical control engineering applications is unavoidable. At the same time, they drive the closed-loop system’s response away from the desired behavior. For this reason, the attenuation of disturbance effects is a primary goal of the control loop. Fractional-order controllers have now been researched intensively in terms of improving the closed-loop results and robustness of the control system, compared to the standard integer-order controllers. In this study, a novel tuning method for fractional-order controllers is developed. The tuning is based on improving the disturbance attenuation of periodic disturbances with an estimated frequency. For this, the reference–to–disturbance ratio is used as a quantitative measure of the control system’s ability to reject disturbances. Numerical examples are included to justify the approach, quantify the advantages and demonstrate the robustness. The simulation results provide for a validation of the proposed tuning method.

Data-driven MIMO model-free reference tracking control with nonlinear state-feedback and fractional order controllers

Background: As a high-performance functional material, stacked piezoelectric actuator can produce a displacement under the effect of changing voltage. Its advantages of fast response and easy operation make it to be widely applied in the precision structure field. However, its small displacement stroke and hysteresis nonlinearity affect the accuracy of the output. : In the next step, some experiments were undertaken based on the constructed platform. Methods: In order to enlarge the displacement of piezoelectric actuator and reduce the influence of hysteresis, this study designs a diamond-shaped amplifying mechanism to amplify the output of the piezoelectric actuator, and then develops a self-tuning fuzzy fractional-order PIλDμ controller for the high precision displacement control of the proposed amplifying mechanism. After analyzing the working principle and modeling the amplifying mechanism, the fractional-order PIλDμ control model of the proposed mechanism was built and discretized according to the theoretical base of the fractional calculus in the time domain. Moreover, the fuzzy control algorithm was also introduced to achieve self-turning of parameters. Besides, the amplifying mechanism was also adopted for a microdroplet jetting dispenser to verify the practicability of the mechanism and control strategy. In the next step, some experiments were undertaken based on the constructed platform. Results: Experiments show that the displacement overshoots, the times of reaching a steady state of the traditional integer-order controller and the fractional-order controller are 5.08%, 1.17% and 17.25 s, 12.00 s, respectively. However, the fuzzy PIλDμ controller lowers the overshoot and the time of reaching a steady state to 0.95% and 9.00 s, respectively. The control algorithm can not only improve the follow-ability of the output displacement of the proposed mechanism, but also maintain the deviation within the range of 0.4% after the displacement stroke is stable and reduce the entering time of the mechanism up to 47.8%. In actual application, the droplet volume of micro-droplet jetting dispenser under fuzzy fractional-order PID control method is more stable, and its repeatability accuracy can reach up to 1.6475%. Conclusion: Experimental results indicate that the self-tuning fuzzy fractional-order PIλDμ controller can significantly improve the tracking performances of the PID and the integer-order PID with regard to the amplifying mechanism with the advantages of good dynamic character and regulation precision. Furthermore, the diamond-shaped amplification mechanism and control strategy can be applied for some micro-droplet jetting dispensers used in microelectronic packaging, life science and 3D printing fields.

The cart‐inverted pendulum is a non‐minimum phase system having right half s‐plane pole and zero in close vicinity to each other. Linear time invariant (LTI) classical controllers cannot achieve satisfactory loop robustness for such systems. Therefore, in the present work the fractional order PIλDμ (FOPID) controller is addressed for robust stabilization of the system, since fractional order controller design allows more degrees of freedom compared to its integer order counterparts by virtue of its two parameters λ and μ. The controller parameters are tuned by three evolutionary optimization techniques. In order to select the controller parameters optimally, a novel non‐linear fitness function using integral time square error (ITSE), settling‐time, and rise time is proposed here. The control algorithm is implemented successfully in real‐time. Moreover, stability analysis of the system compensated with a fractional order controller is presented using Riemann surface. Robustness of the physical cart‐inverted pendulum system towards multiplicative gain variations and plant parameter variations is verified. In this regard, it is shown that the fractional order controller provides satisfactory robust performance in both simulation and real‐time system.

