Design of Compensators for Actuator Saturation

1995 ◽  
Vol 209 (3) ◽  
pp. 157-164 ◽  
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.

scholarly journals Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

2021 ◽  
Vol 26 (1) ◽  
pp. 21
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Nashwa Ahmad Kamal
Keyword(s):  
Design Methodology ◽  
Closed Loop ◽  
Complex Analysis ◽  
Controller Design ◽  
Filter Design ◽  
Design Procedure ◽  
Elliptic Functions ◽  
Loop System ◽  
Closed Loop System ◽  
Loop Shaping

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

Application of Approximate I/O Linearization to Aircraft Flight Control

1994 ◽  
Vol 116 (3) ◽  
pp. 429-436 ◽  
Author(s):  
A. W. Lee ◽  
J. K. Hedrick
Keyword(s):  
Control Problem ◽  
Flight Control ◽  
Closed Loop ◽  
Performance Enhancement ◽  
Design Method ◽  
Loop System ◽  
Closed Loop System ◽  
Aircraft Flight Control ◽  
Original Plant ◽  
Control Saturation

This paper examines the performance enhancement of a statically unstable aircraft subject to the input and state constraints. Under control saturation, i/o linearizability is destroyed and the state trajectories may not be attracted to the sliding surface. If the reference signals are sufficiently large and the zero-dynamics is lightly damped, the i/o linearizing control may become unreasonably large in magnitude, making the closed-loop system susceptible to the damaging effects of control saturation. In addition to performance degradations such as increased tracking errors, control saturation can drive the closed-loop system to instability. In this paper, a new design method called approximate i/o linearization is presented to enhance the performance of the SISO longitudinal flight control problem under saturation. The new approximate i/o linearization law is obtained by solving a pointwise minimization problem. The function to be minimized consists of a surface whose relative degree is one, its derivative, and weighted square of the input u. The advantages of the approximate i/o linearization is that the adverse effects of control saturation can be minimized by properly selecting the weight on the usage of the control. The only requirement for the new technique is that the original plant be locally i/o linearizable. Thus approximate i/o linearization does not impose additional strict requirements on the plant. In the remaining sections of the paper, stability and bounded tracking properties of the approximate i/o linearization are proven. Finally, a longitudinal flight control problem is used to demonstrate the application of approximate i/o linearization.

scholarly journals Actuator Saturation and Control Design for Buildings Structural Systems with Improved Uncertainty Description

2013 ◽  
Vol 20 (2) ◽  
pp. 297-308 ◽  
Author(s):  
Y.C. Ding ◽  
F.L. Weng ◽  
Z.A. Yu
Keyword(s):  
Closed Loop ◽  
Actuator Saturation ◽  
Input Saturation ◽  
Lyapunov Theory ◽  
Loop System ◽  
Structural Systems ◽  
Control Input ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Earthquake Excitation

The problem of robustly active vibration control for a class of earthquake-excited structural systems with time-delay and saturation in the control input channel and parameter uncertainties appearing in all the mass, damping and stiffness matrices is concerned in this paper. The objective of the designing controllers is to guarantee the robust stability of the closed-loop system and attenuate the disturbance from earthquake excitation. Firstly, by using the linear combination of some matrices to deal with the system's uncertainties, a new system uncertainties description, namely rank-1 uncertainty description, is presented. Then, by introducing a linear varying parameter, the input saturation model is described as a linear parameter varying model. Furthermore, based on parameter-dependent Lyapunov theory and linear matrix inequality (LMI) technique, the LMIs-based conditions for the closed-loop system to be stable are deduced. By solving those conditions, the controller, considering the actuator saturation, input delay and parameters uncertainties, is obtained. Finally, a three-storey linear building structure under earthquake excitation is considered and simulation results are given to show the effectiveness of the proposed controllers.

scholarly journals Decentralised PI controller design based on dynamic interaction decoupling in the closed-loop behaviour of a flotation process

2021 ◽  
Vol 11 (6) ◽  
pp. 4865
Author(s):  
Nomzamo Tshemese-Mvandaba ◽  
R. Tzoneva ◽  
M. E. S. Mnguni
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Design Procedure ◽  
Loop System ◽  
Closed Loop System ◽  
Flotation Process ◽  
Loop Control ◽  
Decoupling Method ◽  
Pi Controllers ◽  
Interconnected Model

An enhanced method for design of decenralised proportional integral (PI) controllers to control various variables of flotation columns is proposed. These columns are multivariable processes characterised by multiple interacting manipulated and controlled variables. The control of more than one variable is not an easy problem to solve as a change in a specific manipulated variable affects more than one controlled variable. Paper proposes an improved method for design of decentralized PI controllers through the introduction of decoupling of the interconnected model of the process. Decoupling the system model has proven to be an effective strategy to reduce the influence of the interactions in the closed-loop control and consistently to keep the system stable. The mathematical derivations and the algorithm of the design procedure are described in detail. The behaviour and performance of the closed-loop systems without and with the application of the decoupling method was investigated and compared through simulations in MATLAB/Simulink. The results show that the decouplers - based closed-loop system has better performance than the closed-loop system without decouplers. The highest improvement (2 to 50 times) is in the steady-state error and 1.2 to 7 times in the settling and rising time. Controllers can easily be implemented.

