Stabilizing the second-order nonholonomic systems with chained form by finite-time stabilizing controllers

Robotica ◽  
2015 ◽  
Vol 34 (10) ◽  
pp. 2344-2367 ◽  
Author(s):  
Guangping He ◽  
Chenghao Zhang ◽  
Wei Sun ◽  
Zhiyong Geng
Keyword(s):  
Mechanical System ◽  
Controller Design ◽  
Design Method ◽  
Nonholonomic Systems ◽  
Second Order ◽  
Test Bed ◽  
Underactuated Mechanical Systems ◽  
Hölder Continuous ◽  
Good Test ◽  
Stabilizing Controllers

SUMMARYAn underactuated mechanical system is generally a good test bed for advanced nonlinear controllers and can be applied to design a novel mechanical system with better energy efficiency and good controllability. It has been shown that the dynamics of many underactuated mechanical systems could be transformed into the chained canonical form. To improve the performance of the controllers presented in the literature, a novel controller design method is proposed in this paper. It is shown that the set-point stabilization problem of the second-order chained form systems can be changed into a trajectory-tracking problem based on the nonsmooth Hölder continuous feedback. By designing the tracked trajectory, the presented controller permits the achievement of exponential stability. Some numerical simulations demonstrate the stability of the proposed controller for an underactuated Hovercraft system.

scholarly journals Optimization of design for mechatronic system based on virtual prototyping technology

2017 ◽  
Vol 20 (K5) ◽  
pp. 51-57
Author(s):  
Tran Ngoc Le
Keyword(s):  
Mechanical System ◽  
Computer Aided Design ◽  
Design Method ◽  
Control Strategies ◽  
Virtual Prototyping ◽  
Test Bed ◽  
Mechatronic System ◽  
Modeling And Analysis ◽  
Integrated Simulation ◽  
Virtual Prototyping Technology

According to the traditional design method, in order to manufacture a mechatronic system, from the initial idea, the designer designs the mechanical system by CAD (Computer-Aided-Design), this system is then fabricated, finally, the system will be tested on the working condition. If the system does not work properly, the design of the system will be changed, and hardware is re-manufactured. This method is more time-consuming and cost for repairing and manufacturing hardware repeatedly. To save design time and reduce the cost of the manufacturing hardware as well as to optimize the design process of a mechatronics system, this paper introduces an engineering model it is called a virtual prototyping technology which allows optimizing the designs on the computer before manufacturing the test-bed system. Based on the concept of the system working, the mechatronics system is designed on SOLIDWORKS and then exported to the ADAMS software (Automated Dynamic Analysis of Mechanical System). The flexible element is also modeling and analysis in ANSYS software then exported to ADAMS. The integrated simulation in ADAMS environment is executed to investigate the dynamic behaviors of the mechanical system and design will be adjusted. Virtual prototyping model will then be exported to MATLAB/Simulink to develop the control strategies. Co-simulation results in some contexts to evaluate the effectiveness of the proposed mechatronic system before implementing on test-bed

Robust Finite Time Controller Design for Second Order Underactuated Mechanical Systems

2013 ◽  
Vol 284-287 ◽  
pp. 2310-2314 ◽  
Author(s):  
Kuang Shine Yang ◽  
Chi Cheng Cheng ◽  
Jung Hua Yang
Keyword(s):  
Lyapunov Stability ◽  
Finite Time ◽  
Controller Design ◽  
Tracking Error ◽  
Mechanical Systems ◽  
Second Order ◽  
Underactuated Systems ◽  
Underactuated Mechanical Systems ◽  
Pendulum System ◽  
Finite Time Convergence

Stabilization and tracking control of nonlinear uncertain underactuated systems are always challenging problems because underacturated systems have fewer independent control actuators than degrees of freedom to be controlled. For a class of second order underactuated mechanical systems, a robust finite time control strategy is developed in this paper. The robust finite time controller is to drive the tracking error to be zero at the fixed final time. In fact, finite time convergence implies nonsmooth or non-Lipschitz continuous autonomous systems with nonuniqueness of solution. In order to prove the stability, we present a generalized Lyapunov stability proof for the second order underactuated mechanical system. By utilizing a Lyapunov stability theorem, we can achieve finite time tracking of desired reference signals for underactuated systems, which is subject to both external disturbances and system uncertainties. The proposed control scheme is demonstrated by actual experiments on a Furuta pendulum system. Based on the experiment results, the finite time convergence of system errors can be assured.

