Fractional-order Disturbance Observer Research Articles

Mechanical resonance suppression of the high-speed parallel robot based on fractional order disturbance observer

Considering the flexibility of the transmission shaft system, this paper presents an approach for mechanical resonance suppression of the high-speed parallel robot based on fractional order disturbance observer. First, in order to evaluate mechanical resonance, a decoupled mechatronic dynamics model is built. Based on the proposed decoupled dynamics model, the mechanical resonance under different influence factors is analyzed. Then, based on the three closed-loop control structure of servo system, a model-based parameter tuning method is adopted in the controller parameter tuning. Finally, inspired by the traditional disturbance observer, a fractional order disturbance observer is established by introducing a fractional order filter. Results show that due to the flexibility of the transmission shaft system, under the combined action of mechanical disturbance torque and electromagnetic driving torque, the joint transmission system will generate mechanical resonance phenomena. Therefore, this paper proposes a method for the mechanical resonance suppression of the high-speed parallel robot based on the fractional order disturbance observer. And the proposed method can be applied to other mechatronic device including flexible transmission shaft system.

Fractional-Order Control Method Based on Twin-Delayed Deep Deterministic Policy Gradient Algorithm

In this paper, a fractional-order control method based on the twin-delayed deep deterministic policy gradient (TD3) algorithm in reinforcement learning is proposed. A fractional-order disturbance observer is designed to estimate the disturbances, and the radial basis function network is selected to approximate system uncertainties in the system. Then, a fractional-order sliding-mode controller is constructed to control the system, and the parameters of the controller are tuned using the TD3 algorithm, which can optimize the control effect. The results show that the fractional-order control method based on the TD3 algorithm can not only improve the closed-loop system performance under different operating conditions but also enhance the signal tracking capability.

Adaptive neural backstepping control of nonlinear fractional-order systems with input quantization

This article addresses the tracking control problem of uncertain fractional-order nonlinear systems in the presence of input quantization and external disturbance. An adaptive backstepping scheme is proposed by combining with radial basis function (RBF) neural networks (NNs), fractional-order disturbance observer (FODO), and backstepping method. The RBF NNs are used to approximate the unknown nonlinearities of fractional-order systems. The FODO is designed to compensate for disturbance and uncertain parameters. The hysteresis quantizer is used to avoid chattering that possibly appears in actual application. The stability of the proposed controller is proved by fractional-order Lyapunov method. In addition, all the signals in the closed-loop system are bounded. The effectiveness of the proposed method is confirmed by the simulation results.

Command-filtered adaptive neural network backstepping quantized control for fractional-order nonlinear systems with asymmetric actuator dead-zone via disturbance observer

An adaptive neural network backstepping quantized control of fractional-order nonlinear systems with asymmetric actuator dead-zone and unknown external disturbance is investigated in this paper. An adaptive NN mechanism is designed to estimate uncertain functions. A command filter is introduced to estimate the virtual control variable as well as its derivative, so that the “explosion of complexity” problem existed in the classical backstepping method can be avoided. To handle the unknown external disturbance, a fractional-order disturbance observer is developed. Moreover, a hysteresis-type quantizer is used to quantify the final input signal to overcome the system performance damage caused by the actuator dead-zone. The quantized input signal can ensure that all the involved signals stay bounded and the tracking error converges to an arbitrarily small region of the origin. Finally, two examples are presented to verify the effectiveness of the proposed method.

Disturbance observer-based fractional-order sliding mode control for free-floating space manipulator with disturbance

This paper proposes a fractional-order sliding mode control scheme based on disturbance observer for tracking control of free-floating space manipulators (FFSM), regarding system uncertainties and disturbances. To mitigate the effect of disturbance, a fast fractional-order disturbance observer (FFODOB) is proposed, which can estimate the disturbances in finite time. It relaxes the assumption of first-order differentiable of the disturbances, which is common in many existing disturbance observers, to continuous but not necessarily differentiable, making it more suitable for practical applications. Besides, a new fractional-order nonsingular terminal sliding mode (FONTSM) controller is designed, in which, a fractional-order integral term is introduced into the conventional nonsingular terminal sliding mode surface. The presented FONTSM improves the transient response and tracking precision of FFSM. Stability of the closed-loop system and finite-time convergence are proved theoretically. Simulations are performed for different situations, and the results demonstrate the effectiveness and superiorities of the proposed methods over the existing methods.