Adaptive robust stabilization of a class of uncertain non-linear systems with mismatched time-varying parameters

2011 ◽  
Vol 226 (2) ◽  
pp. 204-214 ◽  
Author(s):  
M M Arefi ◽  
M R Jahed-Motlagh
Keyword(s):  
Linear Systems ◽  
Closed Loop ◽  
Robust Stabilization ◽  
Lyapunov Theory ◽  
Loop System ◽  
Time Varying ◽  
Closed Loop System ◽  
Mismatched Uncertainties ◽  
Non Linear ◽  
Non Linear Systems

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.

Robust Control of Double-Machine Wind Turbines with DFIG Using Hamiltonian Energy Method

2012 ◽  
Vol 443-444 ◽  
pp. 941-947
Author(s):  
Bing Wang ◽  
Xiao Ling Yuan ◽  
Jin Zhu
Keyword(s):  
Robust Control ◽  
Control Problem ◽  
Wind Turbines ◽  
Energy Method ◽  
Closed Loop ◽  
Loop System ◽  
Closed Loop System ◽  
Machine System ◽  
Nonlinear Design ◽  
Finite Gain

- In this paper, the robust control problem of the doubly fed induction generator (DFIG) wind turbines is investigated based on Hamiltonian energy method. A nonlinear design method is proposed for the double-machine system, such that the closed-loop system is stable simultaneously under the action of the controller. Moreover, we study the robust control problem of double-machine system in the presence of disturbances. On the basis of the proposed theorem, the Hamiltonian controller is designed to render the closed-loop system finite-gain stable. In order to illustrate the effectiveness of the proposed method, the simulations are performed which show that the gotten nonlinear controller can enhance the transient stability and improve the robustness property of the closed-loop system.

Sliding Controller Design for Aero-Engines With the Rate Limitation of Actuators

2017 ◽  
Author(s):  
Shubo Yang ◽  
Xi Wang
Keyword(s):  
Closed Loop ◽  
Actuator Saturation ◽  
Sliding Mode ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Tracking Error ◽  
Loop System ◽  
Sliding Surface ◽  
Closed Loop System ◽  
Aero Engines

With the relevant theories fully developed, sliding mode control (SMC), a kind of nonlinear control strategy having particularly strong robustness and disturbance rejection properties, has been applied in a considerable number of fields, such as robotic manipulator control, power generation control in wind turbines, robust stepper motor control, etc. For aero engines, remarkable progress of adopting SMC has been made. For instance, Richter has published his research of limit management in aircraft engine controls which suggests that replacing the linear regulators with sliding controllers can overcome the obstacle of traditional min-max approach. It is revealed from publication that researchers who design sliding controller for aero engines have made every effort to focus on the sliding surface and control law of SMC while they seldom paid attention to the constraints in actuators, such as saturation and rate limitation. In practical engineering, the performance of the ideal controller is infeasible under the situation that unavoidable constraints exist. Although the actuator saturation can be avoided by introducing a velocity form controller, rate limitation can still degenerate the control performance severely. In this paper, therefore, the design of a sliding controller for aero engines with rate limitation is discussed. A speed tracking problem is described based on the engine model simplified from a nonlinear system to a piecewise linear system at selected equilibrium points. A sliding surface is defined as the generalized tracking error, and a SMC law is designed with Lyapunov analysis of the closed loop system. Simulation results verify the stability of the closed-loop system, and show that the proposed sliding controller is capable of regulating a turbofan engine for large thrust commands in a stable fashion with proper tracking performance, which can mitigate the negative effect of actuator rate limitation.

Anti-windup: Definitions, Objectives, and Architectures

2011 ◽  
Author(s):  
Luca Zaccarian ◽  
Andrew R. Teel
Keyword(s):  
Closed Loop ◽  
Actuator Saturation ◽  
Loop System ◽  
Sampled Data ◽  
Closed Loop System ◽  
Closed Loop Systems ◽  
Output Stability ◽  
Response Recovery ◽  
Quantitative Performance ◽  
Nonlinear Performance

This chapter discusses definitions, objectives, and architectures relevant to anti-windup. It begins by focusing on the unconstrained closed-loop system, actuator saturation, and the saturated closed-loop system. It then considers the qualitative objectives of anti-windup augmentation, including small signal preservation, global vs. regional internal stability, global vs. regional input–output stability, and unconstrained response recovery. It also describes the augmented closed-loop system, linear vs. nonlinear augmentation, continuous-time closed-loop systems vs. sampled data, static vs. dynamic augmentation, external vs. full authority augmentation, and algebraic loops introduced by proper anti-windup filters. Finally, it examines the quantitative performance objectives of anti-windup augmentation, taking into account nonlinear performance measures.

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

2017 ◽  
Vol 40 (10) ◽  
pp. 3222-3231 ◽  
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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