Nonlinear sliding surface based second order sliding mode controller for uncertain linear systems (original) (raw)
Related papers
International Journal of Robotics and Automation, 3(3): 192-211, 2012
Refer to this research, a baseline error-based tuning sliding mode controller (LTSMC) is proposed for robot manipulator. Sliding mode controller (SMC) is an important nonlinear controller in a partly uncertain dynamic system’s parameters. Sliding mode controller has difficulty in handling unstructured model uncertainties. It is possible to solve this problem by combining sliding mode controller and adaption law which this method can helps improve the system’s tracking performance by online tuning method. Since the sliding surface gain (λ) is adjusted by baseline tuning method, it is continuous. In this research new λ is obtained by the previous λ multiple sliding surface slopes updating factor δ. Baseline error-based tuning sliding mode controller is stable model-based controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in baseline error-based tuning sliding mode controller based on switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.4 second, steady state error = 1.8e-10 and RMS error=1.16e-12).
A second-order smooth sliding mode control
Heart Lung and Circulation, 2001
Presented is a method of continuous sliding mode control design to provide for the second-order sliding mode on the selected sliding surface. The control law is a nonlinear dynamic feedback that in the absence of unknown disturbances provides for finite-time convergence of the second-order reaching phase dynamics. The application of the second-order disturbance observer in combination with the proposed continuous
International Journal of Control and Automation, 5(3): 217-236, 2012
Refer to this research, a linear error-based tuning sliding mode controller (LTSMC) is proposed for robot manipulator. Sliding mode controller (SMC) is an important nonlinear controller in a partly uncertain dynamic system’s parameters. Sliding mode controller has difficulty in handling unstructured model uncertainties. It is possible to solve this problem by combining sliding mode controller and adaption law which this method can helps improve the system’s tracking performance by online tuning method. Since the sliding surface gain ( ) is adjusted by new linear tuning method, it is continuous. In this research new is obtained by the previous multiple sliding surface slopes updating factor which is a coefficient varies between half to one. Linear error-based tuning sliding mode controller is stable model-based controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in linear error-based tuning sliding mode controller based on switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.4 second, steady state error = 1.8e-10 and RMS error=1.16e-12).
Fast second-order sliding mode control design based on lyapunov function
We design a new kind of fast terminal sliding mode controller for second-order uncertain systems with a single control input. In contrast to the reported techniques, which are based on the Terminal Sliding Mode Control, the proposed controller design is based on Lyapunov methods. Sufficient conditions are given to ensure the finite-time stability of the close-loop system with the proposed discontinuous controller. The performance is compared with others Fast Terminal Sliding Mode controllers by means of a simulation example.
On multi-input chattering-free second-order sliding mode control
IEEE Transactions on Automatic Control, 2000
A solution to the problem of eliminating the chattering effect, which is always associated with practical implementations of variable structure control, is presented in this paper with reference to a class of uncertain multi-input nonlinear systems. The solution procedure relies on the application of an original control approach capable of enforcing a second-order sliding mode (i.e., a sliding regime on a surface [ ()] = 0 in the system state space, with _[ ()] identically equal to zero, a regime enforced by a control signal depending on [ ()], but directly acting only on [ ()]). Such an approach, in its original formulation, only applies to single-input nonlinear systems with particular types of uncertainties. In the present paper, its validity is extended to multi-input nonlinear systems characterized by uncertainties of more general nature, covering a wide class of real processes.
International Journal of Modelling, Identification and Control, 2017
The sliding mode control concept has been extensively investigated during the last decade, where it has been proved that such a control strategy is not so simple to be efficiently applied in dynamical and mechanical systems, because of the too strong sensitivity of such systems to the chattering phenomenon. In this paper, a reformulated second order sliding mode controller has been implemented into a robotic system for a trajectory tracking task, both in the case of ideal operation as well as for real systems submitted to parameter uncertainties. A comparative study performed through the obtained simulation results has been presented. Then, an adaptive extension of the second order sliding mode control has been treated seeking to resolve the challenging problems of real systems reflected by the presence of physical and environmental disturbances and especially parametric uncertainties. The proposed adaptive second order SMC has the advantage that it allows not only to remedy disturbing phenomena but also to retain all properties and system performances. Simulation results performed on a robotic manipulator system have illustrated improved performances with the proposed adaptive second order sliding mode control design.
A survey of applications of second-order sliding mode control to mechanical systems
International Journal of Control, 2003
The effective application of sliding mode control to mechanical systems is not straightforward because of the sensitivity of these systems to chattering. Higher-order sliding modes can counteract this phenomenon by confining the switching control to the higher derivatives of the mechanical control variable, so that the latter results are continuous. Generally, this approach requires the availability of a number of time derivatives of the sliding variable, and, in the presence of noise, this requirement could be a practical limitation. A class of second-order sliding mode controllers, guaranteeing finite-time convergence for systems with relative degree two between the sliding variable and the switching control, could be helpful both in reducing the number of differentiator stages in the controller and in dealing with unmodelled actuator dynamics. In this paper different second-order sliding mode controllers, previously presented in the literature, are shown to belong to the above cited class, and some challenging control problems involving mechanical systems are addressed and solved. Simulations and experimental results are provided throughout the paper.
Stability analysis of discrete input output second order sliding mode control
International Journal of Modelling, Identification and Control, 2014
The success of the sliding mode control (SMC) is due to the simplicity of its implementation and its robustness against external disturbances via state space and input output model. In spite of this characteristic, the sliding mode control (SMC) suffers from a main drawback known as the 'chattering phenomenon'. In order to overcome this problem, a new discrete second order sliding mode control via input output model is proposed in this paper. A stability analysis of the proposed control was then studied. To illustrate the effectiveness of the proposed discrete second order sliding mode control law, a classical discrete sliding mode control and discrete second order sliding mode control were applied to a real discrete second order system via input output model. The experimental results of the proposed discrete sliding mode control law show good performances in terms of the rejection of the external disturbances and the reduction of the chattering phenomenon.
A novel sliding mode controller scheme for a class of nonlinear uncertain systems
International Journal of Modelling, Identification and Control, 2018
This paper considers a continuous sliding mode control for a class of nonlinear systems with uncertainties including both parameter variations and external disturbances. Under the framework of sliding mode and using the upper bounds of the uncertainties, the proposed controller is derived to guarantee the stability of an overall closed-loop system and ensure robustness against modelling errors, parameter uncertainties and external disturbances. As for chattering elimination in sliding mode control, a boundary layer around the sliding surface is used and the continuous control is applied within the boundary. Moreover, an extended schema of a higher-order sliding mode controller is developed in this paper as another solution to avoid the problem of chattering effect. Simulation results demonstrate the efficacy of the proposed control methodology to stabilise an inverted pendulum, which is a standard nonlinear benchmark system. The applicability of the proposed algorithm will be extended, via suitable modifications, to the case of multivariable nonlinear systems with uncertainties of more general type, covering a wide class of processes.
An Improved Second-Order Sliding-Mode Control Scheme Robust Against the Measurement Noise
IEEE Transactions on Automatic Control, 2004
In this note the second-order sliding-mode control problem is addressed and solved by explicitly taking into account the presence of measurement error with unknown upper bound δ. Under sensible assumptions regarding the uncertain dynamics of a broad class of nonlinear plants, a new switching controller is proposed guaranteeing a sliding accuracy of order O(τ 2 ) + O(δ), τ being the sampling interval. Simulations highlight the effectiveness of the proposed approach and confirm the expected precision order.