Passivity-Based Stabilization of Underactuated Mechanical Systems

2013 ◽  
Vol 421 ◽  
pp. 16-22
Author(s):  
Shan Shan Wu ◽  
Wei Huo
Keyword(s):  
Closed Loop ◽  
Control Method ◽  
Controller Design ◽  
Design Method ◽  
Mechanical Systems ◽  
Matching Condition ◽  
Loop System ◽  
Closed Loop System ◽  
Underactuated Mechanical Systems ◽  
Stabilization Control

A new stabilization control method for underactuated linear mechanical systems is presented in this paper. By proper setting the desired closed-loop system, the matching condition for controller design is reduced to one equation and an adjustable parameter (damping coefficient) is introduced to the controller. Stability of the closed-loop system is proved based on passivity. As an application example, stabilization control of 2-DOF Pendubot is studied. The system is linearized at its equilibrium point and the proposed controller design method is applied to the linearized system. The procedure of solving matching condition and design controller for the Pendubot is provided. The simulation results verify feasibility of the proposed method.

scholarly journals Supervisory Control for Wireless Networked Power Converters in Residential Applications

Energies ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 1911
Author(s):  
S. M. Rakiul Islam ◽  
Sung-Yeul Park ◽  
Shaobo Zheng ◽  
Song Han ◽  
Sung-Min Park
Keyword(s):  
Power Converters ◽  
Reactive Power ◽  
Controller Design ◽  
Design Method ◽  
Small Scale ◽  
Power Network ◽  
Test Bed ◽  
Texas Instrument ◽  
Supervisory Controller ◽  
Communication Links

This paper presents a methodology to design and utilize a supervisory controller for networked power converters in residential applications. Wireless networks have been interfaced to multiple power factor correction (PFC) converters which are proposed to support reactive power. Unregulated reactive power support from PFC converters could cause reactive power deficiency and instability. Therefore, a supervisory controller is necessary to govern the operation of PFC converters. WiFi and WirelessHART networks have been used to implement the supervisory controller. Different nodes of the power network are connected by wireless communication links to the supervisory controller. Asynchronous communication links latency and uncertain states affect the control and response of the PFC converters. To overcome these issues, the supervisory controller design method has been proposed based on the system identification and the Ziegler-Nichols rule. The proposed supervisory controller has been validated by using a hardware-in-the-loop (HIL) test bed. The HIL testbed consisted of an OP4510 simulator, a server computer, Texas Instrument-Digital Signal Controllers (TI-DSCs), WiFi and WirelessHART modules. Experimental results show that the proposed supervisory controller can help to support and govern reactive power flow in a residential power network. The proposed method of controller design will be useful for different small-scale power and wireless network integration.

ROBUST FINITE TIME CONTROLLER DESIGN FOR SECOND ORDER NONLINEAR UNDERACTUATED MECHANICAL SYSTEMS

2013 ◽  
Vol 37 (3) ◽  
pp. 549-557 ◽  
Author(s):  
Chi-Cheng Cheng ◽  
Kuang-Shine Yang ◽  
Jung-Hua Yang
Keyword(s):  
Lyapunov Stability ◽  
Finite Time ◽  
Controller Design ◽  
Tracking Error ◽  
Mechanical Systems ◽  
Second Order ◽  
System Stability ◽  
Underactuated Mechanical Systems ◽  
Pendulum System ◽  
Time Control

For a class of second order underactuated mechanical systems, a robust finite time control strategy is developed in this paper. The robust finite time controller is to drive the tracking error to be zero at the fixed final time. In order to assure system stability, we present a generalized Lyapunov stability proof for the second order underactuated mechanical system. By utilizing a Lyapunov stability theorem, we can achieve finite time tracking of desired reference signals for underactuated systems, which are subject to both external disturbances and system uncertainties. The proposed control scheme is demonstrated by actual experiments on a Furuta pendulum system.

