Sliding-Mode Controller Based on Fractional Order Calculus for a Class of Nonlinear Systems

Fixed wing Unmanned Aerial Vehicles (FWUAVs) are widely utilized in both military and civilian sectors due to their ability to perform risky, inaccessible operations. The mathematical model of FWUAVs is complex, incorporating physical laws and coordinate systems with transformation matrices. In addition, controlling FWUAVs is challenging due to their nonlinear and coupled dynamics. This paper focuses on tracking trajectories for fixed wing unmanned aerial vehicles (FWUAVs) using a Robust Fractional Order Sliding Mode Controller (RFOSMC). An RFOSMC, which combines a conventional Sliding Mode Controller (SMC) with flexible fractional calculus, is proposed in this paper. Particle Swarm Optimization (PSO) is used to tune the control gains of RFOSMC. External disturbances and parameter variation are added to evaluate the controller’s performance. Comparative studies have been done with Linear Quadratic Regulator (LQR), Fractional Order PID (FOPID), SMC, and robust FOSMC. RFOSMC performs better than LQR, FOPID, and SMC in tracking accuracy, response speed, and overshoot. In addition, the performance comparison of RFOSMC and conventional SMC has been done based on performance index values of errors (ITAE), and RFOSMC showed a 76.5918% improvement. For a step input, RFOSMC showed the smallest settling time of 0.835s compared with 2.724s for SMC and 4.8573s for FOPID. Open-loop model verification and overall control system of FWUAV are done using MATLAB/Simulink software.

Fractional order neural sliding mode control based on the FO-Hammerstein model of piezoelectric actuator

Adaptive fractional order sliding mode controller with neural estimator

In this paper, the vehicle's dynamical behaviour is first described through a bifurcation analysis to give some insights for its robust control synthesis. Then a novel adaptive fractional-order sliding mode controller (AFOSMC) is designed to effectively control the uncertain supercavitating vehicle against payload changes, nonlinear planing force and external disturbances. The control scheme utilises the fractional calculus and the adaptive law for the sliding mode control (SMC) to provide active control actions. The fractional calculus can guarantee more flexibility and more freedom for tuning active control synthesis than the integer-order counterpart. The adaptation law has been presented to directly handle the payload change effects. The dynamic performance of the proposed controller is verified through extensive simulation results, which demonstrate faster responses than existing integer order controllers. Furthermore, the fractional order controller shows its effectiveness in dealing with external disturbance, when eliminating most of the uncertainty effect.

Fractional order sliding mode control of a pneumatic position servo system

In this paper a novel controller for a flexible link manipulator based on fractional calculus is proposed. A hybrid system that combines the advantages in terms of robustness of the fractional control and the sliding mode control is proposed. Due to adding the extra degree of freedom, the fractional order sliding mode controller can achieve better control performance than the integer order sliding mode controller. For the problem of determining the design parameters, the particle swarm optimization (PSO) algorithm is used. The proposed controller is applied for a single‐link flexible manipulator robot. Finally, the performance and the significance of the closed loop system are investigated. The simulation results signify the performance of the proposed controller.

In this paper, a robust Fractional order sliding mode controller (FOSMC) is proposed for the speed control of a permanent magnet synchronous motor (PMSM). The sliding mode controller (SMC), which is insensitive to uncertainties, is studied widely in the application of PMSM drive. Furthermore, it is remarkable to see the increasing number of studies related to the theory and application of fractional order controller (FOC), especially PIλDμ controller, in many areas of science and engineering. Research activities are focused on developing new analysis and design methods for fractional order controllers as an extension of classical control theory. In this study, with the exponent reaching law, a fractional order sliding surface is introduced and a FOSMC is designed and applied to a speed control of PMSM, which is typical nonlinear multivariable coupled system. The performance and robustness of the proposed method are tested for nonlinear load torque disturbance, and simulation results show the effectiveness of the proposed algorithm.

In this paper, a hybrid system that combines the advantages in terms of robustness of the fractional control and the Sliding Mode Control (SMC) will be proposed. The proposed fractional order SMC is applied to a level control in a nonlinear coupled tank, as a case study. To investigate the capability of the method, a Sliding Mode Controller is alternatively designed. Primarily a sliding surface based on linear compensation networks PD or PID is designed. The work is followed by designation of a fractional form of these networks, PDμ or PIλDμ. Finally, the performance of the proposed technique is also investigated under disturbance and variation in parameters of system. The simulation results indicate the significance of the fractional order sliding mode controllers.

