The precision cutting process as a non-linear closed loop system

In this paper, an adaptive robust stabilization algorithm is presented for a class of non-linear systems with mismatched uncertainties. In this regard, a new controller based on the Lyapunov theory is proposed in order to overcome the problem of stabilizing non-linear time-varying systems with mismatched uncertainties. This method is such that the stability of the closed-loop system is guaranteed in the absence of the triangularity assumption. The proposed approach leads to asymptotic convergence of the states of the closed-loop system to zero for unknown but bounded uncertainties. Subsequently, this method is modified so that all the signals in the closed-loop system are uniformly ultimately bounded. Eventually, numerical simulations support the effectiveness of the given algorithm.

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Design of Compensators for Actuator Saturation

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1243/pime_proc_1995_209_380_02 ◽

1995 ◽

Vol 209 (3) ◽

pp. 157-164 ◽

Cited By ~ 4

Author(s):

C W Chan ◽

K Hui

Keyword(s):

Control Problem ◽

Closed Loop ◽

Actuator Saturation ◽

Design Procedure ◽

Loop System ◽

Linear Control ◽

Closed Loop System ◽

Set Point ◽

Non Linear ◽

Linear Disturbance

Actuator saturation is a common non-linear control problem; if it is not being compensated properly, the system can become unstable. When the actuator saturates, the control that cannot be implemented can be interpreted as a non-linear disturbance being injected into the closed-loop system. After transformation, the applied set-point is altered by the disturbance, giving the effective set-point. If the effective instead of the applied set-point is used to calculate the control, no actuator saturation occurs. Since the effective set-point always replaces the applied set-point whenever the actuator saturates, a compensator can be designed aiming to produce a more acceptable effective set-point. The conditions for its implementation are given, followed by the properties of the effective set-point. A procedure for selecting the parameter of the compensator is also described. Examples are presented to illustrate the design procedure and to compare the performance of the proposed and the existing compensators.

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Stochastic disturbance observer-based adaptive anti-disturbance control for non-linear systems with stochastic non-harmonic multiple disturbances

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217718051 ◽

2017 ◽

Vol 40 (10) ◽

pp. 3222-3231 ◽

Cited By ~ 1

Author(s):

Yanpeng Pan

Keyword(s):

Linear Systems ◽

Disturbance Observer ◽

Closed Loop ◽

Loop System ◽

State Feedback Control ◽

Closed Loop System ◽

Stochastic Disturbance ◽

Multiple Disturbances ◽

Non Linear ◽

Non Linear Systems

In this paper, the problem of anti-disturbance control is studied for non-linear systems with stochastic multiple disturbances. The multiple disturbances include two types: one is the stochastic harmonic disturbance and the other non-harmonic noise generated by a linear stochastic exogenous system. An adaptive stochastic disturbance observer (ASDO) is constructed to estimate both the two aforementioned disturbances. Combining the disturbance estimation with a conventional state feedback control law, a composite anti-disturbance control scheme is constructed such that the closed-loop system is stochastically stable, and different types of disturbances may be attenuated and rejected. By using the Lyapunov function method and linear matrix inequalities technique, sufficient conditions for the stochastic stability of the closed-loop system are established. Moreover, an adaptive stochastic extended state observer (ASESO) is proposed for the output feedback case. Finally, an application example is provided to demonstrate the effectiveness of the proposed method.

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Non-linear multivariable flight control of aircraft

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1243/0954410981532207 ◽

1998 ◽

Vol 212 (2) ◽

pp. 137-144 ◽

Cited By ~ 7

Author(s):

S E Lyshevski

Keyword(s):

Flight Control ◽

Closed Loop ◽

Dynamic Performance ◽

Optimization Procedure ◽

Loop System ◽

Closed Loop System ◽

Bounded Control ◽

Performance Improvements ◽

Non Linear ◽

Linear Differential

Innovative design methods are needed for advanced aircraft in response to requirements towards substantial performance improvements. Functionally and operationally, the aircraft must be considered as the highly coupled non-linear multi-input multi-output system, i.e. the aerodynamics have to be mapped by non-linear differential or difference equations. To improve flying and handling qualities, to increase manœuvrability and to expand the operating envelope, an innovative optimization procedure is developed to design the constrained controllers for multi-input multi-output aircraft. In particular, a bounded control law is synthesized by employing the Hamilton-Jacobi theory, and the admissibility concept is used to study the stability of the resulting closed-loop system. The developed optimization procedure is applied to a non-linear ninth-order model of an AFTI/F-16 aircraft. A bounded controller is designed, and modelling results are presented to demonstrate the dynamic performance of the resulting closed-loop system.

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