Shyam Kamal

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.

Finite-Time Stabilization of Fractional Order Uncertain Chain of Integrator: An Integral Sliding Mode Approach

In this technical note, a novel methodology for robust finite-time stabilization of a chain of uncertain fractional order integrator is proposed. This is achieved by first designing a nominal controller which stabilizes the system in finite time. An integral sliding-mode like surface and a switching controller is proposed such that when the system is on the surface the equivalent value of the integral sliding-mode control is the negative of the disturbance and hence the disturbance is cancelled. An improved strategy with more general kind of uncertainty is also proposed. Numerical examples are presented to illustrate the proposed methods.

Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach

In the last two decades fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and many others. It opens a new and more realistic way to capture memory dependent phenomena and irregularities inside the systems by using more sophisticated mathematical analysis. This monograph is based on the authors work on stabilization and control design for continuous and discrete fractional order systems. The initial two chapters and some parts of the third chapter are written in tutorial fashion, presenting all the basic concepts of fractional order system and a brief overview of sliding mode control of fractional order systems. The other parts contain deal with robust finite time stability of fractional order systems, integral sliding mode control of fractional order systems, co-operative control of multi-agent systems modeled as fractional differential equation, robust stabilization of discrete fractional order systems, high performance control using soft variable structure control and contraction analysis by integer and fractional order infinitesimal variations.

Fault tolerant control allocation via continuous integral sliding-modes

In this paper a continuous fault tolerant control allocation is proposed. This approach is based on a uniform High-Order Sliding-Mode Observer where only measurable outputs are used. The fault tolerant control scheme is developed using, for the first time, a continuous integral sliding-mode and a fixed control allocation technique which provides an approximate estimation of matched faults. The conditions for stability are found by ensuring the stability of the closed loop system in the presence of possible faults in the components, and actuator faults or failures. The effectiveness of the proposed approach is verified through simulation of a linear version of the benchmark B 747 -100/200 civil aircraft model.

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.