Continuous Fixed‐Time Convergent Super‐Twisting Algorithm in Case of Unknown State and Disturbance Initial Conditions

Rodriguez‐Ramirez, Pablo; Garza-Alonso, Alison

doi:10.1002/asjc.1924

Cited by 29 publications

(13 citation statements)

References 34 publications

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“…Definition 4 (see [36]). The system (29) is called fixed-time convergent to the origin, if the origin is globally finite-time stable and the settling time function Tðx 0 Þ is bounded by positive constant T max > 0, i.e., the system state xðt, x 0 Þ ∈ R n is equal to zero, for all t ≥ T max , starting from any initial condition x 0 .…”

Section: Definition and Lemmasmentioning

confidence: 99%

High Precision Control of Rotating Payload Satellite considering Static and Dynamic Unbalanced Disturbance

Zhao

Wei

et al. 2022

International Journal of Aerospace Engineering

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This paper is devoted to suppressing the lumped disturbance, which is mainly composed of static and dynamic unbalanced disturbance, to ensure the imaging quality of the rotating payload satellite system with a five-degree-of-freedom active magnetic bearing. The dynamic model of lumped disturbance in imaging phase is established to design the balancing error index of payload unbalance, and the effect of bearing mechanical characteristics is analyzed. A novel fixed-time extended state observer is proposed to estimate unknown lumped disturbance and uncertainty. On this basis, a novel quaternion-based fixed-time nonsingular terminal sliding mode controller is presented to achieve high precision, high stability, and chattering-free attitude control. The complete proof on the faster convergence performance of the presented sliding mode surface compared to the existing sliding mode surfaces and the fixed-time convergence of the presented controller is provided. Numerical simulation results are carried out to verify the lumped disturbance modeling accuracy and the effectiveness of the proposed controller.

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Section: Definition and Lemmasmentioning

confidence: 99%

High Precision Control of Rotating Payload Satellite considering Static and Dynamic Unbalanced Disturbance

Zhao

Wei

et al. 2022

International Journal of Aerospace Engineering

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“…As follows from Theorem 1, adding the fourth exponential term (6) in the control law (12), Àh (e jv(t)j À1) e jv(t)j (tf Àt) sign(v(t)), makes this finitetime convergence predefined for a time no greater than t f . Finally, as follows from Theorem 1 in Basin et al (2019), adding the second term in the control law (12), Àl 2 jv(t)j p sign(v(t)) with l 2 . 0, yields fixed-time convergence of system states (13) to the origin, if h = 0, and suppression of the disturbance _ z(t).…”

Section: Control Designmentioning

confidence: 99%

“…Fixed-time convergent algorithms, where the convergence times are independent of state initial conditions, are studied starting from Andrieu et al (2008) and Polyakov (2012). Continuous fixed-time convergent scalar and multi-variable control laws are proposed in Basin et al (2019) for a super-twisting system, whose state and disturbance initial conditions are unknown, and the upper estimates of their convergence times are calculated. A continuous fixed-time convergent control law driving the states of a stochastic super-twisting system at the origin for a fixed-time is designed in Guerra-Avellaneda and .…”

Section: Introductionmentioning

confidence: 99%

Predefined-time stabilization of permanent-magnet synchronous motor

Garza-Alonso

Rodriguez‐Ramirez

2021

Transactions of the Institute of Measurement and Control

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This paper designs a predefined-time convergent continuous control algorithm to stabilize a permanent-magnet synchronous motor (PMSM) system. Three cases have been considered: disturbance-free, in presence of a deterministic disturbance satisfying a Lipschitz condition, and in presence of both a stochastic white noise and a deterministic disturbance satisfying a Lipschitz condition. The designed control law is free from the restrictions of exponential control growth and exact initial conditions knowledge. This is the first predefined-time convergent continuous control algorithm applied to stabilizing a PMSM system with both deterministic and stochastic disturbances, which enables one to a priori set the predefined convergence time even in presence of various disturbances of different nature. Numerical simulations are provided for a PMSM system to validate the obtained theoretical results in each of the three considered cases. The simulation results demonstrate that the employed values of the predefined-time convergent control inputs are applicable in practice.

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“…This difficulty in linear system is handled by assigning multi‐step sets associated with scaling parameters which guarantee the closed‐loop H∞ performance using random system trajectories 11 . Further, in Basin et al, 12 a direct extension is provided for the unknown state and disturbance initial conditions of a super‐twisting control algorithm by designing a fixed‐time convergent smooth second‐order observer. The developed approach identified the drawback of zero initial value for the disturbance while calculating the upper estimate of control algorithm convergence time and overcomes it by admitting a disturbance with unknown but bounded initial value.…”

Section: Introductionmentioning

confidence: 99%

Adaptive control using stochastic approach for unknown but bounded disturbances and its application in balancing control

Singh

Bhushan

2021

Asian Journal of Control

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This paper presents a simultaneous perturbation stochastic approximation (SPSA) approach for unknown but bounded disturbances in a typical closed loop system. These random disturbances are represented by a sequence of uncertainties along with the measured system output. Further, the proposed approach constructs a sequence of estimates and formulates an optimization problem which is minimized to achieve the adaptive control. In addition, the convergence conditions and additional generalizations are proposed to enhance the operation of SPSA algorithms for trail perturbation properties. To address the major challenges with unknown disturbances on the closed loop system, a balancing control problem with two degree of freedom (2DoF) ball balancer system and proportional integral derivative (PID) controller is considered. The proposed SPSA method minimizes the optimization problem to obtain the gain values of the PID controller. Simulation and experimental analysis are carried out, and the results substantiate that the PID gains optimized using SPSA provide better control when compared to conventional control approach in terms of tracking response under random uncertainties. K E Y W O R D Sball balancer system, proportional integral derivative (PID), simultaneous perturbation and stochastic approximation, two degree of freedom (2DoF), uncertainties

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Continuous Fixed‐Time Convergent Super‐Twisting Algorithm in Case of Unknown State and Disturbance Initial Conditions

Cited by 29 publications

References 34 publications

High Precision Control of Rotating Payload Satellite considering Static and Dynamic Unbalanced Disturbance

High Precision Control of Rotating Payload Satellite considering Static and Dynamic Unbalanced Disturbance

Predefined-time stabilization of permanent-magnet synchronous motor

Adaptive control using stochastic approach for unknown but bounded disturbances and its application in balancing control

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