Asif Chalanga

Implementation of Super-Twisting Control: Super-Twisting and Higher Order Sliding-Mode Observer-Based Approaches

In this paper, an output feedback stabilization of perturbed double-integrator systems using super-twisting control (STC) is studied. It is shown that when STC is implemented based on super-twisting observer (STO), then it is not possible to achieve second-order sliding mode (SOSM) using continuous control on the chosen sliding surface. Two methodologies are proposed to circumvent the above-mentioned problem. In the first method, control input is discontinuous, which may not be desirable for practical systems. In the second method, continuous STC is proposed based on higher order sliding mode observer (HOSMO) that achieves SOSM on the chosen sliding surface. For simplicity, we are considering here only the perturbed double integrator, which can be generalized for an arbitrary-order systems. Numerical simulations and experimental validation are also presented to show the effectiveness of the proposed method.

Continuous terminal sliding-mode controller

For uncertain systems with relative degree two, a continuous homogeneous sliding-mode control algorithm is proposed. This algorithm ensures finite-time convergence to the third-order sliding set, using only information about the output and its first derivative. We prove the convergence of the proposed algorithm via a homogeneous, continuously differentiable and strict Lyapunov function.

Higher order super-twisting algorithm

Generalization of the Super-Twisting algorithm (STA) for r relative degree system with respect to output, ensuring finite time convergence to the set σ, σ̇,..., π^(r) where σ represents the output via absolutely continuous control signal using information of σ, σ̇,..., π^(r)-1 are discussed. The convergence conditions for the 3-STA algorithm are proposed. The formula for algorithm of arbitrary order is suggested. The simulations results are confirmed the efficiency of the proposed algorithm.

A New Algorithm for Continuous Sliding Mode Control With Implementation to Industrial Emulator Setup

This paper presents a new control algorithm for obtaining continuous sliding mode control, based on integral sliding-mode control (ISMC), where the discontinuous part of the ISMC is replaced with a continuous control. It is shown that the well-known super twisting control (STC), which replaces the discontinuous part of the ISMC acts as a disturbance observer, and hence, cancels the matched disturbance. As the overall controller is continuous the proposed method is advantageous over the existing ISMC, which has a discontinuous term. Also from the practical implementation point of view, in particular for mechanical systems, discontinuous term will result in chattering, which is undesirable. The proposed algorithm has been implemented on a practical system and its superiority has been demonstrated.

How to implement Super-Twisting Controller based on sliding mode observer?

Implementation of the Super-Twisting Control (STC) requires the first time derivative of the sliding surface must be Lipschitz in time. It is shown that if we will use STC based on the absolutely continuous estimation of the surface, controller can not be implemented. In this paper two methodologies are proposed to avoid the above problem. For simplicity we are considering here only perturbed double integrator which can be generalized for an arbitrary order. Numerical simulations are also presented to show the effectiveness of the proposed method.

Continuous integral sliding mode control: A chattering free approach

The integral sliding mode control, existing in literature is a combination of nominal control and a discontinuous feedback control. Discontinuity in feedback control, is not suitable for many practical applications due to the practical limitations of actuators, known as chattering. In this paper, the integral sliding-mode control law is modified for linear as well as nonlinear systems with matched disturbance replacing the discontinuous part of the feedback control by a super-twisting control. Replacement is possible due to the unique feature of disturbance observation property of the super-twisting algorithm. The proposed controller is continuous due to the combination of two continuous controls. The effectiveness of the modified control law is shown by the simulation on a practical setup-Quanser SRV-02 for position control.

Continuous Nested Algorithms : The Fifth Generation of Sliding Mode Controllers

The history and evolution of Sliding Mode Controllers in the last three decades is revisited. The new generation of continuous sliding-mode controllers, and continuous nested sliding-mode controllers is presented. Such controllers generate an continuous control signal, ensuring, for the systems with relative degree r, the finite–time convergence to the (r + 1) − th sliding-mode set using only information on the sliding output and its derivatives up to the (r − 1) order.

Smooth integral sliding mode controller for the position control of Stewart platform.

This paper proposes the application of a new algorithm for the position control of a Stewart platform. The conventional integral sliding mode controller is a combination of nominal control and discontinuous feedback control hence the overall control is discontinuous in nature. The discontinuity in the feedback control is undesirable for practical applications due to chattering which causes the wear and tear of the mechanical actuators. In this paper the existing integral sliding mode control law for systems with matched disturbances is modified by replacing the discontinuous part by a continuous modified twisting control. This proposed controller is continuous in nature due to the combinations of two continuous controls. The desired position of the platform has been achieved using the proposed controller even in the presence of matched disturbances. The effectiveness of the proposed controller has been proved with the simulation results.

Multivariable continuous integral sliding mode control

This paper proposes multivariable integral sliding mode controller for any Multi Input Multi Output (MIMO) system. The conventional integral sliding mode controller consists of a nominal control and a discontinuous feedback control such that the overall control is discontinuous in nature. The discontinuity in feedback control is undesirable for practical applications due to chattering. In this paper the existing integral sliding mode control law for MIMO systems with matched disturbances is modified by replacing the discontinuous part by a multivariable super twisting algorithm. This proposed controller is continuous in nature due to the combinations of two continuous controls and also disturbance can be rejected successfully. The effectiveness of the proposed control method has been demonstrated with the simulation results.

State estimation and non vanishing unmatched disturbance reconstruction using modified super twisting algorithm

The super-twisting second-order sliding-mode algorithm is modified for a class of nonlinear systems with non vanishing unmatched disturbance. The proposed method is based on the modified super-twisting algorithm where the states can be estimated exactly in the presence of non vanishing unmatched disturbance. The value of the equivalent output injection is used to reconstruct disturbance directly. The effectiveness of the modified algorithm is shown by simulation.