Fractional order controllers have been used intensively over the last decades in controlling different types of processes. The main methods for tuning such controllers are based on a frequency domain approach followed by optimization routine, generally in the form of the Matlab fminsearch, but also evolving to more complex routines, such as the genetic algorithms. An alternative to these time consuming optimization routines, a simple graphical method has been proposed. However, these graphical methods are not suitable for all combinations of the imposed performance specifications. To preserve their simplicity, but also to make these graphical methods generally applicable, a modified graphical method using a very straightforward and simple optimization routine is proposed within the paper. Two case studies are presented, for tuning fractional order PI and PD controllers.

In this paper, two fractional order controllers are employed to control the angular velocity of a permanent magnet DC motor. A fractional order PI controller with isodamping property is appropriately designed to achieve the desired phase margin and gain crossover frequency requirements. Moreover, by selecting a fractional order filter in internal model control (IMC) structure, an IMC-based fractional order controller is designed. These two fractional order controllers are utilised for velocity control of a laboratory DC servomechanism system. The experimental results demonstrate the capability of these fractional order controllers in the desired angular velocity tracking and load disturbance rejection.

Various controller design strategies have been studied in the past for under-actuated and fully actuated robotic systems to control a specific task in the best possible manner. This chapter proposes an adaptive fractional order (FO) controller design for under-actuated and fully actuated robotic manipulators. Adaptive controllers can adapt to a particular uncertainty inside the plant and give the best possible controlled response [1]. The change may due to variation of an individual parameter or may be due to disturbances. A suitable controller is supposed to adapt to these uncertainties and give the best results.

This paper will establish the importance and significance of studying the fractional-order control of nonlinear dynamical systems. The foundation and the sources related to this research scope is going to be set. Then, the paper incorporates a brief overview on how this study is performed and p resent the organization of this study. The present work investigates the effectiveness of the physical-fractional and biological-genetic operators to develop an Optimal Form of Fract ional-order PID Controller (O2Fo-PIDC). The newly developed Fo-PIDC with optimal structure and parameters can, also, imp rove the performances required in the modeling and control of modern manufacturing-industrial process (MIP). The synthesis methodology of the proposed O2Fo-PIDC can be viewed as a mu l ti -level design approach. The hierarchical Multiobject ive genetic algorith m (M GA ), adopted in this work, can be visualized as a comb ination of structural and parametric genes of a controller orchestrated in a h ierarch ical fashion. Then, it is applied to select an optimal structure and knowledge base of the developed fractional controller to satisfy the various design specification contradictories (simplicity, accuracy, stability and robustness). Index Terms—Optimal fractional-order controllers, BIBO stability analysis, Multiobjective genetic algorith m, CE150 Helicopter model.

Voltage-lift is a widely used technique in DC–DC converters to step-up output voltage levels. Several traditional and advanced control techniques applicable to power electronic converters (PEC) have been reported and utilized for voltage-lift applications. Similarly, in recent years the implementation of fractional-order controllers (FOC) in PEC applications has gained interest, aiming to improve system performance, and has been validated in basic converter topologies. Following this trend, this work presents an FOC for a voltage-lift converter, requiring only output voltage feedback. A third-order non-minimal phase system is selected for experimentation to verify FOC implementations for more complex PEC configurations. A simple, straightforward design and approximation methodology for the FOC is proposed. Step-by-step development of the FOC, numerical and practical results on a 50 W voltage-lift converter are reported. The results show that PEC transient and steady-state responses can be enhanced using FOC controllers when compared with classical linear controllers. Extended applications of FOC for improved performance in power conversion is also discussed.

The design of a non-minimal state space fractional-order predictive functional controller for fractional systems of arbitrary order

In this paper, a fractional order controller is designed for a class of nonlinear systems by using the high-order fully actuated (HOFA) system approach. First, the original system in an affine state-space form is transformed into a HOFA system model. Second, a state-feedback controller involving the Caputo fractional derivatives is derived based on the HOFA system model. Then, in the framework of close-loop fractional order linear time invariant (LTI) systems, the gain of the fractional order controller is designed via parametric eigenstructure assignment approach. Finally, numerical simulations verify the efficiency of the designed fractional order controller.