Robust Backstepping Control Combined with Fractional-Order Tracking Differentiator and Fractional-Order Nonlinear Disturbance Observer for Unknown Quadrotor UAV Systems

In this paper, we studied a fractional-order robust backstepping control (BSC) combined with a fractional-order tracking differentiator and a fractional-order nonlinear disturbance observer for a quadrotor unmanned aerial vehicle (UAV) system. A fractional-order filtered error and a fractional-order tracking differentiator were utilized in a conventional BSC system to improve the positioning control performance of a highly coupled nonlinear quadrotor UAV system and bypass the differentiation issue of the virtual control and compensation of the transformation error in the conventional BSC design. A new fractional-order disturbance observer with the sine hyperbolic function was then proposed to enhance the estimation performance of the uncertain quadrotor UAV. Sequential comparative simulations were conducted, demonstrating that the proposed positioning controller and observer utilizing fractional-order calculus outperformed those of the conventional controller and observer systems.

Nonlinear partially saturated control of a double pendulum offshore crane based on fractional-order disturbance observer

The stabilizing control of a double pendulum offshore crane in the presence of matched disturbances, unmatched disturbances and the actuator saturations is a challenging problem. To solve this problem, an anti-swing partially saturated control method is proposed. Specially, a Fractional-Order Disturbance Observer (FODO) is designed to compensate for the matched disturbances and a feedback stabilizing controller is proposed to regulate the hook and cargo to desired positions and suppress swings. Afterwards the closed-loop asymptotical stability is strictly proven. Extensive simulation results are given to demonstrate that the proposed controller could suppress the swing effectively without exceeding the actuator saturations and has strong robustness to various disturbances.

Fractional-Order Nonsingular Terminal Sliding Mode Tension Control for the Deployment of Space Tethered Satellite

In this article, a novel fractional-order nonsingular terminal sliding mode (FONTSM) control scheme is developed, which guarantees the desired deployment performance of space tethered satellite (STS) system. The presented control scheme is to stabilize the underactuated deployment mission with only tension regulation. Based on the underactuated model, a practicable integer-order nonsingular terminal sliding mode (IONTSM) controller is designed to realize the deployment of the STS system, with the finite-time stability. Then, to improve the deployment performance, the fractional-order calculus is introduced to raise the FONTSM controller, whose Mittag-Leffler-based uniform ultimate boundedness is proved to ensure the finite-time convergence and steady-state performance. In the FONTSM controller, a fractional-order disturbance observer and a fractional-order adaptive compensation law are proposed, to eliminate the adverse impacts of external disturbances and input saturation, respectively. Moreover, compared to the reported fractional-order sliding mode control strategy of the STS system, a better deployment performance can be obtained by the IONTSM and FONTSM controllers in this work. Finally, the effectiveness of the proposed controllers is verified by groups of deployment simulations of the STS system.

Integral sliding mode H$$_\infty $$ control of fractional system in presence of unmatched disturbance

In this paper, $${H}_{\infty }$$ control for fractional order linear system in presence of unmatched disturbance is considered. Fractional order disturbance observer is designed to evaluate the unmatched disturbance. With choosing proper observer gain, the bounded convergence of the evaluated error is obtained. Afterwards an integral sliding mode surface is given on the basis of the disturbance estimation. Using linear matrix inequality technology, the state feedback controller is provided, which ensure the closed-loop system satisfy $${H}_{\infty }$$ performance. Finally, numerical example is given to illustrate the robustness of the designed control strategy.

Sliding Mode Disturbance Observer Control Based on Adaptive Hybrid Projective Compound Combination Synchronization in Fractional-Order Chaotic Systems

In this paper, the hybrid projective compound combination synchronization (HPCCS) in a class of commensurate fractional-order chaotic Genesio–Tesi system with unknown disturbance has been investigated. To deal with the problem of bounded disturbance, the nonlinear HPCCS is proposed for the fractional-order chaotic system. Further, by choosing the appropriate control gain parameters, the nonlinear fractional-order disturbance observer can approximate the disturbance efficiently. Based on the sliding mode control (SMC) method, a simple sliding mode surface has been introduced. Moreover, by using the Lyapunov stability theory, the designed adaptive SMC method establishes that the states of the three master and two chaotic slave systems are synchronized expeditiously. Finally, some numerical simulation results are illustrated to visualize the effectiveness and the utility of the developed approach on the considered system in the presence of the external unknown bounded disturbances using MATLAB.

