Determining Strictly Positive Realness from System Modal Characteristics

2007 ◽  
Vol 30 (5) ◽  
pp. 1539-1542 ◽  
Author(s):  
Eric A. Mehiel ◽  
Mark J. Balas
Keyword(s):  
Modal Characteristics ◽  
Positive Realness ◽  
Strictly Positive Realness

scholarly journals Robust Fractional Adaptive Control Based on the Strictly Positive Realness Condition

2009 ◽  
Vol 19 (1) ◽  
pp. 69-76 ◽  
Author(s):  
Samir Ladaci ◽  
Abdelfatah Charef ◽  
Jean Loiseau
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Robust Adaptive Control ◽  
Adaptive Controllers ◽  
Actuator Dynamics ◽  
Control Scheme ◽  
Positive Realness ◽  
Robust Adaptive ◽  
Model Reference Adaptive ◽  
Strictly Positive Realness

Robust Fractional Adaptive Control Based on the Strictly Positive Realness ConditionThis paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed control scheme is based on the Almost Strictly Positive Realness (ASPR) property of the plant. We show that this condition implies also robust stability in the case of fractional order controllers. An application to Model Reference Adaptive Control (MRAC) with a fractional order adaptation rule is provided with an implementable algorithm. A simulation example of a SISO robust adaptive control system illustrates the advantages of the proposed method in the presence of disturbances and noise.

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