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1.
Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. In this paper, we consider a general class of fully actuated mechanical systems described by Euler–Lagrange dynamics and the class of underactuated systems represented by mobile robot dynamics that are required to reach and maintain the desired trajectory in finite time. An approach known as the terminal sliding mode control (TSMC) involves non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time thus ensuring finite-time tracking. The main advantage of this control scheme is in fast converging times without excessive control effort. Such controllers are known to have singularities in some parts of the state space and, in this paper, we propose a method of partitioning the state space into two regions where the TSMC is bounded and its complement. We show that the region of bounded TSMC is invariant and design an auxiliary sliding mode controller predicated on linear smooth sliding surface for the initial conditions outside this region. Furthermore, we extend these results to address TSMC for underactuated systems characterized by the mobile robot dynamics. We demonstrate the efficacy of our approach by implementing it for a scenario when multiple dynamic agents are required to move in a fixed formation with respect to the formation leader. Finally, we validate our results experimentally using a wheeled mobile robot platform.  相似文献   

2.
Gas flow has fractional order dynamics; therefore, it is reasonable to assume that the pneumatic systems with a proportional valve to regulate gas flow have fractional order dynamics as well. There is a hypothesis that the fractional order control has better control performance for this inherent fractional order system, although the model used for fractional controller design is integer order. To test this hypothesis, a fractional order sliding mode controller is proposed to control the pneumatic position servo system, which is based on the exponential reaching law. In this method, the fractional order derivative is introduced into the sliding mode surface. The stability of the controller is proven using Lyapunov theorem. Since the pressure sensor is not required, the control system configuration is simple and inexpensive. The experimental results presented indicate the proposed method has better control performance than the fractional order proportional integral derivative (FPID) controller and some conventional integral order control methods. Points to be noticed here are that the fractional order sliding mode control is superior to the integral order sliding mode counterpart, and the FPID is superior to the corresponding integral order PID, both with optimal parameters. Among all the methods compared, the proposed method achieves the highest tracking accuracy. Moreover, the proposed controller has less chattering in the manipulated variable, the energy consumption of the controller is therefore substantially reduced.  相似文献   

3.
This paper proposes a dual terminal sliding mode control scheme for tracking tasks of rigid robotic manipulators. As a significant novelty, the presented design technique integrates the individual sliding mode surfaces to achieve the finite time convergence of tracking errors utilizing specially designed construct, and accordingly the convergence time is easily obtained due to the integral design. The underactuated issue and input limitation are specially considered in this paper, i.e., the underactuated issue is solved by introducing the hierarchical methodology into the basic dual sliding mode controller. The proposed method can easily combine with the adaptive technique to eliminate the negative effect caused by the input limitation in the rigorous stability analysis. These newly proposed methods also have the characteristics of nonsingularity and chattering suppression, and the effectiveness and high efficiency are verified by stabilizing the motions of the overhead crane and the tracking tasks of the rigid robotic manipulator. Simulation results validate the theoretical analyses about the proposed method.  相似文献   

4.
In this study, an adaptive fractional order sliding mode controller with a neural estimator is proposed for a class of systems with nonlinear disturbances. Compared with traditional sliding mode controller, the new proposed fractional order sliding mode controller contains a fractional order term in the sliding surface. The fractional order sliding surface is used in adaptive laws which are derived in the framework of Lyapunov stability theory. The bound of the disturbances is estimated by a radial basis function neural network to relax the requirement of disturbance bound. To investigate the effectiveness of the proposed adaptive neural fractional order sliding mode controller, the methodology is applied to a Z-axis Micro-Electro-Mechanical System (MEMS) gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed control system can improve tracking performance as well as parameter identification performance.  相似文献   

