Closed Loop Automobile Maneuvers Using Describing Function Models

1982 ◽  
Author(s):  
W. Riley Garrott ◽  
Douglas L. Wilson ◽  
Richard A. Scott
Keyword(s):  
Closed Loop ◽  
Describing Function ◽  
Function Models

Characterization and Attenuation of Sandwiched Deadband Problem Using Describing Function Analysis and Its Application to Electro-Hydraulic Systems Controlled by Closed-Center Valves

2004 ◽  
Author(s):  
Song Liu ◽  
Bin Yao
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Function Analysis ◽  
Nonlinear Behavior ◽  
Hydraulic Systems ◽  
Describing Function ◽  
Widespread Application ◽  
Actuator Dynamics ◽  
Loop Bandwidth ◽  
Highly Nonlinear

Sandwiched deadbands can be seen in a wide variety of systems, such as electro-hydraulic systems controlled by closed-center valves. In such a system, the deadband is between the plant and actuator dynamics and therefore can not be compensated directly like an input deadband. Though this sandwiched deadband problem may be attenuated to certain degree through sophisticated advanced control techniques, the increased cost and the necessity of actuator state feedback prohibit their widespread application in the industry. An economical and popular method is to add an inverse deadband function in the controller to cancel or compensate the highly nonlinear behavior of the deadband. However, such a solution requires that the dynamics before the deadband (eg. the valve dynamics) is fast enough to be neglected — a requirement that can not be met in reality unless the closed loop bandwidth of the overall system is limited very low. To raise the achievable closed loop bandwidth for a much improved control performance, it is essential to be able to precisely characterize the effect of this sandwiched deadband on the stability and performance of the overall closed-loop system, which is the main focus of the paper. Specifically, a describing function based nonlinear analysis will be conducted to predict when the instability will occur and how the resulting limit cycle depends on the actuator dynamics and the targeted closed-loop bandwidth. Based on the analysis, the optimal closed-loop bandwidth can be determined to maximize the achievable overall system performance. The technique is applied to an electro-hydraulic system controlled by closed-center valves to optimize the controller design.

Pilot describing function models for nonlinear controlled elements

1970 ◽  
Author(s):  
Leon C. Duggar ◽  
James T. Mannen ◽  
Russell A. Hannen
Keyword(s):  
Describing Function ◽  
Function Models

Controller Design For Nonlinear Systems Based on Simultaneous Stabilization Theory and Describing Function Models

1988 ◽  
Vol 110 (2) ◽  
pp. 134-142 ◽  
Author(s):  
A. Nassirharand ◽  
J. H. Taylor ◽  
K. N. Reid
Keyword(s):  
Position Control ◽  
Controller Design ◽  
Design Procedure ◽  
Describing Function ◽  
Simultaneous Stabilization ◽  
Single Input Single Output ◽  
Single Output ◽  
Highly Nonlinear ◽  
Sinusoidal Input ◽  
Function Models

A new systematic and algebraic linear control system design procedure for use with highly nonlinear plants is developed. This procedure is based on simultaneous stabilization theory and sinusoidal-input describing function models of the nonlinear plant, and is presently applicable to single-input single-output, time-invariant, deterministic, stable, and continuous-time systems which are representable in standard state-variable differential equation form. Three software utilities to implement the controller design procedure are also outlined. This method and the associated software is applied to a position control problem of the sort encountered in robotics, and the results are compared with those previously obtained using both linear and nonlinear PID control.

Characterization and Attenuation of Sandwiched Deadband Problem Using Describing Function Analysis and Application to Electrohydraulic Systems Controlled by Closed-Center Valves

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Song Liu ◽  
Bin Yao
Keyword(s):  
Closed Loop ◽  
Function Analysis ◽  
Closed Loop Control ◽  
Control Performance ◽  
Nonlinear Feedback ◽  
Describing Function ◽  
Loop Control ◽  
Actuator Dynamics ◽  
And Performance ◽  
The Stability

Unlike input deadband, the sandwiched deadband between actuator and plant dynamics is very difficult to be explicitly compensated for due to the proceeding actuator dynamics whose effect may not be negligible. The paper presents a practical way to overcome the design conservativeness of existing methods in dealing with sandwiched deadband. Specifically, a describing function based nonlinear analysis method is proposed to characterize the effect of the sandwiched deadband on the stability and performance of the overall closed-loop system. The analysis results can be used to determine the highest closed-loop bandwidth that can be achieved without inducing residual limit cycles and instability. Optimal controller parameters can then be found to maximize the achievable closed-loop control performance. The technique is applied to an electrohydraulic system controlled by closed-center valves and a nonlinear feedback controller. Simulation results showed severe oscillations as the feedback control gains are increased to the predicted threshold values. Comparative experimental results also showed the effectiveness of the proposed method in reducing the conservativeness of traditional design and the improved closed-loop control performance in implementation.

The Response of Nonlinear Closed-Loop Systems to Random Inputs

1964 ◽  
Vol 86 (1) ◽  
pp. 132-138 ◽  
Author(s):  
J. E. Gibson ◽  
R. Sridhar
Keyword(s):  
Nonlinear Systems ◽  
Autonomous System ◽  
Closed Loop ◽  
Random Noise ◽  
Correlation Method ◽  
Random Component ◽  
Describing Function ◽  
Random Inputs ◽  
Closed Loop Systems ◽  
The Stability

A dual-input describing function (DIDF) is derived for sine waves and Guassian noise. The derivation follows the correlation method used in [1]. In this paper only single-valued nonlinearities are discussed but extension to multivalued nonlinear elements appears possible. The DIDF is used to investigate the stability and closed-loop response of nonlinear systems excited by random noise. Previous investigations have provided only for the random component at the input to the nonlinear element. It is shown that previous work is invalid insofar as it neglects the possibility of oscillations in the nonautonomous system if the autonomous system is stable and vice versa. Two examples are presented which show (i) the necessity of the DIDF approach for systems which are stable without input, and (ii) the possibility of successfully obtaining stable response to certain classes of inputs with systems which appear unstable without inputs. The present investigation is an extension of the authors’ previous work on the stability and closed-loop response of nonlinear systems excited by sinusoidal inputs [2].

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