Half-bridge converter series microgrid (HBCS-MG) is susceptible to a variety of uncertainties and disturbances during operation, and therefore, the use of the traditional integer-order models cannot accurately reflect the effects of environmental variations on internal components of the off-grid system, such as converters, filters, and loads, including factors like time delays, memory effects, and multi-scale coupling. The fractional-order control method is better equipped to deal with these disturbances, thereby enhancing the robustness and stability of the system. In the off-grid state, a fractional-order PI (FOPI) controller is employed for double-closed-loop control, and the load voltage feedforward control is utilized to offset the impact of load voltage fluctuations on the system. A new simplified equivalent circuit calculation method for the fractional-order inductor is proposed, and a complete fractional mathematical model of the system in the dq rotating coordinate system is established to obtain the transfer function between the load voltage and the input voltage. Furthermore, the impact of the fractional-order variation of the FOPI controllers and the fractional elements on system performance in the frequency domain and time domain is described in detail. The simulation results are compared with the theoretical analysis to demonstrate the accuracy of the mathematical model. The overshoot of the load voltage at the switching instant of 0.7 s is reduced by 4.2% compared with the integer-order PI controller, which proves that the fractional-order controller can improve the system control accuracy.

In most of the industrial process plants, PI/PID controllers have been widely used because of its simple design, easy tuning, and operational advantages. However, the performance of these controllers degrades for the processes with long dead-time and variation in set-point. Up next, a PPI controller is designed based on the Smith predictor to handle dead-time processes by compensation technique, but it failed to achieve adequate performance in the presence of external noise, large disturbances, and higher-order systems. Furthermore, the model-based controllers structure is complex in nature and requires the exact model of the process with more tunable parameters. Therefore, in this research, a fractional-order predictive PI controller has been proposed for dead-time processes with added filtering abilities. The controller uses the dead-time compensation characteristics of the Smith predictor and the fractional-order controller's robustness nature. For the high peak overshoot, external noise, and disturbance problems, a new set-point and noise filtering technique is proposed, and later it is compared with different conventional methods. In servo and regulatory operations, the proposed controller and filtering techniques produced optimal performance. Multiple real-time industrial process models are simulated with long dead-time to evaluate the proposed technique's flexibility, set-point tracking, disturbance rejection, signal smoothing, and dead-time compensation capabilities.

This paper studies the design and implementation of a robust non linear fractional-order PI controller for a coupled tank system. The proposed control scheme is formed of two nested loops. The inner-loop consists in a feedback linearization control law closed to the water level of the upstream tank which reduces the effect of the uncertainty of the parameters of the actuator. The outer-loop is a fractional-order PI controller closed to the water level of the downstream tank which is robust to flow changes caused by variations of the cross sections of the outputs of the two tanks. The control signal generated by the outer-loop controller is the reference of the inner-loop. A new frequency-response technique is proposed to tune the robust outer-loop controller in such a way that the closed-loop system is not only robustly stable but also yields a nearly constant damping (overshoot) when the output cross sections change.

Fractional-order modeling and controller design by a simplified way is the demanding research area and is gearing more and more momentum. This paper is the attempt of application of fractional-order modeling and controller design for the power plant gas turbine. The Gas Turbine is most important equipment in power, aviation and automotive industry. It converts the thermal energy of fuel into the mechanical power. Therefore, important requirement of gas turbine system is to control the flow of input fuel. The existing identified model of the gas turbine between the input fuel flow and the output speed, is of high-order and integer type, which is reduced to the simple and compact integer-order (IO) and fractional-order (FO) models using local optimization technique. The fractional-order internal model controller (FO-IMC) is designed and to show the performance efficacy it is compared with integer-order internal model controller (IO-IMC), which is also designed using the same methodology and specification. Simulation results show that FO-IMC based controller gives better performance for the set point tracking, plant uncertainty and disturbance rejection than the IO-IMC. FO-IMC controller also satisfy the robust stability condition.