5.
《Journal of The Franklin Institute》2022,359(18):10653-10675
Without considering identical systems, this paper investigates the finite-time lag projective synchronization of nonidentical fractional delayed memristive neural networks (FDMNN) by designing a novel fractional sliding mode controller (SMC). Due to the existence of memristor, the research is under the framework of Filippov solution. We firstly construct a fractional integral sliding mode surface (SMS). Based on sliding mode control theory and Lyapunov stability theorem, a novel fractional SMC is proposed to realize the lag projective synchronization of nonidentical FDMNN in finite time, and the synchronization setting time is less conservative than the existing results. As the special cases, some sufficient conditions are extended to projective synchronization, lag synchronization, anti-lag synchronization of nonidentical FDMNN in finite time, which improve and enrich some existing results. At last, a simulation example is given to prove the validity of the conclusions.  相似文献   

6.
This paper investigates the frequency change problem of hydraulic turbine regulating system based on terminal sliding mode control method. By introducing a novel terminal sliding mode surface, a global fast terminal sliding mode controller is designed for the closed loop. This controller eliminates the slow convergence problem which arises in the terminal sliding mode control when the error signal is not near the equilibrium. Meanwhile, following consideration of the error caused by the actuator dead zone, an adaptive RBF estimator based on sliding mode surface is proposed. Through the dead zone error estimation for feed-forward compensation, the composite terminal sliding mode controller has been verified to possess an excellent performance without sacrificing disturbance rejection robustness and stability. Simulations have been carried out to validate the superiority of our proposed methods in comparison with other two other kinds of sliding mode control methods and the commonly used PID and FOPID controller. It is shown that the simulation results are in good agreement with the theoretical analysis.  相似文献   

7.
In order to improve the anti-disturbance performance of a bearingless induction motor (BIM) control system, a fractional-order sliding mode control (FOSMC) strategy based on improved load torque observer is proposed on the basis of the sliding mode speed regulation system. Using the information memory and genetic characteristics of the fractional calculus operator, the fractional integral term of the speed error is introduced in the design of the traditional sliding surface, which reduces the influence of disturbance on the speed regulation system. The fractional-order sliding mode control law is derived based on the BIM mathematical model, and the stability of the control law is proved by Lyapunov theorem. An improved observer is constructed based on the BIM state equations, and the real-time observed load torque is introduced into the fractional-order sliding mode controller. To improve the observer's convergence speed, the proportional integral form is used to replace the integral form in the traditional reduced order load observer. And the state error feedback coefficients of the improved load observer are calculated. Both simulation and experimental results verified the effectiveness of the proposed control strategy.  相似文献   

8.
This study investigates the passivity analysis of fractional-order Takagi-Sugeno (T-S) fuzzy systems subject to external disturbances and nonlinear perturbations under an adaptive integral sliding mode control (AISMC) methodology. To better accommodate the features of the T-S fuzzy dynamical model, a novel fractional-order memory-based integral-type sliding manifold function is defined, which is different from the existing sliding manifold function. With the help of Caputo fractional-order derivative properties and quadratic Lyapunov functional, some linear matrix inequality (LMI)-based sufficient criteria are derived to ensure the asymptotic stability conditions of resulting sliding mode dynamics with passive performance index. Besides that, an adaptive sliding mode control law is designed for the addressed systems to guarantee the system state variables onto the predefined integral sliding manifold. Finally, the effectiveness of the proposed controller is validated based on derived sufficient conditions with two practical models, such as fractional-order interconnected power systems and fractional-order permanent-magnet synchronous generator (PMSG) model, respectively.  相似文献   

9.
This paper deals with the sliding mode control problem for semi-Markovian jump systems with state saturation, in which the controller may not be synchronized with the considered systems. A mode-detector is introduced to estimate the unavailable system mode, based on which an asynchronous sliding mode controller is designed. Then, both the μ-exponential mean-square stability and the reachability of sliding surface are analyzed. Furthermore, a solving algorithm is given to acquire the feasible controller gains. Finally, the proposed asynchronous sliding mode control approach under state-saturation is illustrated via simulation results.  相似文献   

