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.

Autonomous Flight Control of Unmanned Small Hobby-Class Helicopter Report 2: Modeling Based on Experimental Identification and Autonomous Flight Control Experiments

2003 ◽  
Vol 15 (5) ◽  
pp. 546-554 ◽  
Author(s):  
Kensaku Hazawa ◽  
◽  
Jinok Shin ◽  
Daigo Fujiwara ◽  
Kazuhiro Igarashi ◽  
...  
Keyword(s):  
Flight Control ◽  
Position Control ◽  
Control Structure ◽  
Controller Design ◽  
Autonomous Flight ◽  
Velocity Models ◽  
Single Output ◽  
Hover Control ◽  
Function Models ◽  
And Control

We developed a small autonomous hobby-class unmanned helicopter that weighs about 9 kg, focusing on attitude and velocity models and controller design. Simge Input Single Output (SISO) transfer function models are derived from brief kinematical analysis and system identification for each of the helicopter dynamics of pitch, roll, yaw, and three direction velocities. We designed six separate controllers based on derived models using LQG and LQI control theory. The models and control structure are verified by experimental results. Accurate position control, namely, hover control and trajectory-following control, is achieved by a simple control algorithm using a designed attitude and velocity control structure. Robustness of the controller against wind was confirmed in a windy-day experiment. To verify robustness against the perturbation of physical helicopter parameters, the controller is applied to a larger helicopter.

Utilization of Control Effort Constraints in Linear Controller Design

1989 ◽  
Vol 111 (3) ◽  
pp. 378-381 ◽  
Author(s):  
A. Galip Ulsoy
Keyword(s):  
Feedback Control ◽  
Controller Design ◽  
Design Procedure ◽  
Maximum Energy ◽  
Control Effort ◽  
Single Input Single Output ◽  
State Variable ◽  
Linear Controller ◽  
Single Output ◽  
Controlled Systems

A linear controller design procedure, which accounts for constraints on control effort, is developed by requiring that the control system utilize the maximum energy delivering capability of the final control elements under some specified test conditions (e.g., maximum step reference input). Results using this approach are available from previous studies for low-order single-input single-output controlled systems. This paper presents results for multi-input multi-output systems where the number of inputs is equal to the number of states. Both state variable feedback control for regulation, and integral plus state variable feedback control for tracking are considered and illustrated with an example problem.

scholarly journals Direct tuning of gain-scheduled controller for electro-pneumatic clutch position control

2021 ◽  
Vol 13 (8) ◽  
pp. 168781402110360
Author(s):  
Shuichi Yahagi ◽  
Itsuro Kajiwara
Keyword(s):  
Position Control ◽  
Control Method ◽  
Controller Design ◽  
Design Procedure ◽  
Unknown Coefficient ◽  
Trial And Error ◽  
Highly Nonlinear ◽  
Gain Scheduled Controller ◽  
Gain Scheduled ◽  
Controlled Object

This study proposes a gain-scheduled controller with direct tuning for the position control of a pneumatic clutch actuator that is installed in heavy-duty trucks. Pneumatic clutch actuators are highly nonlinear systems and cannot be easily controlled. Industries require a simple controller design that is easy to understand and requires few trial-and-error calibrations. Therefore, we adopted a gain-scheduled proportional integral derivative (PID) control law, which is a well-known and easy-to-understand nonlinear control method. In this approach, a gain scheduler is expressed using polynomials composed of coefficient parameters and controlled object states. The unknown coefficient parameters of the polynomials are directly tuned from the controlled object input/output data without having to use a controlled object model. The proposed controller design procedure is simple and does not require system identification or trial-and-error tuning. The effectiveness of the proposed method is verified by an experiment using an actual vehicle. The experimental results confirm the effectiveness of the proposed method for the position control of pneumatic clutch actuators.

Controller Synthesis Methodology for Multivariable Nonlinear Systems With Application to Aerospace

2004 ◽  
Vol 126 (3) ◽  
pp. 595-604 ◽  
Author(s):  
Amir Nassirharand ◽  
Hassan Karimi
Keyword(s):  
Controller Design ◽  
Design Procedure ◽  
Controller Synthesis ◽  
Model Matching ◽  
Nonlinear Dynamic Model ◽  
Highly Nonlinear ◽  
Matching Procedure ◽  
Synthesis Methodology ◽  
Function Models ◽  
Multivariable Nonlinear Systems

In this paper, a new systematic controller synthesis methodology for use with highly nonlinear multivariable and nonautonomous systems with application to a class of multivariable nonlinear aerospace systems is presented. The procedure is applied to a typical liquid propellant engine, and the performance of the resulting new control system is presented. In this research, the nonlinear dynamic model of the engine, which includes both soft and hard nonlinearities, is developed. The systematic controller design procedure is based on describing function models of the engine coupled with a new multivariable exact model matching procedure.

