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The classical super-twisting algorithm (STA) has many advantages, such as the simplicity, finite-time convergence, high accuracy, and robustness. However, its scalar input and output may hinder its applications in affine systems with multiple inputs and multiple outputs (MIMO). Therefore, the classical STA has been extended into multivariable versions in the literature to overcome such a limitation. The problem is that, the multivariable STA inherits another downside of the classical STA during implementation, that is, the numerical chattering for large sizes of the sampling period or gains of the STA, which deteriorates the control performance in MIMO systems. This brief proposes a new discrete-time implementation scheme for the multivariable STA with a semi-implicit Euler discretization approach. It attenuates the numerical chattering while reserving the robustness of the multivariable STA. The advantages of the proposed scheme are demonstrated numerically with comparisons with the classical STA and the multivariable STA implementation method through simulations. [ABSTRACT FROM AUTHOR]

The significant numerical chattering hinders control applications of the twisting algorithm in digital environments. Previous implicit discrete-time implementation algorithms have the potential to attenuate the numerical chattering, but they require numerical solvers or do not consider the zero-order hold (ZOH) effect of Analog to Digital Converter (ADC) devices in digital control applications. This brief introduces an enhanced implementation algorithm for the famous twisting algorithm with the ZOH discretization method. It entails no numerical solvers and takes the ZOH effect into account, which enables control applications of the twisting algorithm in practice. The stability properties of the proposed realization algorithm are also analyzed with Lyapunov methods. Comparing to the previous implicit-Euler based implementation scheme for the twisting algorithm, the proposed one significantly attenuates the chattering in the presence of the ZOH effect without the requirement of any numerical solver. [ABSTRACT FROM AUTHOR]

In this technical note, free-will arbitrary time terminal sliding mode control design is proposed. With such a design, it is possible to control the time duration of sliding in the sliding phase. Under the assumption that the chosen arbitrary time is greater than the reaching phase time ($t_{r}$), it is shown that the $n^{\textrm {th}}$ order chain of integrators converges to zero within the selected arbitrary time. An algorithm is also proposed for the case when $t_{r}$ is not known to the designer. Stability analysis based on Lyapunov theory has been provided. [ABSTRACT FROM AUTHOR]

In this article, the free-will arbitrary time consensus is formulated for multiagent systems. This consensus protocol is independent of initial conditions and any other system parameters. With such a protocol, the multiagent system is shown to attain consensus as well as average consensus within the prespecified arbitrary time. Agents rendezvous can also be accomplished with the given protocol. Communication imperfections are easily handled with the designed protocol. Robust free-will arbitrary time consensus protocol is also designed. The stability of such nonlinear nonautonomous protocols is established using suitable Lyapunov functions. Simulation examples confirm the theoretical findings. [ABSTRACT FROM AUTHOR]

The work presented in this brief describes the design of a discrete-time super-twisting algorithm based fractional-order observer for a class of non-linear fractional-order systems. The proposed observer is shown to achieve higher performance as compared to the conventional integer-order observers in terms of robustness and convergence time. It generalizes the design of observers for the class of non-linear fractional-order systems. The peaking phenomenon is observed to be less significant in the proposed approach. Chattering is suppressed with the Fractional Adams-Moulton Method, which is an implicit Euler discretization technique. The significance of the proposed observer is illustrated through a simulation example. [ABSTRACT FROM AUTHOR]

A Hands-off control law is investigated to asymptotically stabilize a nonlinear system with input-quantization. The quantization parameters generated at the coder and decoder sides of the communication channel are mismatched and a time-varying ratio is modeled to show the non-synchronous adjustment of the quantization parameters. By the means of $[\mathcal {K,KL}]$ sector, the state-space is roughly divided into an attractive and non-attractive regions and a controller based on On-Off logic is utilized to remove the model uncertainties caused by the mismatch of the quantization parameters with limited control effort. Finally, the illustration of the proposed scheme is verified for an electronic circuit. [ABSTRACT FROM AUTHOR]

For uncertain systems with relative degree two, an output feedback based twisting algorithm is proposed. This algorithm ensures practical asymptotic convergence to the origin based on the information of output and its artificially delayed version. We prove the convergence of the proposed algorithm by a continuous, weighted homogeneous and strict Lyapunov function. [ABSTRACT FROM AUTHOR]

