Vibration attenuation of spacecraft in the presence of parametric and unmodeled dynamics uncertainties using collocated and noncollocated control: A comparative study

Abstract

µ-control synthesis offers the advantage of maintaining robust performance and stability in the presence of plant uncertainties. Expressions relating the 2-norm of the vector of regulated outputs and closed-loop modal damping to the weights used for µ-control synthesis are derived in this paper. By using these expressions, the amount of damping added to each mode can be controlled individually while maintaining equal importance for each controlled mode. Hence, the selection of weights for synthesizing a suitable µ-controller is greatly simplified. Furthermore, a comparative study of µ-controllers designed by the proposed procedure and positive position feedback (PPF) controllers designed by analytically derived optimal parameters is also presented. The techniques are compared for their vibration attenuation, energy utilization, and stability characteristics, in the presence of parametric and unmodeled dynamics uncertainties. Results for both time domain and frequency domain simulations are presented. As in some cases (sandwich plate structures etc.) the noncollocation of actuator/sensor becomes crucial for achieving good performance, the above-mentioned characteristics are evaluated for both collocated and noncollocated sensor locations.

Determination of optimal positive position feedback parameters by using nonsmooth H∞ synthesis

“…Considering that piezoelectric actuators and strain gauges which are used as actuators and sensors, respectively, have very little delay and the availability of fast computing hardware, a conservative time-delay value of 50 ms is used (Preumont et al, 1992), while considering the main parametric uncertainty from modeling, a random error of ±20% in each modal frequency is used as (Khushnood et al, 2018; Peruzzi et al, 2016)where ω˜i is the disturbed natural frequency of the i th mode and r(t) is the normally distributed random function (Peruzzi et al, 2016).…”

“…Further details of procedure used for obtaining system model from ANSYS and aforementioned modification required for control synthesis are available in Khushnood et al (2016). For achieving desired modal damping, the weights Wdist, Wbound, Wact, and Wmod shown in Figure 3(b) can be selected by following the same procedure as used for unconstraint H∞ synthesis (Khushnood et al, 2018).…”

A Study on Optimal Compensation Design for Meteorological Satellites in the Presence of Periodic Disturbance

“…For many studies about vibration suppression of flexible spacecraft, their simplified mathematical model can be expressed as a 2-order vibration system, for example, like the model used in [7]. This means the 2-order vibration system can be used to illustrate the vibration characters of flexible spacecraft.…”

“…The application of spaceborne microwave imaging instruments has substantially improved the image definition, but poor effects on attitude accuracy are also brought about by their known-law rotating imbalance [4][5][6]. Furthermore, characteristics like flexibility and low weight make spacecraft vulnerable to vibrations caused by numerous sources [7]. In this paper, we focus on the compensation of known-law long-lasting periodic disturbances and attenuation of vibrations to improve the attitude accuracy of meteorological satellites.…”

Multiple-input multiple-output robust vibration control for constrained gyroelastic solar panel considering parametric and un-modeled dynamic uncertainties

“…Based on the principle of minimizing the scaled infinite norm of the system (Balas and Doyle, 1994; Zhou et al, 1996), μ-synthesis breaks through H∞ control’s conservative limitation and can effectively solve the robust controller design problem with structured uncertainties. In the previous study, μ-synthesis is generally used to suppress the vibration of the flexible structure with piezoelectric actuators (Hu and Xu, 2013; Khushnood et al, 2018; Kumar, 2013; Li et al, 2003; Oveisi and Gudarzi, 2012), and there are few researches on its application for gyroelastic body. In addition, although the selection method of design weights for SISO system is studied by Atif (Khushnood et al, 2018), MIMO system still needs to be further study.…”