Robust Approach for Position Control of Hydraulic Differential Cylinder

2007 ◽  
Author(s):  
Yan Liu ◽  
Dirk So¨ffker
Keyword(s):  
Feedback Linearization ◽  
Position Control ◽  
Single Input Single Output ◽  
Control Approach ◽  
Luenberger Observer ◽  
Single Output ◽  
Cylinder Test ◽  
Highly Nonlinear ◽  
Feedback Linearization Control ◽  
Feedback Linearization Approach

The paper introduces a robust nonlinear control approach for the position control of hydraulic differential cylinder. The behavior of a hydraulic differential cylinder is highly nonlinear. A perfect model is usually not available. So nevertheless a robust control is required, to guarantee the performance of the cylinder, usually based on an imperfect model. The presented approach combining the classical feedback linearization approach and an extended Luenberger observer technique is robust to model uncertainties or unknown effects acting to the system, for example as unknown load, and can be applied to single-input single-output (SISO) nonlinear systems. It improves the robustness and extends the application area of feedback linearization control. The approach is implemented and tested on a hydraulic differential cylinder test rig. Theoretical proofs and experimental results are presented.

scholarly journals Limit Cycle Prediction Based on Evolutionary Multiobjective Formulation

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
M. Katebi ◽  
H. Tawfik ◽  
S. D. Katebi
Keyword(s):  
Limit Cycle ◽  
Mimo Systems ◽  
Describing Function ◽  
Single Input Single Output ◽  
Single Output ◽  
Harmonic Signals ◽  
Sinusoidal Input ◽  
Single Input ◽  
Siso Systems ◽  
Function Matrix

This paper is concerned with an evolutionary search for limit cycle operation in a class of nonlinear systems. In the first part, single input single output (SISO) systems are investigated and sinusoidal input describing function (SIDF) is extended to those cases where the key assumption in its derivation is violated. Describing function matrix (DMF) is employed to take into account the effects of higher harmonic signals and enhance the accuracy of predicting limit cycle operation. In the second part, SIDF is extended to the class of nonlinear multiinput multioutput (MIMO) systems containing separable nonlinear elements of any general form. In both cases linearized harmonic balance equations are derived and the search for a limit cycle is formulated as a multiobjective problem. Multiobjective genetic algorithm (MOGA) is utilized to search the space of parameters of theoretically possible limit cycle operations. Case studies are presented to demonstrate the effectiveness of the proposed approach.

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.

Design and Realtime Implementation of an Adaptive Variation Absorber for Uncertain Mechanical Systems Subjected to Unknown Disturbances

2004 ◽  
Vol 10 (1) ◽  
pp. 55-84
Author(s):  
Raffi Derkhorenian ◽  
Nader Jalili ◽  
D M Dawson
Keyword(s):  
Degrees Of Freedom ◽  
Controller Design ◽  
Linear Time ◽  
Vibration Absorber ◽  
Primary System ◽  
Control Input ◽  
Adaptation Algorithm ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output

In this paper we describe the design and implementation of a nonlinear adaptive disturbance rejection approach for single-input-single-output linear-time-invariant uncertain systems subject to sinusoidal disturbances with unknown amplitude and frequency. This is an extension of our earlier study to a more complicated plant, a two-degrees-of-freedom (2DOF) system representing a vibration absorber setting. The controller design is based on a single Lyapunov function incorporating both the error states and the update laws and, hence, global stability and improved transient performance are readily achieved. Utilizing only the system output, a virtual control input is used in place of non-measurable and unknown signals. The performance of the adaptation algorithm is demonstrated through real-time simulations, both for regulation and tracking, on a 2DOF system representing an active vibration absorber setup. It is shown that when the primary system is subjected to an unknown sinusoidal disturbance, the proposed controller in the absorber subsection completely suppresses the primary system vibration in the presence of unknown disturbance.

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