Output tracking of some class non-minimum phase nonlinear systems via output redefinition

Abstract

Abstract. In this paper, we present the output tracking for a class non-minimum phase nonlinear. To achive the output tracking, we will apply the modified steepest descent control. To apply the modified steepest descent control, the output of the system will be redefined such that the system will become minimum phase with respect to a new output.

Output tracking control of non‐minimum phase systems using on‐line output redefinition approach based on barrier function method

“…In some works, although the output redefinition technique has been used, it has not been applied in an inverse dynamics control structure [6,17,20]. In reference [6], the output redefinition is used in the state feedback control and in reference [20], it is used in a modified gradient descent based control structure.…”

“…In reference [17], the redefined output has been designed just for linear dynamical systems and in reference [20], it has been designed for systems with relative degree n (dimension of the system) or $$n-1$$.…”

“…The contribution of this paper is therefore summarized as follows: (i)Considering a general form of the parametric redefined outputs applicable for general non‐linear systems.

Reference Control method Plant Reference Signal Redefinition General Reference Signal On‐line Output Redefinition [5]Inverse dynamicsHypersonic vehiclesYesYesNo[6]State feedbackHigh speed trainsYesYesNo[8]Inverse dynamicsUnderactuated shipsNoYesNo[16]Inverse dynamicsGeneral formNoNoNo[17]Learning controlLinear dynamicsNoNoNo[18]Input–output linearizationGeneral formNoNoNo[19]Feedback linearizationGeneral formNoNoNo[20]Gradient descent methodSystems with special relative degreesNoYesNo[21]Sliding mode controlHypersonic vehiclesYesYesNo[22, 23]Inverse dynamicsFlexible linksNoYesYes[24]Neural network based feedback linearizationUnmanned aerial vehiclesNoNoNo[25]Neural network and inverse dynamicsFlexible linksYesYesYes[26]Adaptive fuzzy sliding modeAnti‐ship missilesNoYesNo[

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“…This approach was introduced by Gopalswamy and Hedrick [16], and its idea is to define new output functions such that the new zero dynamics become stable. Various procedures have been suggested for output redefinition in the literature [5,6,8,[16][17][18][19][20][21][22][23][24][25][26][27][28]. In most of them, the proposed methods are not applicable for general form of non-linear systems and they have been only designed for a specific system like flexible links [22,23,25,27], hypersonic vehicles [5,21], high speed trains [6], unmanned aerial vehicles [24], anti-ship missiles [26] and underactuated ships [8].…”