scholarly journals Modeling and adaptive tracking for stochastic nonholonomic constrained mechanical systems

2016 ◽  
Vol 21 (2) ◽  
pp. 166-184 ◽  
Author(s):  
Zhongcai Zhang ◽  
Yuqiang Wu
Keyword(s):  
Dynamic Model ◽  
Controller Design ◽  
Internal State ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Design Parameters ◽  
Unknown Parameters ◽  
Constrained Mechanical Systems ◽  
Adaptive Tracking ◽  
Tracking Controller

This paper is devoted to the problem of modeling and trajectory tracking for stochastic nonholonomic dynamic systems in the presence of unknown parameters. Prior to tracking controller design, the rigorous derivation of stochastic nonholonomic dynamic model is given. By reasonably introducing so-called internal state vector, a reduced dynamic model, which is suitable for control design, is proposed. Based on the backstepping technique in vector form, an adaptive tracking controller is then derived, guaranteeing that the mean square of the tracking error converges to an arbitrarily small neighborhood of zero by tuning design parameters. The efficiency of the controller is demonstrated by a mechanics system: a vertical mobile wheel in random vibration environment.

scholarly journals Direct Adaptive Tracking Control for a Class of Pure-Feedback Stochastic Nonlinear Systems Based on Fuzzy-Approximation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Huanqing Wang ◽  
Xiaoping Liu ◽  
Qi Zhou ◽  
Hamid Reza Karimi
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
Controller Design ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Adaptive Controller ◽  
Stochastic Nonlinear Systems ◽  
Fuzzy Logic Systems ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking

The problem of fuzzy-based direct adaptive tracking control is considered for a class of pure-feedback stochastic nonlinear systems. During the controller design, fuzzy logic systems are used to approximate the packaged unknown nonlinearities, and then a novel direct adaptive controller is constructed via backstepping technique. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error eventually converges to a small neighborhood around the origin in the sense of mean quartic value. The main advantages lie in that the proposed controller structure is simpler and only one adaptive parameter needs to be updated online. Simulation results are used to illustrate the effectiveness of the proposed approach.

Optimal Feed-Forward Digital Tracking Controller Design

1994 ◽  
Vol 116 (4) ◽  
pp. 583-592 ◽  
Author(s):  
Tsu-Chin Tsao
Keyword(s):  
Controller Design ◽  
Reference Model ◽  
Phase Error ◽  
Tracking Error ◽  
Reference Signal ◽  
Tracking Performance ◽  
Design Parameters ◽  
Matching Problem ◽  
Feed Forward ◽  
Tracking Controller

This paper presents an approach for optimal digital feed-forward tracking controller design. The tracking problem is formulated as a model matching problem, in which the distance between a specified tracking reference model and the achievable tracking performance by feedforward compensation is minimized. Desired input/output characteristics, finite length preview action, tracking of specific classes of constrained signals, time domain reference signal velocity or acceleration bound, and frequency domain weighting are conveniently incorporated in the proposed controller design and their roles in tracking performance are discussed. The tracking error bound is also explicitly expressed in terms of the controller design parameters. An l1 norm optimal tracking controller is proposed as a solution to the mechanical tolerance control problem. A motion control example illustrates the design approach and several aspects of the resulting optimal feedforward controller, including the optimality of the zero phase error tracking controller.

scholarly journals Robust adaptive tracking for Markovian jump nonlinear systems with unknown nonlinearities

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
Jin Zhu ◽  
Hong-Sheng Xi ◽  
Hai-Bo Ji ◽  
Bing Wang
Keyword(s):  
Tracking Error ◽  
Small Neighborhood ◽  
Parametric Uncertainty ◽  
Control Law ◽  
Fourth Moment ◽  
Closed Loop System ◽  
Markovian Jump ◽  
Adaptive Tracking ◽  
Adaptive Law ◽  
Robust Adaptive

Robust adaptive tracking problems for a class of Markovian jump parametric-strict-feed-back systems with both parametric uncertainty and unknown nonlinearity are investigated. The unknown nonlinearities considered herein lie within some “bounding functions,” which are assumed to be partially known. By using a stochastic Lyapunov method and backstepping techniques, a parameter adaptive law and a control law were obtained, which guarantee that the tracking error could be within a small neighborhood around the origin in the sense of the fourth moment. Moreover, all signals of the closed-loop system could be globally uniformly ultimately bounded.

Nonlinear Parameter Estimation in a Typical Industrial Air Handler Unit

2017 ◽  
Author(s):  
Lujia Feng ◽  
Pierluigi Pisu ◽  
Laine Mears ◽  
Jörg Schulte
Keyword(s):  
Parameter Estimation ◽  
Energy Demand ◽  
Controller Design ◽  
Nonlinear Parameter ◽  
Working Environment ◽  
Design Parameters ◽  
Hvac System ◽  
Commercial Building ◽  
Unknown Parameters ◽  
Nonlinear Parameter Estimation