In this brief, a new discrete-time implementation is proposed for the super-twisting control with a semi-implicit Euler method. In contrast to the conventional realization methods, the proposed implementation scheme exploits two signum functions in the super-twisting algorithm (STA) such that the numerical chattering is totally avoided and the control precision is enhanced in terms of smallest control errors in the steady state. It has an advantage that the control accuracy is insensitive to the gain overestimation of STA, which benefits the gain tuning of the STA in practice. These superiorities of the proposed scheme are demonstrated through simulations and comparisons with other state of the art relevant to STA realization methods. [ABSTRACT FROM AUTHOR]

This brief proposes an adaptive first-order sliding mode control (SMC) with a predefined convergence time in a digital framework. It is based on an implicit Euler discretization of the set-valued signum function in SMC and a time-dependent adaptive gain scheme. Two typical cases are discussed and their stability analysis is provided, simple affine systems with first-order SMC and LTI systems with equivalent control-based sliding mode control (ECB-SMC), both in the presence of unknown perturbations. Numerical simulations show that, compared with the conventional SMC, the proposed implicit discrete-time SMC guarantees the convergence of the states within any predefined arbitrary time. [ABSTRACT FROM AUTHOR]

One of the main problems of terminal sliding mode control (TSMC) is the severe numerical chattering caused by its discretization during the discrete-time realization, which significantly deteriorates the control performances. This brief proposes two novel realization schemes for the second-order TSMC based on implicit Euler methods. The first one treats the TSMC as the first-order SMC by solving the nonlinear equation of sliding surface. The latter one treats the second-order TSMC as nested signum functions without solving the nonlinear equation. Both schemes reduce the magnitude of numerical chattering while the second one totally remove the numerical chattering after attaining on the discrete-time sliding surface. The proposed two novel realizations have higher control performances in term of smaller control errors of steady state. These advantages of the proposed schemes are demonstrated through a buck converter circuit system in the presence of model uncertainties by comparing to the conventional implementations of TSMC. [ABSTRACT FROM AUTHOR]

This brief proposes an adaptive observer based on the super-twisting algorithm (STA) and its discrete-time realization with a predefined convergence time. In contrast to conventional adaptive STA that tries to adaptively reduces the gain sizes as much as possible in accordance with external disturbances, the proposed adaptive observer increases the gain sizes such that the convergence time is ensured to be within the predefined convergence-time period. The numerical chattering associated with these large gains is suppressed by employing the proposed discrete-time realization based on an implicit Euler discretization method. While keeping the property of predefined convergence time, the observation precision of the proposed discrete-time scheme is consistent with the STA, i.e., standard asymptotical second-order accuracy level. The superiority of the adaptive observer and its realization scheme is demonstrated through a circuit system example. [ABSTRACT FROM AUTHOR]

This brief proposes a discrete-time fractional-order differentiator based on the super-twisting algorithm for second-order systems. The differentiator achieves higher performance with respect to the classical ones of integer order in terms of convergence time and robustness. It relaxes the classical boundedness condition required to be satisfied by the second-order derivatives of the functions in conventional differentiators. The numerical integration is performed by an implicit Euler discretization technique based on the Fractional Adams-Moulton method, which significantly suppresses the chattering. The significance of the proposed differentiator is demonstrated through a simulation example, comparing with the classical ones. [ABSTRACT FROM AUTHOR]

This brief proposes a new discrete-time realization of the super-twisting algorithm based observer. While keeping the property of chattering suppression, the estimation precision of the proposed realization scheme is consistent with the continuous-time super-twisting algorithm (STA), that is, in the absence of noises, the estimation errors satisfy the standard asymptotical accuracy level, i.e., |e1| ~ μ1h2 and |e2|~ μ2h with sampling time h and two positive constants μ1 and μ2. Comparing to the conventional explicit Euler method, the proposed scheme is more exact in the term of smaller constants μ1 and μ2. The superiority of the proposed scheme is demonstrated through an example of typical buck converter circuit system. [ABSTRACT FROM AUTHOR]

A new strategy for the design of controller and state observer is proposed based on the vector based contraction framework. The methodology gives relaxation over the conventional contraction theory as there is no requirement to guarantee the negative definiteness of the complex Jacobian matrix to derive convergence results. The vector framework is used to simplify the problem through the comparison systems. Specifically, suitable choice of comparison system derives the convergence of squared distance between any pair of trajectories in a reduced way. The examples of controller design for duffing system and observer design for Chua’s circuit are illustrated to see the implementation of the proposed results. Furthermore, results are observed through simulation. [ABSTRACT FROM AUTHOR]

