Design of rate and amplitude saturation compensators using three degrees of freedom controllers

Abstract

This paper proposes two frequency-domain design techniques for rate and amplitude saturation compensators formulated as three degrees of freedom controllers. For single constraint systems, it shows an equivalence between the a posteriori compensator design and the a priori controller synthesis proposed by Horowitz. For rate and amplitude constrained systems, the three degrees of freedom controller is a special case of the general saturation compensator. Through multivariable frequency domain analysis of the compensators, hidden properties of the three degrees of freedom controller are revealed. These inherent properties are utilized in compensator designs by techniques shaping the characteristic loci and speci® cation of singular values. Simulated examples illustrate the success of the design methods.

Performance enhancement of internal model based anti-windup control for input saturation via loop shaping

“…Manipulating L n to achieve saturation compensation was first recognized and performed by Horowitz [4] and was adopted by many others then after [3],[10], [5] . Applying this decomposition, we can have the following representation of the AW system in Fig.2, shown in Fig.3.…”

Output feedback control with H∞ performance for saturated linear systems with magnitude and rate constraints

“…The output feedback controller defined in equation ( 5) can achieve a stabilized closed-loop controlled system with a minimized H ' performance level g à if there exist synthesis matrix variables X,Y,F u ,F,G,L È É such that the LMIs ( 13) and ( 15) can be established for g à .0. The remaining controller parameters A c ,B c ,C c È É for equation ( 5) can be constructed from equation (16). Moreover, the magnitude and rate constraints for the control effort can be satisfied if the LMIs in equation ( 23) for the admissible ellipsoidal invariant set X 0 P , equation ( 29) for the control magnitude constraint, and equation (35) for the control rate constraint can be established for the considered initial condition, x 0 , and the specified control effort magnitude and rate constraints u i,max , _ u i,max .…”

“…Both of them were constructed under the magnitude constraint u max = 1. For the controller designed with the rate constraint _ u max = 1 the achieved H ' performance level was g à = 4:0605 and the synthesized controller variables from Theorem 1 and equation (16) were For the design with rate constraint _ u max = 10 À1 the achieved H ' performance level was g à = 15:5720, and the synthesized controller matrix variables as shown in equation ( 5) were obtained as It is noted that the numbers in the system matrix A c vary by about six orders of magnitude, which is comparable to the designated relative stability a = 5310 À2 and radius r = 10 3 for pole placement constraints. A restrictive pole placement region can reduce the magnitude order of the system matrix A c and at the same time, limit the obtainable H ' performance levels.…”

“…The magnitude and rate saturation were considered in an antiwindup problem [3,13,14] and in a low-gain controller [1,15]. The approaches in references [16][17][18] synthesized the magnitude and rate saturation compensators using frequency domain techniques whereas the approach taken in references [13,19] was based on an online optimization performed in the framework of model predictive control. Another approach reported in the literature is the use of convex computation methods [20][21][22][23] including the use of linear matrix inequalities (LMIs) [24].…”