Three-axis attitude stabilization of a flexible satellite using non-linear PD controller

Abstract

In this paper, after complete modelling of a flexible satellite equipped with a control moment gyroscope (CMG) actuator, it is shown that a PD-like controller can globally asymptotically stabilize this satellite by using Lyapunov’s direct method. Despite the simplicity, simulations show that the controller can stabilize the flexible satellite in a three-axis manoeuvre even in the presence of external disturbances. Then, using a non-linear variable gains PD controller, which only uses angular velocity of the rigid body and the attitude parameters as the inputs, the performance of the control system is improved in some important aspects such as reducing maximum control torque, reducing maximum peak of deflection of the appendages and increasing robustness of the controller against the orbital disturbances. In addition, locally asymptotically stability of the non-linear variable gain PD controller is guaranteed using a novel Lyapunov candidate function. Considering the difficulty in measuring the appendages’ deflection and the primarily existence of parameter uncertainties, and as this controller is independent of changes in these parameters, such a control system is very useful and applicable. In order to validate the system’s mathematical model and the control system performance, an exact model of the satellite is constructed in the ADAMS/View software that is linked to the MATLAB software. The efficacy of the proposed approach is demonstrated by several numerical examples.

General Planar Motion Modeling and Control of a Smart Rigid-Flexible Satellite Considering Large Deformations

“…Therefore, the equations of piezoelectric sensors are also the results of using the extended Hamilton's principle, which are obtained as: ( 1, 2,..., ) The Galerkin method is used to discretize the equations of motion ( 12)-( 16) and the equations of piezoelectric sensors (18) and (19). Therefore, the transverse displacements of the flexible appendages are approximated as follows:…”

“…Of course, ODEs of motion can be obtained directly (e.g., the Rayleigh-Ritz method) or ODE-PDEs can be obtained first and then they can be discretized and converted to a set of ODEs (e.g., the Galerkin method) [16]. Other controllers designed based on ODEs of motion of the flexible satellites and similar systems in previous researches include robust adaptive control for three axes attitude maneuver of a flexible satellite in orbital motion [5], hybrid adaptive sliding mode/Lyapunov control for one axis maneuver of a satellite with nonlinear flexible appendages in orbital motion using the singular perturbation theory [6], fractional-order sliding mode control for a rotating Euler-Bernoulli beam [8], multivariable predictive control for active vibration control of a flexible one-link manipulator [17], variable structure control for a flexible spacecraft in attitude maneuver [18], nonlinear PD control for three axes attitude stabilization of a flexible satellite [19] and active vibration suppression and high accuracy attitude control for a flexible satellite with piezoelectric actuators via fixed-time prescribed performance control [20].…”

Satellite Attitude Control Using Control Moment Gyroscopes

“…Kojima et al (2020) proposed a new CMG design that minimize singularities, named the doublegimbal scissored-pair CMG (DGSPCMG), which controls it by using a quaternion feedback law. Some studies focus on nonlinear control techniques to overcome external disturbances, parameters uncertainties and wider operation ranges, such as Toriumi and Angélico (2020), who developed a nonlinear feedback linearization control in a cascade structure and compared the simulations with experimental results, and Baghi et al (2018) considered a satellite with large flexible appendages, employing a nonlinear PD controller and proving its globally asymptotical stability using a Lyapunov function.…”

Stabilised LQR Control and Optimised Spin Rate Control for Nanosatellites

“…The use of the quaternion model with linearized dynamics is proven to be controllable and globally stabilizes the nonlinear satellite model [15]. A Proportional-Derivative (PD) like control law also can be used to attain a certain attitude control precision as it is known to asymptotically stabilize the system with application of control torques in three linearly independent directions [16].…”