Reaction Wheels Desaturation Using Magnetorquers and Static Input Allocation

Abstract

Considering the most widely spread configuration of actuators for low orbit satellites, namely a set of reaction wheels and a set of magnetorquers, we revisit the classical "cross product control law" solution for achieving attitude stabilization and momentum dumping. We show how the classical solution has a quasi-cascade structure that, under a suitable input-tostate (ISS) assumption, can be stabilized by high gain, thereby making the actuators more inclined to saturate. Motivated by this, we propose a revisited version of this control law that transforms the quasi-cascade into a real cascade. Then we show that both strategies are such that the attitude control is affected by the momentum dumping, and that they both require a suitable ISS property. To overcome these drawbacks, we propose a new allocation-based controller which makes the attitude dynamics completely independent of the momentum dumping and induces global asymptotic stability without any ISS requirement. Several formal statements and simulation results support our discussions and highlight the pros and cons of the different control strategies.

Spacecraft Attitude and Reaction Wheel Desaturation Combined Control Method

“…The nonlinear model of (21) can be used to design control systems. One popular design method for nonlinear model involves Lyponuv stability theorem, which is actually used in [8,9]. A design based on this method focuses on stability but not on performance.…”

“…Since both attitude control and reaction wheel desaturation are performed at the same time using the same magnetic torque coils, the control system design should consider these two design objectives at the same time and some very recent research papers tackled the problem in this direction, for example, [8,9]. In [8], Tregouet et al studied the problem of the spacecraft stabilization and reaction wheel desaturation at the same time. They considered time-variation of the magnetic field in body frame, and their reference frame was the inertial frame.…”

Positiveμmodification as an anti-windup mechanism

“…After using the adaptive updates from equation (18) and equation (27), the time derivative of the Lyapunov function (28) is given bẏ…”

“…Therefore, referring to the equation (27), it follows thatė ∈ L ∞ since all terms on the right hand side are bounded. Next note thaẗ…”

“…Researchers have long been aware of the sensitivity of adaptive controllers to input saturation and many papers have appeared on the topic see [33,22,15,14,29,27] Email address: mct6@le.ac.uk (Matthew C. Turner).…”