The energy usage inside of a manufacturing plant is mainly from two sources: energy demand from the production lines to support manufacturing processes, and the plant building temperature control to maintain a comfortable working environment. It is reported that in the US, 14% of the primary energy and 32% of electricity is used by the industry and commercial building heating, ventilation and air conditioning (HVAC) system. As an important part of the HVAC system, the air handler unit (AHU) is a comprehensive air control system consisting of multiple sub-units. Accurate modeling of the supply air temperature of AHU is important for later controller design and fault detection, but it is also challenging because of the application of variable frequency drive (VFD) systems, overall degradation, and limited sensor information and meter data. Parameter estimation of the industry AHU is therefore worth studying. In this study, the authors intend to establish a deterministic physical model of AHU system, identify the unknown parameters based on the limited meter inputs, and compare the nonlinear parameter estimation results with the design parameters, in order to achieve the goal of improving the modeling accuracy without installing expensive metering systems.

scholarly journals Bounded Analysis and Practical Tracking Control of Complex Stochastic Nonlinear Systems with Unknown Control Coefficients

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Long-Chuan Guo ◽  
Xiang-Kun Fang
Keyword(s):  
Nonlinear Systems ◽  
Tracking Error ◽  
Upper And Lower Bounds ◽  
Design Parameters ◽  
Stochastic Nonlinear Systems ◽  
Tracking Controller ◽  
Unknown Control Coefficients ◽  
Unknown Control ◽  
Theoretical Results ◽  
Control Coefficients

This paper mainly focuses on the output practical tracking controller design for a class of complex stochastic nonlinear systems with unknown control coefficients. In the existing research results, most of the complex systems are controlled in a certain direction, which leads to the disconnection between theoretical results and practical applications. The authors introduce unknown control coefficients, and the values of the upper and lower bounds of the control coefficients are generalized by constants to allow arbitrary values to be arbitrarily large or arbitrarily small. In the control design program, the design problem of the controller is transformed into a parameter construction problem by introducing appropriate coordinate transformation. Moreover, we construct an output feedback practical tracking controller based on the dynamic and static phase combined by Ito stochastic differential theory and selection of appropriate design parameters, ensuring that the system tracking error can be made arbitrarily small after some large enough time. Finally, a simulation example is provided to illustrate the efficiency of the theoretical results.

scholarly journals Adaptive Output Feedback Tracking Controller Design of Stochastic Nonlinear Systems with Parameter Uncertainty for Polynomial Function Growth Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Long-Chuan Guo
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Controller Design ◽  
Polynomial Function ◽  
Tracking Error ◽  
Parametric Uncertainty ◽  
Growth Conditions ◽  
Stochastic Nonlinear Systems ◽  
Tracking Controller ◽  
Feedback Tracking

This paper mainly focuses on output feedback practical tracking controller design for stochastic nonlinear systems with polynomial function growth conditions. Mostly, there are some studies on output feedback tracking control problem for general nonlinear systems with parametric certainty in existing achievements. Moreover, we extend it to stochastic nonlinear systems with parametric uncertainty and system nonlinear terms are assumed to satisfy polynomial function growth conditions which are more relaxed than linear growth conditions or power growth conditions. Due to the presence of unknown parametric uncertainty, an output feedback practical tracking controller with dynamically updated gains is constructed explicitly so that all the states of the closed-loop systems are globally bounded and the tracking error belongs to arbitrarily small interval after some positive finite time. An example illustrates the efficiency of the theoretical results.

Robust Control for a Class of Nonlinear Systems Based on Backstepping

2011 ◽  
Vol 50-51 ◽  
pp. 110-114
Author(s):  
Nai Bao He ◽  
Qian Gao
Keyword(s):  
Robust Control ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Control Law ◽  
Closed Loop System ◽  
Unknown Parameters ◽  
Feedback Form ◽  
Output Tracking ◽  
Adaptive Parameter ◽  
Adaptive Parameter Control

Based on coordinate transform, the paper deduced the principle with which Chua’s chaotic system can be translated into the so-called general strict-feedback form. Combining the backstepping method with robust control technology, an adaptive parameter control law is developed and thus the output tracking is successfully accomplished for the system with unknown parameters and dynamic uncertainties. It is proved that all states of the closed-loop system are globally uniformly　ultimately bounded, and lead the system tracking error to a small neighborhood. Finally simulation results are provided to show the effectiveness of the proposed approach.

Optimal Tracking Controller Design for Invariant Dynamics Direct-Drive Arms

1986 ◽  
Vol 108 (4) ◽  
pp. 360-365 ◽  
Author(s):  
H. A. Pak ◽  
P. J. Turner
Keyword(s):  
Controller Design ◽  
Optimal Solution ◽  
Design Parameters ◽  
Response Analysis ◽  
Direct Drive ◽  
Current Feedback ◽  
Actuator Dynamics ◽  
Reference Velocity ◽  
Tracking Controller ◽  
Tracking Behavior

This paper presents an optimal solution to the problem of tracking controller design for a category of direct-drive robot arms, mechanically constructed to have invariant and decoupled joint actuator dynamics. The controller acts on joint actuators consisting of d.c. servo motors driven via servo amplifiers containing an analog current feedback loop. For good tracking behavior, the controller uses future reference positions of a joint to anticipate the changes in reference velocity. An explicit acceleration feedforward term is avoided improving the power to noise ratio of the control signal. For good regulation behavior, the controller uses position and velocity feedback. An integral of error term is also avoided, reducing the probability of the occurrence of limit cycle oscillations caused by saturation of the actuator torque rating. The correlations between the classical and the optimal design parameters are discussed using transient response analysis followed by experimental observations.

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