This brief proposes new discrete-time algorithms of the super-twisting observer and the twisting controller to be applied to second-order systems. The algorithms are based on the full implicit-Euler discretization, which contributes to the elimination of chattering. Proofs of some stability properties of the discretized twisting controller are also provided. Simulations show that, as compared to traditional explicit-Euler schemes, the proposed scheme avoids the chattering both in trajectory tracking output and control input in the presence of external disturbances. [ABSTRACT FROM AUTHOR]

This brief suggests an approach to design a robust ${[\mathcal {K,KL}]}$ sector for nonlinear system subjected to parametric/model uncertainty and this design relies on the Matrosov’s results. The nonlinear surface to decide the boundaries of a sector is designed by using a control-Lyapunov function. Here, a Hands-Off control consists of constant and state-dependent gain is used to force the state vectors to the interior of robust ${[\mathcal {K,KL}]}$ sector and shows asymptotic stability with minimum support to the nonlinear system by avoiding the redundant control effort. The usefulness of the proposed design is illustrated by a nonlinear electronic circuit. [ABSTRACT FROM AUTHOR]

This brief addresses the global stabilization of uncertain single input and single output (SISO) dynamical systems using sliding mode control with multiple delayed partial state feedback. It is shown that using only delayed partial state information, it is possible to stabilize a large class of SISO uncertain dynamical systems. Artificial stabilizing delay is introduced in the partial state feedback to make the reduced-order sliding mode dynamics of a given system asymptotically stable. It is demonstrated that despite the order of dynamical systems, using the information of just three states together with their delayed terms, can asymptotically stabilize the uncertain SISO dynamical system. A numerical example of a ball and wheel system is provided to demonstrate the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

This brief addresses the problem of finite-time constrained stabilization of nonlinear systems with matched uncertainties. The constrained stabilization refers to designing of higher order finite-time control law such that the output $ {\sigma }$ of the system remains in some prescribed range, i.e., $ {\sigma \in (- c, c)}$ , ${c}$ is chosen as constant while all the higher derivative of the output $ {\sigma }$ satisfy, ${\sigma }=\ddot {\sigma }= \cdots =\dot {\sigma }^{n}=0$ in some finite interval of time. The above problem of relative degree ${n}$ with respect to output $ {\sigma }$ cannot be directly solved by using higher order sliding mode control. Therefore, a new coordinate transformation has been proposed in this brief to reduce the relative degree of such systems by one in some pre-specified range of space. However, in the remaining space, the problem of stabilization can be solved by higher order sliding mode controller having the same relative degree. The segway application is considered as an example to demonstrate the efficacy of the proposed theory. [ABSTRACT FROM AUTHOR]

Finding and tracking maximum power point are two important dynamics in the control of variable-speed wind turbines since they determine the efficiency of wind turbines. The conventional hill climbing possesses the problems of wrong directionality and low performance since it does not take the inertial effect into account. In this paper, a novel hill climbing method is proposed by considering the inertial effect to solve these problems. Besides, employing the exact model knowledge of the generator in the maximum power tracking control deteriorates the efficiency considerably; therefore, it is required to design a parameter independent and robust control system if possible. Thus, the third-order super-twisting sliding mode and continuous integral sliding mode controllers are designed for the control of generator and grid-side converters to track the maximum power trajectory accurately, and they are compared to each other for the chattering in experimental results. A comparison is also performed between the conventional and proposed hill climbing methods based on the captured energy from the wind. Experimental results, with a wind turbine emulator, demonstrate that the proposed hill climbing method relaxes the wrong directionality and sluggish performance of the conventional one. [ABSTRACT FROM AUTHOR]

The tracking problem of desired signal can be transformed to an equivalent stabilization problem about the origin in the error co-ordinate provided the desired signal is differentiable. If the desired signal is not differentiable, then it is not straightforward to solve the tracking problem. In this brief, a methodology based on fractional operators has been suggested to solve this tracking problem, for those classes of non-differentiable reference signals which are integrable. The simulation results of its application to a switch controlled RL circuit is demonstrated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]