Design of Swinging-Up Controller Based on LyapunovFunction and Fuzzy Control for Under-Actuated Mechanical System

2014 ◽  
Vol 971-973 ◽  
pp. 440-443
Author(s):  
Xiao Gang Xiong ◽  
Min Wu
Keyword(s):  
Fuzzy Control ◽  
Mechanical System ◽  
Controller Design ◽  
Design Method ◽  
Control Technique ◽  
Control Performance ◽  
Control Rule

This paper proposes a improved swing up controller design method. Throughusing the derivative of Lee Yap Andrianof function is negative to calculate theswing up control rule, and using fuzzy control technique to select controlparameters to avoid the swing up controller of the odd value and to improve thesystem control performance.

scholarly journals Controller design by the motion separation method with applying stability criterions for non-linear objects with transport delays

2021 ◽  
pp. 39-60
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Controller Design ◽  
Design Method ◽  
Second Order ◽  
Smith Predictor ◽  
Separation Method ◽  
Transient Processes ◽  
Peltier Element ◽  
Transport Delay ◽  
Nyquist Criterion ◽  
Non Linear

Controllers and feedback are applied for performing many technical tasks, for example, maintaining the desired temperature stabilization in the thermostat and speed electric motor stabilization. Different methods such as the time-scale separation method, the frequency-response design method, and the Ziegler–Nichols method are applied to design controllers. The Ziegler–Nichols method does not provide the required transient process quality. The Smith predictor is sometimes applied to control objects with a transport delay. However, it may be difficult to apply the Smith predictor when a mathematical model is not fully known. There is a paper where the application of the motion separation method with a delay is considered. However, the calculation method proposed in that work requires solving a system of four nonlinear equations for a second-order object. Therefore, in this paper, we investigate the possibility of a simpler method for calculating the controller, namely, the possibility of using the Mikhailov criterion in the synthesis of a controller by the motion separation method for nonlinear objects with a delay. Also, the application of the Nyquist stability criterion with a simpler than the proposed earlier calculation procedure is considered in the paper. The values of the regulator coefficients obtained using the Nyquist criterion and the Mikhailov criterion are compared. The Mikhailov criterion and the Nyquist criterion are applied to estimate the stability of the fast motions subsystem. The derivation of formulas to calculate the parameters of the controller designed by the motion separation method for first-order non-linear objects with transport delays and second-order non-linear objects with transport delays with the use of the Mikhailov criterion is also considered in the paper. Transient processes are studied by numerical simulation. Transient processes plots are also given. The parameters of the controller that are needed to improve the performance of transient processes in the presence of a delay are found. The Peltier element, an aircraft strength test stand, a thermostat, and equipment for metal rolling are non-linear control objects with a transport delay. The Mikhailov hodographs for objects with a transport delay are presented.

Passivity-Based Tracking Control Design for Underactuated Mechanical Systems

2012 ◽  
Vol 591-593 ◽  
pp. 1225-1230 ◽  
Author(s):  
Shan Shan Wu ◽  
Wei Huo
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Controller Design ◽  
Design Method ◽  
Mechanical Systems ◽  
Matching Condition ◽  
Loop System ◽  
Closed Loop System ◽  
Underactuated Mechanical Systems ◽  
Design Procedures

Passivity-based tracking control of the underactuated linear mechanical systems is investigated in this paper. As our main contribution, the matching condition is decreased into two equations and an adjustable gain (damping gain) is introduced into the controller by setting the desired closed-loop system properly. Stability of the closed-loop system is proved based on passivity of the system. Furthermore, as examples, tracking control of 2-DOF Acrobot and 2-DOF Pendubot are studied. The systems are linearized at their equilibriums and the passivity-based controller design method is applied to the linearized systems. Matching conditions are solved and the design procedures of associate controllers for the two robots are provided. The simulation results show that the designed controllers can realize asymptotical tracking for the given desired trajectories.

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