New Application of an Adaptive Controller Based on Robust Fixed Point Transformations

2015 ◽  
pp. 45-66
Author(s):  
Imre J. Rudas ◽  
József K. Tar
Keyword(s):  
Fixed Point ◽  
Adaptive Controller ◽  
Point Transformations

Robust Fixed Point Transformations in the Model Reference Adaptive Control of a Three DoF Aeroelastic Wing

2013 ◽  
Vol 300-301 ◽  
pp. 1505-1512 ◽  
Author(s):  
József Kázmér Tar ◽  
Imre J. Rudas ◽  
János F. Bitó ◽  
Krisztián Kósi
Keyword(s):  
Fixed Point ◽  
Reference Model ◽  
Tracking Error ◽  
External Control ◽  
Underactuated System ◽  
Control Parameters ◽  
Model Reference ◽  
Adaptive Controllers ◽  
Point Transformations ◽  
Model Reference Adaptive

The Model Reference Adaptive Controllers (MRAC) of dynamic systems have the purpose of simulating the dynamics of a reference system for an external control loop while guaranteeing precise tracking of a prescribed nominal trajectory. Such controllers traditionally are designed by the use of some Lyapunov function that can guarantee global and sometimes asymptotic stability but pays only little attention to the primary design intent, has a great number of arbitrary control parameters, and also is a complicated technique. The Robust Fixed Point Transformations (RFPT) were recently introduced as substitutes of Lyapunov’s technique in the design of adaptive controllers including MRACs, too. Though this technique guarantees only stability (neither global nor asymptotic), it works with a very limited number of control parameters, directly concentrates on the details of tracking error relaxation, and it is very easily can be designed. In the present paper this novel technique is applied for the MRAC control of a 3 Degrees-of-Freedom (DoF) aeroelastic wing model that is an underactuated system the model-based control of which attracted much attention in the past decades. To exemplify the efficiency of the method via simulations it is applied for PI and PID-type prescribed error relaxation for a reference model the parameters of which considerably differ from that of the actual system.

Control of Uncertain Systems: A Combined Approach

2015 ◽  
Vol 1117 ◽  
pp. 241-244
Author(s):  
Terez A. Várkonyi ◽  
József Kázmér Tar ◽  
Annamária R. Várkonyi-Kóczy ◽  
Imre J. Rudas
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Uncertain Systems ◽  
Control Process ◽  
Learning Ability ◽  
Combined Approach ◽  
Control Engineering ◽  
Point Transformations ◽  
Control Of Uncertain Systems

Nowadays, in the field of control engineering, neural networks (NNs) are very useful, because of their learning ability. In case of control tasks, they are often used to adapt to the unknown or changing behavior of the system to be controlled. When the system is unknown, or partially known, at the beginning, it is very difficult to set the controller properly, and imprecision may occur in the control process. In this case, some extra calculations are needed to get more accurate results. One of the possible solutions is the application of Robust Fixed Point Transformations (RFPT). In this paper, it is shown that RFPT can improve the accuracy of the control achieved by a traditional NN controller.

Comparison of Fractional Robust- and Fixed Point Transformations- Based Adaptive Compensation of Dynamic Friction

2007 ◽  
Vol 11 (9) ◽  
pp. 1062-1071 ◽  
Author(s):  
József K. Tar ◽  
◽  
Imre J. Rudas ◽  
Béla Pátkai ◽  
Keyword(s):  
Fixed Point ◽  
Sliding Mode ◽  
Time Derivative ◽  
Variable Structure ◽  
Adaptive Controller ◽  
Dynamic Friction ◽  
Adaptive Controllers ◽  
Error Metrics ◽  
Tilting Angle ◽  
Sliding Mode Variable Structure

The features of fractional order robust and fixed-point transformation based adaptive controllers of a “Ball-Beam System” are compared to each other. The speciality of this task is that the position of the ball along the beam is indirectly controlled via directly controlling the other axis, the tilting angle of the beam. It is assumed that this tilting axle suffers from considerable dynamic friction mathematically approximated by the LuGre model. By neglecting the internal physics of the tilting drive this system can be modeled as a 4thorder one because only the 4thtime-derivative of the ball’s position can directly be influenced by the tilting torque. The system also has saturation since the available acceleration of the ball is limited by the gravitation. It is shown that little reduction of the order of the differential equation controlling the decay of the error metrics in a Sliding Mode / Variable Structure controller considerably improves the robust controller. However, really precise solution can be obtained by the adaptive controller. These statements are illustrated and substantiated via simulation.

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