Robust Control of Nonlinear System with Input and Output Nonlinear Constraints

2017 ◽  
Vol 29 (6) ◽  
pp. 1073-1081 ◽  
Author(s):  
Shuhui Bi ◽  
Lei Wang ◽  
Chunyan Han ◽  
◽  
Keyword(s):  
Robust Control ◽  
Nonlinear System ◽  
Robust Stability ◽  
System Structure ◽  
Tracking Performance ◽  
Nonlinear Constraints ◽  
Nonlinear Constraint ◽  
Output Tracking ◽  
Input And Output ◽  
Output Constraints

With the development of modern technology, actuators and sensors composed of smart materials, such as piezoceramic and magnetostrictive materials, have been widely used in practice owing to their various advantages. However, in the working process of a smart material based actuator and sensor, non-smooth nonlinear constraints in their output responses may induce inaccuracies and oscillations, which severely degrade system performance. Therefore, input and output nonlinear constraints brought about by actuators and sensors should be considered. Generally, the output nonlinear constraint, namely, non-smooth effects from sensors, has been ignored. Therefore, in this paper, a robust control for a system with an output constraint as well as with both input and output constraints will be considered. Firstly, the generalized Prandtl-Ishlinskii (PI) hysteresis model is used for describing the input and output nonlinearities owing to its excellent characteristics, the model has proved suitable in theoretical operator based settings. Further, a robust control for a nonlinear system with an output nonlinear constraint is considered by using operator based robust right coprime factorization approach. Here, operator based robust stability is considered, and the control system structure including feedforward and feedback controllers is presented with a derivation of sufficient conditions for stable controller operation. Based on the proposed conditions, the influence from an output nonlinear constraint is rejected, the systems are robustly stable, and output tracking performance can be realized. Moreover, robust stability and output tracking performance for a nonlinear system with both input and output nonlinear constraints are also analyzed.

Indirect Neural Network Adaptive Robust Control of Linear Motor Drive System

2002 ◽  
Author(s):  
J. Q. Gong ◽  
Bin Yao
Keyword(s):  
Neural Network ◽  
Robust Control ◽  
Tracking Error ◽  
Linear Motor ◽  
Adaptive Robust Control ◽  
Operating Conditions ◽  
Tracking Performance ◽  
Motor Drive ◽  
Output Tracking ◽  
On Line

In this paper, an indirect neural network adaptive robust control (INNARC) scheme is developed for the precision motion control of linear motor drive systems. The proposed INNARC achieves not only good output tracking performance but also excellent identifications of unknown nonlinear forces in system for secondary purposes such as prognostics and machine health monitoring. Such dual objectives are accomplished through the complete separation of unknown nonlinearity estimation via neural networks and the design of baseline adaptive robust control (ARC) law for output tracking performance. Specifically, recurrent neural network (NN) structure with NN weights tuned on-line is employed to approximate various unknown nonlinear forces of the system having unknown forms to adapt to various operating conditions. The design is actual system dynamics based, which makes the resulting on-line weight tuning law much more robust and accurate than those in the tracking error dynamics based direct NNARC designs in implementation. With a controlled learning process achieved through projection type weights adaptation laws, certain robust control terms are constructed to attenuate the effect of possibly large transient modelling error for a theoretically guaranteed robust output tracking performance in general. Experimental results are obtained to verify the effectiveness of the proposed INNARC strategy. For example, for a typical point-to-point movement, with a measurement resolution level of ±1μm, the output tracking error during the entire execution period is within ±5μm and mainly stays within ±2μm showing excellent output tracking performance. At the same time, the outputs of NNs approximate the unknown forces very well allowing the estimates to be used for secondary purposes such as prognostics.

Operator-Based Control System Analysis and Design for Nonlinear System with Input and Output Constraints

2018 ◽  
Vol 30 (6) ◽  
pp. 950-957
Author(s):  
Shuhui Bi ◽  
Lei Wang ◽  
Shengjun Wen ◽  
Liyao Ma ◽  
◽  
...  
Keyword(s):  
Control System ◽  
Nonlinear System ◽  
System Analysis ◽  
Sufficient Conditions ◽  
Input Constraint ◽  
Analysis And Design ◽  
Input And Output ◽  
Output Constraints ◽  
The Stability ◽  
Output Constraint

Smart material-based actuators and sensors have been widely used in practice owing to their various advantages. However, in the working process of these actuators and sensors, their output responses always deduce non-smooth nonlinear constraints. The constraint resulting from the actuator is called the input constraint and the constraint caused by the sensor is called the output constraint. These input and output constraints may induce inaccuracies and oscillations, severely degrading system performance. Therefore, the input and output constraints brought about by actuators and sensors should be considered in control system design. In this paper, system analysis for a nonlinear system with input and output constraints will be considered. The effect from the input constraint to the internal signal in the control system will be discussed. Moreover, the influence of the output constraint on the whole system will be studied. Further, the sufficient conditions for maintaining the stability of the system are obtained. Then, by using the robust right coprime factorization approach, an operator-based internal model like control structure is proposed for mitigating the input and output constraints. Finally, the effectiveness of the proposed design scheme will be confirmed through numerical simulation.