10.
In this paper, the consensus control problem of Takagi-Sugeno (T-S) fuzzy multiagent systems (MASs) is investigated by using an observer based distributed adaptive sliding mode control. A distributed nonfragile observer is put forward to estimate the unmeasured state of agents. Based on such an observer, a novel distributed integral sliding surface is designed to suppress the disturbance and uncertainty of T-S fuzzy MASs. In order to achieve the consensus objective, a nominal distributed protocol and an adaptive sliding mode controller are separately designed. Futhermore, the nominal distributed protocol solves the consensus control problem of T-S fuzzy MASs in the absence of disturbance and uncertainty by using the information of adjacent agents obtained by the observer, while the adaptive sliding mode controller suppresses the disturbance and uncertainty. Finally, the proposed method is applied to two examples. Example 1 verifies the superiority of the method by comparing with the fuzzy-based dynamic sliding mode controller. Example 2 is used to illustrate that our control scheme can effectively solve the consensus control problem of T-S fuzzy MASs.  相似文献   

11.
This paper proposes a novel fast terminal sliding mode (FTSM) control scheme, which accelerates convergence of the controlled system both in its approaching and after reaching the sliding manifold. The novelty lies in the design of time-varying sliding surface without a priori knowledge of the initial system states, so achieving insensitivity to the uncertainty of the initial states. Based on this, we design a corresponding FTSM control strategy, where the singularity problem of conventional terminal sliding mode (TSM) control systems is overcome by restricting the TSM surfaces to non-singular areas. We prove stability and finite-time convergence of the system with the proposed controller. Furthermore, we extend the proposed FTSM control scheme to high-order systems and discuss its application in practical systems. Preliminary simulation results and comparative studies demonstrate the validity of the proposed FTSM control scheme with the designed sliding surface.  相似文献   

12.
This paper investigates the design problem of asynchronous output feedback controller via sliding mode for a class of discrete-time fuzzy Markovian jump systems. Considering the non-synchronization phenomenon between the Markovian jump systems and the sliding controller, an asynchronous control method with a stochastic variable is adopted to describe the connections of the systems and controller. On the other hand, not full of states are accessible for the controller since it is impossible or very expensive to estimate all of states, while the output information can be acquired to the controller all the time. Based on the above aspects, the asynchronous output feedback controller via sliding mode for fuzzy Markovian jump systems is investigated to ensure the sliding mode dynamics to be stochastically stable, besides, several sufficient conditions are given to find a set of feasible solutions of the controller parameters. The asynchronous sliding mode control law is synthesized to guarantee the reachability of the trajectories of the closed-loop systems. Finally, a simulation example is to verify the effectiveness of the control strategy.  相似文献   

13.
This paper studies the problem of output feedback sliding mode control (OFSMC) for fractional order nonlinear systems. A necessary and sufficient condition for the existence of a sliding surface is obtained by a new singular system approach and a linear matrix equality (LMI), which reduces the conservativeness of the system. Then an OFSMC law is designed based on a fractional order Lyapunov method, which ensures that the resulting fractional closed-loop system is asymptotically stable and the states of the fractional closed-loop system converge to the sliding surface in finite time. A fractional electrical circuit is discussed to illustrate the effectiveness of the proposed approach.  相似文献   

14.
This paper proposes a data-driven terminal sliding mode decoupling controller with prescribed performance for a class of discrete-time multi-input multi-output systems in the presence of external disturbances and uncertainties. First, utilizing a discrete-time extended state observer and a compact form dynamic linearization data model, we derive a new data-driven mothod and establish the relationship between the input and output signals of controlled plant. Moreover, the disturbances, uncertainties, and couplings are suppressed owing to the application of the terminal sliding mode technique. Combined with the principle of prescribed performance control, the terminal sliding mode law with prescribed performance is derived. With the proposed data-driven method, the tracking error is lower, and the decoupling ability is improved. Furthermore, the stability of the control system is proven. Finally, a simulation is conducted on a three-tank system to demonstrate the effectiveness of the proposed scheme.  相似文献   

15.
This paper investigates a composite controller for load frequency control (LFC) in multi-region interconnected power systems via sliding mode observer design. State observers (SOs) and disturbance observers (DOs) are implied for the LFC based on the load variations with communication delays and quantization output measurements. A nonlinear integral sliding surface combined with a composite controller is developed to optimize control performance. Moreover, a three-area power system model is used to demonstrate the effectiveness of the proposed scheme in the illustrative example, confirming that frequency deviations can be rejected despite delays, uncertainties, and quantization during transmission.  相似文献   