Adaptive sliding mode output tracking control based-FODOB for a class of uncertain fractional-order nonlinear time-delayed systems

An adaptive sliding mode control (ASMC) method, based on fractional-order disturbance-observer (FODOB), is presented for a class of fractional-order nonlinear time-delay systems (FONTDS) with uncertainties to solve the target output tracking problem. The external disturbances are estimated by FODOB, and the unknown internal perturbations of the system are adaptively estimated by sliding mode control (SMC). Furthermore, Gronwalls inequality approach is used to ensure that the output tracking error is uniformly bounded for FONTDS. Firstly, a fractional-order sliding mode control (FOSMC) based FODOB is proposed for a fractional-order linear time-delay system (FOLTDS). Secondly, combined with adaptive estimation, the ASMC of FONTDS is studied. Finally, a numerical example of FONTDS is used to verify the effectiveness of the proposed methods.

Compound synchronization using disturbance observer based adaptive sliding mode control technique

This manuscript addresses a methodology for investigating compound synchronization in a class of commensurate FO chaotic Genesio-Tesi system using DOB adaptive sliding mode control technique among fractional order chaotic systems with unknown bounded disturbances. The unknown disturbances are estimated using the nonlinear fractional order disturbance observer. Sliding mode technique has been employed by considering a simple sliding surface among four identical fractional order chaotic systems to achieve the desired synchronization which is further based on Lyapunov stability theory. The obtained results have been compared with prior published literature to realize the robustness of the proposed strategy. Finally, some numerical results using MATLAB are illustrated for visualizing the effectiveness and the correctness of the developed approach on the considered system in the presence of external disturbances.

Compound synchronization using disturbance observer based adaptive sliding mode control technique

This manuscript addresses a methodology for investigating compound synchronization in a class of commensurate FO chaotic Genesio-Tesi system using DOB adaptive sliding mode control technique among fractional order chaotic systems with unknown bounded disturbances. The unknown disturbances are estimated using the nonlinear fractional order disturbance observer. Sliding mode technique has been employed by considering a simple sliding surface among four identical fractional order chaotic systems to achieve the desired synchronization which is further based on Lyapunov stability theory. The obtained results have been compared with prior published literature to realize the robustness of the proposed strategy. Finally, some numerical results using MATLAB are illustrated for visualizing the effectiveness and the correctness of the developed approach on the considered system in the presence of external disturbances.

FO improved fast terminal sliding mode control method for permanent‐magnet synchronous motor with FO disturbance observer

This study proposes a fractional-order (FO) improved fast terminal sliding mode controller for permanent-magnet synchronous motor speed regulation system. By designing an FO proportional-integral controller for current loops, an FO model between reference q -axis current and speed output is proposed. By introducing an FO terminal sliding mode surface, a novel FO terminal sliding mode controller is designed for speed loop to improve the speed tracking performance. The proposed FO controller can make speed reach reference value in finite time. Moreover, it is proved that the control time of the FO sliding mode controller is shorter than integer-order (IO) sliding mode controller. To further enhance the convergence speed, the fast terminal sliding mode control method is used. Meanwhile, FO disturbance observer is utilised to enhance the disturbance-rejection ability. The control law of the proposed controller is designed according to Lyapunov stability theorem. Finally, Simulation and experimental results demonstrate the effectiveness, high control performance and high disturbance-rejection ability of the proposed composite FO controller in comparison with IO controller.

Performance improvement of a sigma-delta modulator using fractional-order disturbance observer

This paper proposes a novel design of a high order closed-loop Sigma-Delta modulator using a fractional-order disturbance observer, which can reduce the influence of possible dispersions of the sensing element and offset the effect of the external disturbance. The proof mass can maintain near its position of equilibrium by using the proposed fractional-order disturbance observer, which ensures a better control of the proof mass displacement, and the small proof mass displacement can enhance the sensor resolution and the overall system performance. Fractional-order disturbance observer possesses stronger robust stability of interference elimination, because the introduction of fractional calculus makes Q-filter expanding from an integer domain to a real-number domain. Experimental results from the proposed architecture shows an increase of more than 2X improved in signal quantization noise ratio compared to the pure high-order closed-loop Sigma-Delta modulator, and also the proposed Sigma-Delta modulator with a fractional-order disturbance observer improves the performance of disturbance attenuation and system robustness.

