Closed-loop Reference Models for Output-Feedback Adaptive Systems

Closed-loop reference models have recently been proposed for states accessible adaptive systems. They have been shown to have improved transient response over their open loop counter parts. The results in the states accessible case are extended to single input single output plants of arbitrary relative degree.Comment: v1 Submitted to European Control Conference 2013, v2 Typos correcte

Adaptive Output-Feedback Control for A Class of Multi-Input-Multi-Output Plants with Applications to Very Flexible Aircraft

A dominant presence of parametric model uncertainties necessitates an adaptive approach for control of very flexible aircraft (VFA). This paper proposes an adaptive controller that includes a baseline design based on observers and parameter adaptation based on a closed-loop reference model (CRM), and is applicable for a class of multi-input multi-output (MIMO) plants where number of outputs exceeds number of inputs. In particular, the proposed controller allows the plant to have first-order actuator dynamics and parametric uncertainties in both plant and actuator dynamics. Conditions are delineated under which this controller can guarantee stability and asymptotic reference tracking, and the overall design is validated using simulations on a nonlinear VFA model.Boeing Strategic University Initiativ

Supplementary Materials to "Adaptive Output-Feedback Control for A Class of Multi-Input-Multi-Output Plants with Applications to Very Flexible Aircraft"

A dominant presence of parametric model uncertainties motivates an adaptive approach for control of very flexible aircraft (VFA). This paper proposes an adaptive controller that includes a baseline design based on observers and parameter adaptation based on a closed-loop reference model (CRM), and is applicable for a class of multi-input multi-output (MIMO) plants where number of outputs exceeds number of inputs. In particular, the proposed controller allows the plant to have first-order actuator dynamics and parametric uncertainties in both plant and actuator dynamics. Conditions are delineated under which this controller can guarantee stability and asymptotic reference tracking, and the overall design is validated on a nonlinear VFA model.Boeing Strategic University Initiative

Squaring-Up Method for Relative Degree Two Plants

Abstract--- Non-square multi-input-multi-output (MIMO) plants are becoming increasingly common, as the addition of multiple sensors is becoming prevalent. However, square systems are needed sometimes as an leverage when it comes to design and analysis, as they possess desirable properties such as strict positive realness. This paper presents a squaring up method that adds artificial inputs to a class of MIMO plants with relative degree two and stable transmission zeros, where number of outputs exceeds number of inputs. The proposed method is able to produce a square plant that has stable transmission zeros and uniform/nonuniform relative degree, and is used to carry out adaptive control of this class of plants and shown to lead to satisfactory performance in a numerical study.Boeing Strategic University Initiativ

Analysis of Slow Convergence Regions in Adaptive Systems

We examine convergence properties of errors in a class of adaptive systems that corresponds to adaptive control of linear time-invariant plants with state variables accessible. We demonstrate the existence of a sticking region in the error space where the state errors move with a finite velocity independent of their magnitude. We show that these properties are also exhibited by adaptive systems with closed-loop reference models which have been demonstrated to exhibit improved transient performance as well as those that include an integral control in the inner-loop. Simulation and numerical studies are included to illustrate the size of this sticking region and its dependence on various system parametersthe Boeing University Strategic Initiativ

On approximate dynamic inversion and proportional-integral control

Approximate dynamic inversion (ADI) has been established as a method to control minimum-phase, nonaffine-in-control systems. Previous results have shown that for single-input nonaffine-in-control systems, every ADI controller admits a linear proportional-integral (PI) realization that is largely independent of the nonlinear function that defines the system. This paper extends these previous results in three ways. First, we present an extension of ADI that renders the closed loop error dynamics independent of the reference model dynamics. It is then shown that the equivalence between the ADI and PI controllers only holds for the time response when applied to the exact system. Finally, key robustness properties of the two control approaches are compared using linear system techniques. These results indicate that the PI realization is preferable when accurate knowledge of the nonlinear system dynamics is not available, and that the ADI realization would be preferred if time delays are the major limitations in the system