The main goal of vehicle active suspension system is to upgrade the ride quality and stability of heavy duty vehicle (HDV) regardless of road surface. The mathematical modelling of HDV with two degrees of freedom is developed and simulated in MATLAB/Simulink environment. The simple and effective control techniques such as proportional integral and derivative (PID) controller, sliding mode controller (SMC) and fractional order sliding mode controller (FOSMC) are designed to detach the vibration from the passenger under step, sinusoidal and random road profile. Literature reveals that the FOSMC can eliminate steady state error and chattering effect unlike SMC and PID. The dynamic analysis of designed controllers is examined in terms of time domain, frequency domain and ride comfort analysis as per ISO 2631. The stability of SMC and FOSMC is confirmed by Lyapunouv stability for three different road profiles. The FOSMC shows satisfactory simulation results than SMC, PID and passive suspension system in reducing suspension deflection and body acceleration of HDV to upgrade the ride quality. Further, the efficacy of proposed FOSMC is proved by comparing the simulation results against existing results of PID controller.

Fractional Order Sliding Mode Controller (FOSMC) is a hybrid one and has been integrated to escalate low voltage ride through (LVRT) during faults in a modular multilevel converter (MMC) based doubly fed induction generator (DFIG) connected wind energy conversion system (WECS). Voltage sag at grid directly affects stator of DFIG, due to its immediate connection. The machine’s rotor is joined to power electronic converters i.e. a rectifier (MSC) and an inverter (GSC) via a DC link. A Fractional Order Sliding Mode controller is used at Grid Side Converter to mitigate fault current and ameliorate parameters at stator, rotor terminals. This paper infers that proposed Fractional Order Super Twisting Algorithm (FOSTA) deployed Sliding Mode Controller (FOSMC) is the exceptional in dealing with symmetrical and asymmetrical faults by refining power quality parameters, LVRT problem. The fault ride capability with FOSMC is good compared to FOPI and SMC controllers.

Fractional order sliding mode control is studied in this paper. The control objectives are achieved by adopting the reaching law approach of sliding mode control. The main contribution of this work is to show that the philosophy of integer order sliding mode control is valid also for the systems represented by fractional order operators. A sufficient condition and its implications for stability are given. Matched and unmatched uncertainties are studied. The attractor nature of the switching manifold is analyzed together with a stable sliding subspace design condition. The claims are justified through a set of simulations and the results obtained are found promising.

In this paper, designing of Fractional Order Sliding Mode Controller (FOSMC) for Twin Rotor MIMO System (TRMS) is done. The sliding surface in fractional order for TRMS is formulated, and control input of TRMS is derived by decoupling the system, i.e., neglecting the inter dependency between both (horizontal and vertical) planes. The stability and the convergence of the decoupled control input in finite time is verified through Lyapunov’s criteria for stability. The parameters like angle error, sliding surface, control law for horizontal plane and the vertical plane are separately matched with the Sliding Mode Control (SMC) in MATLAB/Simulation. Overall controlled trajectory after combining trajectory of vertical plane and horizontal plane respectively is obtained, and the chattering effect due to SMC is dampened out to considerable rate.

Constant fractional order vibration control strategy has been one of research hotspots in recent decades. However, the variable fractional order control method is seldom concerned up to now. In this article, a novel variable fractional order sliding mode control (VOSMC) method is proposed to suppress the responses of building structure caused by seismic excitations, including El Centro, Hachinohe, Northridge, and Kobe earthquakes. Based on the proposed variable fractional order sliding mode surface, the control law of VOSMC is presented. The global asymptotic stability of the control system is analyzed and proved by utilizing variable fractional order Lyapunov stability theorem. Besides, the corresponding constant fractional order sliding mode control (COSMC) method is also given. The control effects of VOSMC and COSMC methods are discussed by four performance indices. Finally, the utilizability and reasonability of the proposed control method is verified by using two examples (include two-story and five-story shear buildings). Compared with the COSMC method, the proposed variable fractional order controller not only has a lesser control output, but also has a higher utilization of the output, which is conducive to energy saving.

Adaptive fractional-order sliding-mode disturbance observer-based robust theoretical frequency controller applied to hybrid wind–diesel power system

Fractional order sliding mode control has been applied for speed control of PMSM. However, in many previous works, the effects of the controller's parameters have not been studied. This paper investigates the effects of fractional order on performance of FOSMC speed control of PMSM. In this work, fractional order, α and β of FOSMS-PID were varied, and their performances were compared. The simulation and experimental results show that variation of order of fractional order integration, α and order of fractional order differentiation, β can affect the performance of the FOSMC-PID controller. Selection of α and β values determines balancing strategies between integral and differentiation portion of the controller. Proper value selection and combination of these variables can further contribute to obtain optimum speed tracking, disturbance rejection and chattering reduction abilities.