16.
This paper precedes chaos control of fractional-order chaotic systems in presence of uncertainty and external disturbances. Based on some basic properties on fractional calculus and the stability theorems, we present a hybrid adaptive intelligent backstepping-sliding mode controller (FAIBSMC) for the finite-time control of such systems. The FAIBSMC is proposed based on the concept of active control technique. The asymptotic stability of the controller is shown based on Lyapunov theorem and the finite time reaching to the sliding surfaces is also proved. Illustrative and comparative examples and simulation results are given to confirm the effectiveness of the proposed procedure, which consent well with the analytical results.  相似文献   

17.
This paper addresses the optimal controller problem for a linear system over linear observations with respect to different Bolza–Meyer criteria, where (1) the integral control and state energy terms are quadratic and the non-integral term is of the first degree or (2) the control energy term is quadratic and the state energy terms are of the first degree. The optimal solutions are obtained as sliding mode controllers, each consisting of a sliding mode filter and a sliding mode regulator, whereas the conventional feedback LQG controller fails to provide a causal solution. Performance of the obtained optimal controllers is verified in the illustrative example against the conventional LQG controller that is optimal for the quadratic Bolza–Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode controllers.  相似文献   

18.
This paper focuses on a systematic constrained fuzzy integral sliding mode controller design for a class of uncertain discrete-time nonlinear systems which can be represented as Takagi-Sugeno (T-S) fuzzy models. The contributions are to consider constraints on the control input amplitude and control input amplitude rate and to extend the existing pole-placement design technique for designing gain matrices of the fuzzy sliding surface. Moreover, a dynamic-gain observer along with H∞ performance is proposed for attenuating disturbance, which generalizes the existing results on the Proportional Observer (PO), the Proportional Integral Observer (PIO) and the dynamic observer (DO). Finally, the dynamic-observer-based constrained fuzzy integral sliding mode controller is designed. All the proposed design conditions are represented in terms of LMIs-based ones. The methods are studied for not only single-input single-output (SISO) but also multi-input multi-output (MIMO) systems. In the end, the proposed approaches are evaluated on practical and numerical systems to illustrate the superiority of the proposed control scheme.  相似文献   

19.
This paper studies the problem of observer based fast nonsingular terminal sliding mode control schemes for nonlinear non-affine systems with actuator faults, unknown states, and external disturbances. A hyperbolic tangent function based extended state observer is considered to estimate unknown states, which enhances robustness by estimating external disturbance. Then, Taylor series expansion is employed for the non-affine nonlinear system with actuator faults, which transforms it to an affine form system to simplify disturbance observer and controller design. A finite time disturbance observer is designed to address unknown compound disturbances, which includes external disturbances and system uncertainties. A fast nonsingular terminal sliding mode with exponential function sliding mode is proposed to address output tracking. Simulation results show the proposed scheme is effective.  相似文献   

20.
This paper studies the robust stochastic stabilization problem for a class of fuzzy Markovian jump systems with time-varying delay and external disturbances via sliding mode control scheme. Based on the equivalent-input-disturbance (EID) approach, an online disturbance estimator is implemented to reject the unknown disturbance effect on the considered system. Specifically, to obtain exact EID estimation Luenberger fuzzy state observer and a low-pass filter incorporated to the closed-loop system. Moreover, novel fuzzy EID-based sliding mode control law is constructed to ensure the stability of the closed-loop system with satisfactory disturbance rejection performance. By employing Lyapunov stability theory and some integral inequalities, a new set of delay-dependent robust stability conditions is derived in terms of linear matrix inequalities (LMIs). The resulting LMI is used to find the gains of the state-feedback controller and the state observer a for the resulting closed-loop system. At last, numerical simulations based on the single-link arm robot model are provided to illustrate the proposed design technique.  相似文献   

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