Fractional order sliding mode control via disturbance observer for a class of fractional order systems with mismatched disturbance,

This article proposes a novel fractional order sliding mode control for a class of fractional order and integer order systems with mismatched disturbances. First, a new fractional order disturbance observer is designed to estimate the fractional order differential of the mismatched disturbance directly. Second, the fractional order sliding surface and controller are proposed based on the designed disturbance observer. Our method can deal with mismatched disturbance and has better control performance with faster response speed, lower overshoot, and less chattering effect. The simulations on Quad–Rotor UAV and Maglev suspension systems demonstrate the effectiveness of the proposed method.

Disturbance observer-based adaptive sliding mode hybrid projective synchronisation of identical fractional-order financial systems

In this paper, we have studied the hybrid projective synchronisation for incommensurate, integer and commensurate fractional-order financial systems with unknown disturbance. To tackle the problem of unknown bounded disturbance, fractional-order disturbance observer is designed to approximate the unknown disturbance. Further, we have introduced simple sliding mode surface and designed adaptive sliding mode controllers incorporating with the designed fractional-order disturbance observer to achieve a bounded hybrid projective synchronisation between two identical fractional-order financial model with different initial conditions. It is shown that the slave system with disturbance can be synchronised with the projection of the master system generated through state transformation. Simulation results are presented to ensure the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. Also, synchronisation error for commensurate, integer and incommensurate fractional-order financial systems is studied in numerical simulation.

Fractional Order Sliding Mode Control via Disturbance Observer for a Class of Fractional Order Systems With Mismatched Disturbance

This paper investigates a novel fractional order sliding mode control for a class of fractional order and integer order systems with mismatched disturbances. First, a new fractional order disturbance observer is designed to estimate the fractional order differential of the mismatched disturbance directly. Second, the fractional order sliding surface and controller are proposed based on the designed disturbance observer. This method can deal with mismatched disturbance and has better control performance with faster response speed, lower overshoot, and less chattering effect. The simulations on Maglev suspension system demonstrate the effectiveness of the proposed method.

Fractional order disturbance observer based adaptive sliding mode hybrid projective synchronization of fractional order Newton–Leipnik chaotic system

This manuscript, presents the fractional order disturbances observer based adaptive sliding mode hybrid projective synchronization of commensurate and incommensurate fractional order Newton–Leipnik chaotic system with disturbance. Firstly, a fractional order disturbance observer (FODO) based on adaptive sliding mode control laws for a fractional order Newton–Leipnik system with unknown bounded disturbance is studied. The appropriate control gain parameters are chosen such that the disturbance observer can approximate the unknown disturbance well. Further, we design a simple sliding mode surface based on sliding mode control technique incorporating with the designed fractional order disturbance observer for developing a bounded hybrid projective synchronization control scheme. Numerical simulation results are given to demonstrate the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. To analyse the superiority of proposed methodology we have compared our results with earlier published results as well. Moreover, as an application, the proposed scheme is then applied to a secure communication system. Simulation results verify the proposed schemes success in the communication application.

Fractional order disturbance observer based adaptive sliding mode synchronization of commensurate fractional order Genesio-Tesi system

In this manuscript, we have studied the adaptive sliding mode synchronization of commensurate fractional order Genesio-Tesi system with disturbance. Firstly, we have discussed the fractional order disturbance observer (FODO) which is based on adaptive sliding mode control laws for a commensurate fractional order Genesio-Tesi system with unknown bounded disturbance. Appropriate control gain parameters have been chosen in such a manner, so that the disturbance observer can approximate the unknown disturbance well. Further, we have designed a simple sliding mode surface based on sliding mode control technique, incorporating the designed fractional order disturbance observer for developing a bounded synchronization control scheme. Finally, the viability and the efficacy of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance for fractional order Genesio-Tesi system is established by the numerical simulation results. We have observed that for different parameters and fractional orders of Genesio-Tesi system the synchronization time varies, which is also demonstrated in numerical simulations. To visualize the robustness and effectiveness of proposed methodology we have compared our results with earlier published results as well. Moreover, as an application, the proposed scheme is then applied to a secure communication scheme. Simulation results verify the proposed schemes success in the communication application.