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This paper investigates the attitude stabilization problem of rigid spacecraft subject to actuator constraints, external disturbances, and attitude measurements only. An output feedback control framework with input saturation is proposed to solve this problem. The general saturation function is utilized in the proposed controller design and a unified control method is developed for the asymptotic stabilization of rigid spacecraft without velocity measurements. Asymptotic stability is proven by Lyapunov stability theory. Moreover, a new nonlinear disturbance observer is designed to compensate for external disturbances. Then, a composite controller is presented by combining a unified saturated output feedback control with a nonlinear disturbance observer. Desirable features of the proposed control scheme include the intuitive structure, robustness against external disturbances, avoidance of model information and velocity measurements, and ability to ensure that the actuator constraints are not violated. Finally, numerical simulations have been carried out to verify the effectiveness of the proposed control method.

The stabilization of spacecraft has been studied intensively in the last few decades. Several control results that stabilize the attitude of the spacecraft have been proposed in the literature. For example, Egeland and Godhavn [

However, all these aforementioned works assume that the actuator can generate any required control torque. This is quite conservative. In practice, when the requested control torque exceeds the maximum value that the actuator can supply, the performance of the controlled system cannot be guaranteed and this may cause instability [

While these controllers consider the actuator constraints, they assume that all the states can be measured and used in the controller. In practice, while the velocity can be measured by the sensor, it is influenced easily by the noise. Thus, the accuracy cannot be guaranteed and the performance will be degraded. This makes a velocity-free controller more desirable [

The major contributions of this paper are summarized as follows.

(

(

Advantages of the proposed approach include the intuitive structure, easy implementation, avoidance of model information and velocity measurements, robustness against external disturbances, and avoidance of violation of actuation limits.

The remainder of this paper is organized as follows. The problem of designing a saturated output feedback controller for rigid spacecraft is formulated in Section

The following notations are used throughout this paper.

The unit quaternion is used to describe the kinematics of rigid spacecraft because it is free of singularity. The unit quaternion is a vector defined as

The kinematic model of rigid spacecraft can be described by [

The dynamic equation for spacecraft is governed by [

We assume that each actuator has a known maximum torque,

Before the control design, the definition for the generalized saturation function given in [

Given a positive constant

The matrix

By the definition of

By calculating

Using the fact that the eigenvalues of

As a consequence,

Now, the unified saturated output feedback controller is designed in the presence of actuator constraints and attitude measurements only. We propose the USOF controller for asymptotic stabilization of rigid spacecraft as

The first main result of this paper is given in Theorem

Consider the spacecraft dynamic and kinematic equations (

Consider the following Lyapunov function candidate:

Using Definition

As a result, one can conclude that the proposed Lyapunov function given by (

Differentiating (

Substituting (

Using the fact given by (a) in Definition

The proposed controller can be considered as a nonlinear proportional-derivative (PD) control method. This controller has the advantages of the intuitive structure, the absence of modeling information and velocity measurements, and the ability to guarantee that the actuator constraints are not violated. Moreover, the stability of the closed loop with the proposed controller does not depend on a specific saturation function. This offers an additional appealing property that it may obtain an improved performance by choosing the saturation function freely.

In (

The control development in Section

Thus, there exist constants

Next, the second main result of this paper is presented in Theorem

Consider the spacecraft dynamic and kinematic equations (

Define

Next, a composite controller is designed by combining the USOF controller with NDO. The proposed NDO-USOF controller is given as

Consider the spacecraft dynamic and kinematic equations (

Consider the Lyapunov function defined in (

Different from NDO-based controllers in [

The spacecraft used in [

The generalized saturation function used in [

The saturated output feedback (SOF) controller proposed in [

All the controller gains are selected by trial and error until a better convergence time is obtained. According to the control constraints (

Quaternion parameters without disturbances.

Angular velocity without disturbances.

Control torque without disturbances.

After that, the simulations in the presence of disturbances have been conducted under the NDO-USOF controller (

Quaternion parameters with disturbances.

Angular velocity with disturbances.

Control torque with disturbances.

Disturbance estimates.

A unified saturation output feedback controller for asymptotic stabilization of rigid spacecraft with external disturbances and actuator saturation has been proposed. Using the linear filter driven by the attitude variable, velocity measurements are not required. Asymptotic stability has been proven by Lyapunov’s direct method. Moreover, a nonlinear disturbance observer is designed to compensate for external disturbance. Then, a composite controller is developed by combining a unified saturated output feedback control with nonlinear disturbance observer. Advantages of the proposed control framework are the intuitive structure, the absence of model information and velocity measurements, avoidance of violation of actuation limits, and robustness against external disturbances. Simulations have verified the effectiveness and improved performance of the proposed controller.

The author declares that there are no conflicts of interest regarding the publication of this paper.

This research was funded by King Mongkut’s University of Technology North Bangkok (Contract no. KMUTNB-60-ART-51).