Stability Analysis for Prioritized Closed-Loop Inverse Kinematic Algorithms for Redundant Robotic Systems

SUMMARYThe paper introduces a novel general feedback control framework, which allows applying the motion controllers originally dedicated for the unicycle model to the motion task realization for the car-like kinematics. The concept is formulated for two practically meaningful motorizations: with a front-wheel driven and with a rear-wheel driven. All the three possible steering angle domains for car-like robots—limited and unlimited ones—are treated. Description of the method is complemented by the formal stability analysis of the closed-loop error dynamics. The effectiveness of the method and its limitations have been illustrated by numerous simulations conducted for the three main control tasks, namely, for trajectory tracking, path following, and set-point regulation.

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Closed-loop Stability Analysis of DC / DC Converter with Input Filter

10.1109/iciba50161.2020.9277259 ◽

2020 ◽

Author(s):

Zhisong Lin ◽

Yong Liu ◽

Xiaobin He ◽

Wei Xie ◽

Mengxue Dong ◽

...

Keyword(s):

Stability Analysis ◽

Closed Loop ◽

Input Filter ◽

Loop Stability

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Closed-Loop Stability Analysis and Controller Design

Stability Analysis and Controller Design of Local Model Networks ◽

10.1007/978-3-658-34008-7_4 ◽

2021 ◽

pp. 55-68

Author(s):

Christian Mayr

Keyword(s):

Stability Analysis ◽

Closed Loop ◽

Controller Design ◽

Loop Stability

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A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

International Journal of Advanced Robotic Systems ◽

10.1177/1729881418819956 ◽

2019 ◽

Vol 16 (1) ◽

pp. 172988141881995

Author(s):

Francisco G Salas ◽

Jorge Orrante-Sakanassi ◽

Raymundo Juarez-del-Toro ◽

Ricardo P Parada

Keyword(s):

Stability Analysis ◽

Performance Index ◽

Closed Loop ◽

Tracking Error ◽

Parallel Robots ◽

Control Loop ◽

Closed Loop System ◽

Proportional Integral ◽

The Stability ◽

Self Organizing

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

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Sufficient Condition-Based Stability Analysis of a Power Converter Applied Switching Transient Waveform Modification Using Kharitonov’s Theorem

Electronics ◽

10.3390/electronics8020245 ◽

2019 ◽

Vol 8 (2) ◽

pp. 245

Author(s):

Tongkai Cui ◽

Qishuang Ma ◽

Ping Xu

Keyword(s):

Stability Analysis ◽

Closed Loop ◽

Power Converters ◽

System Stability ◽

Sufficient Condition ◽

Small Signal ◽

Design Guideline ◽

Saturation Region ◽

Kharitonov’S Theorem ◽

Kharitonov's Theorem

The rapid switching action of power metal-oxide-semiconductor field-effect transistor (MOSFET) causes high-level electromagnetic interference (EMI) in power converters. The switching transient waveform modification method realized by closed-loop gate drive has been recognized as an effective high-frequency EMI reduction approach. However, feedback control of power MOSFET in the saturation region would introduce stability problems. This paper presents a sufficient condition-based stability analysis of all the operating points during turn-off using Kharitonov’s theorem. Firstly, a small-signal MOSFET model during turn-off was used to derive the closed-loop system transfer function. The nonlinear capacitances and the rest constant parameters of the small-signal model were determined based on the device characteristics and the expected outcome of the drain-source voltage. Then we split the turn-off switching transient into several subintervals, during which the system characteristic equation became an interval polynomial due to the nonlinear capacitances. Finally, Kharitonov’s theorem was applied in each subinterval to evaluate the stability, thereby achieving the overall system stability analysis during turn-off. Experiments were conducted to investigate the system’s stability and the results confirmed the validity of the proposed analysis. This work presents an implementable design guideline for the applied switching transient waveform modification of power converters via closed-loop gate drive.

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