Operator-based external disturbance rejection of perturbed nonlinear systems by using robust right coprime factorization

2017 ◽  
Vol 40 (10) ◽  
pp. 3169-3178 ◽  
Author(s):  
Mengyang Li ◽  
Mingcong Deng
Keyword(s):  
Nonlinear Systems ◽  
Adverse Effects ◽  
Robust Stability ◽  
External Disturbance ◽  
Point Of View ◽  
Tracking Performance ◽  
Coprime Factorization ◽  
Output Tracking ◽  
Design Scheme ◽  
Internal Perturbation

In this paper, a class of nonlinear systems with external disturbance and internal perturbation are considered by using operator-based robust right coprime factorization for guaranteeing robust stability, rejecting adverse effects resulting from the existing disturbance and perturbation quantitatively and, meanwhile, realizing output tracking performance. In detail, firstly, robust stability is guaranteed based on a Lipschitz norm inequation using robust right coprime factorization. Secondly, based on the proposed design scheme, a convenient framework is obtained for discussing rejection issues for external disturbance and internal perturbation. Thirdly, from an error signal point of view, the adverse effects resulting from the external disturbance and internal perturbation of the nonlinear system are removed by the designed nonlinear operator. Moreover, output tracking performance is realized using the proposed design scheme simultaneously. Finally, a simulation example is given to confirm the effectiveness of the proposed design scheme of this paper.

Control of Uncertain LTI Systems Based on an Uncertainty and Disturbance Estimator

2004 ◽  
Vol 126 (4) ◽  
pp. 905-910 ◽  
Author(s):  
Qing-Chang Zhong ◽  
David Rees
Keyword(s):  
Time Delay ◽  
Robust Control ◽  
Robust Stability ◽  
Control Strategy ◽  
Time Delay Control ◽  
Delay Control ◽  
Uncertainty And Disturbance Estimator ◽  
Derivatives Of ◽  
Siso Systems ◽  
Disturbance Estimator

This paper proposes a robust control strategy for uncertain LTI systems. The strategy is based on an uncertainty and disturbance estimator (UDE). It brings similar performance as the time-delay control (TDC). The advantages over TDC are: (i) no delay is introduced into the system; (ii) there are no oscillations in the control signal; and (iii) there is no need of measuring the derivatives of the state vector. The robust stability of LTI-SISO systems is analyzed, and simulations are given to show the effectiveness of the UDE-based control with a comparison made with TDC.

scholarly journals Equivalent Transformation of Nonlinear Constraints to Linear Constraints in Petri Nets

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
YuFeng Chen ◽  
Abdulrahman Al-Ahmari ◽  
Chi Tin Hon ◽  
NaiQi Wu
Keyword(s):  
Linear Programming ◽  
Petri Nets ◽  
Integer Linear Programming ◽  
Programming Model ◽  
Linear Constraints ◽  
Linear Programming Model ◽  
Equivalent Transformation ◽  
Nonlinear Constraints ◽  
Nonlinear Constraint ◽  
Integer Linear Programming Model

This paper focuses on the enforcement of nonlinear constraints in Petri nets. An integer linear programming model is formulated to transform a nonlinear constraint to a minimal number of conjunctive linear constraints that have the same admissible marking space as the nonlinear one does in Petri nets. The obtained linear constraints can be easily enforced to be satisfied by a set of control places with a place invariant based method. The control places make up a supervisor that can enforce the given nonlinear constraint. For a case that the admissible marking space decided by a nonlinear constraint is nonconvex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint with respect to the reachable markings. Finally, a number of examples are provided to demonstrate the proposed approach.

scholarly journals Adaptive output regulation for a class of nonlinear systems with guaranteed transient performance

2019 ◽  
Vol 42 (6) ◽  
pp. 1180-1190
Author(s):  
Weijie Sun ◽  
Zhenhua Zhu ◽  
Jianglin Lan ◽  
Yunjian Peng
Keyword(s):  
Nonlinear Systems ◽  
Tracking Error ◽  
High Gain ◽  
Output Regulation ◽  
Control Law ◽  
Stabilization Problem ◽  
Transient Performance ◽  
Adaptive Stabilization ◽  
Output Tracking ◽  
Output Constraints

This paper is dedicated to adaptive output regulation for a class of nonlinear systems with asymptotic output tracking and guarantee of prescribed transient performance. With the employment of internal model principle, we first transform this problem into a specific adaptive stabilization problem with output constraints. Then, by integrating the time-varying Barrier Lyapunov Function (BLF) technique together with the high gain feedback method, we develop an output-based control law to solve the constrained stabilization problem and consequently confine the output tracking error to a predefined arbitrary region. The output-based control law enables adaptive output regulation in the sense that, under unknown exosystem dynamics, all the closed-loop system signals are bounded whilst the controlled output constraints are not violated. Finally, efficacy of the proposed design is illustrated through a simulation example.

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