Linear Parameter-varying Control Theory Research Articles

Attitude Control and Unloading for Spacecraft with Redundant Reaction Wheels under Nonstationary Angular Velocity Requirement

We applied the LPV (Linear Parameter-Varying) control theory to attitude control for spacecraft. With this method, control stability and control performance can be considered at the same time. This method was applied to attitude tracking problems. In this paper, a method to apply the LPV control theory to the tracking problem of the attitude as well as the angular velocity. We focus on spacecraft with multiple RWs (Reaction Wheels). Using the redundancy, an unloading method for the RWs is also described. Numerical simulations assumed a spacecraft with four RWs are conducted to compare the tracking error by the proposed method and by a Lyapunov-based control.

Gain-Scheduling Attitude Control for Complex Spacecraft Based on HOSVD

In this paper, a robust gain-scheduling attitude control scheme for spacecrafts with large rotational appendages is proposed. First, by introducing the higher-order singular value decomposition (HOSVD) method, a polytopic linear parameter varying (LPV) model with a family of weighting coefficients is developed based on the kinetics of a flexible spacecraft. This model eliminates the need of verifying all the gridding points, which is required in conventional controller synthesis process, and reduces the calculation complexity. Second, a generalized plant is derived to guarantee both the system robust stability and the tracking performances. Based on the LPV control theory, a less conservative controller synthesis condition for the polytopic LPV system is deduced. With an online tuning unit, the convex combination of every vertex controller is obtained. For control implementation, the present scheduling parameter is taken as an input for the tuning unit. Numerical results demonstrate the effectiveness and efficiency of the proposed control scheme.

Robust Attitude Control Using a Double-Gimbal Variable-Speed Control Moment Gyroscope

This paper derives a linear parameter-varying (LPV) model for three-axis attitude control of a spacecraft with a single double-gimbal variable-speed control moment gyroscope (DGVSCMG) and magnetic torquers (MTQs) and develops a singularity avoidance steering law. The LPV control theory provides an optimal gain-scheduled (GS) controller while considering both control performance and robustness. However, in the spacecraft attitude control problem, it is impossible to design a GS controller due to excesses of the number of parameters in most mission scenarios. To avoid this difficulty, this paper designs two types of easy-to-use LPV models for adapting an LPV control theory. The first model is developed by linearization of the kinematics around the equilibrium point of the target attitude. The second one is developed by introducing a virtual state variable together with a parameter-dependent coordinate transformation. Next, a GS controller is designed by using linear matrix inequalities with regional pole placement constraints. Besides, the singularity avoidance steering law of a DGVSCMG by using MTQs is proposed. The applicability is demonstrated through numerical simulations of the proposed methods.

Convex Optimization for Power Tracking of Double-Gimbal Variable-Speed Control Moment Gyroscopes

This Paper addresses an integrated power/attitude control system for a spacecraft with two double-gimbal variable-speed control moment gyroscopes. Double-gimbal variable-speed control moment gyroscopes are of interest because a single device is a three-degree-of-freedom attitude actuator. A double-gimbal variable-speed control moment gyroscope has two gimbal axes and one variable-speed wheel. A primary advantage of adopting this actuator is to reduce the number of actuators, which leads to reducing the total mass and volume allocation within the spacecraft. In this Paper, first, the dynamical equations of motion of a spacecraft equipped with multiple double-gimbal variable-speed control moment gyroscopes are developed. Then, two types of steering laws are proposed for two double-gimbal variable-speed control moment gyroscopes. These steering laws attain three-axis attitude control and power tracking by using the wheels as energy storage devices while considering both singularity avoidance and wheel spin equalization. The controller design applies multiobjective gain scheduling with linear parameter-varying control theory, which can evaluate both optimality and robustness. Finally, numerical simulation examples of the orbiting spacecraft attitude tracking problem demonstrate the effectiveness of the proposed gain-scheduling controller and two steering laws for the integrated power/attitude control system.

LPV Control and Singularity Avoidance of a Spacecraft with DGCMGs

In this paper, we analyze the dynamics of a spacecraft with Multiple Double-Gimbal Control Moment Gyros (DGCMGs). After local linearization of this nonlinear dynamics, we develop an easy-to-use Linear Parameter-Varying (LPV) model, in which we deal with 3-axis attitude control of a spacecraft equipped with two parallel DGCMGs. Then, we propose a singularity robustness (SR) steering law together with a sigmoid function as a singularity robust parameter. Although it is hard to consider overall stability and control performance of attitude control at the same time with conventional Lyapunov function-based controllers, this paper attains both of approximate stability and control performance via LPV control theory, while using redefining the control input of the generalized plant. Through a numerical example, usefulness of the proposed method is demonstrated.

A Gain-Scheduling Control Approach for Takagi–Sugeno Fuzzy Systems Based on Linear Parameter-Varying Control Theory

Due to the universal approximation capability of Takagi–Sugeno (T–S) fuzzy models for nonlinear dynamics, many control issues have been investigated based on fuzzy control theory. In this paper, a transformation procedure is proposed to convert fuzzy models into linear fractional transformation (LFT) models. Then, T–S fuzzy systems can be regarded as a special case of linear parameter-varying (LPV) systems which proved useful for nonlinear control problems. The newly established connection between T–S fuzzy models and LPV models provides a new perspective of the control problems for T–S fuzzy systems and facilitates the fuzzy control designs. Specifically, an output feedback gain-scheduling control design approach for T–S fuzzy systems is presented to ensure globally asymptotical stability and optimize H∞ performance of the closed-loop systems. The control synthesis problem is cast as a convex optimization problem in terms of linear matrix inequalities (LMIs). Two examples have been used to illustrate the efficiency of the proposed method.

Pointing control of spacecraft using two SGCMGs via LPV control theory

In this paper, we consider a pointing control of a spacecraft using two single-gimbal control moment gyros (SGCMGs). Our pointing control problem is to make the line-of-sight of a camera or an antenna that is fixed on a body axis aim along a desired direction. To solve this problem, we first state the control objective for the pointing control through the angular momentum conservation principle. Then, we develop a gain-scheduled (GS) controller via linear parameter-varying (LPV) control theory. Finally, the feasibility of the proposed control method is shown by a numerical simulation.

Systematic Gain‐Scheduling Control Design: A Missile Autopilot Example

ABSTRACTThe missile autopilot was designed using linear parameter‐varying (LPV) control techniques. The controller provides exponential stability guarantee and performance bound in terms of induced L2 norm for the missile plant. The systematic gain‐scheduling approach is motivated by the recent development in LPV control theory and provides a well founded and systematic procedure for high performance missile autopilot design problem.

A generalized LPV system analysis and control synthesis framework

In this paper, a new approach for linear parameter-varying (LPV) system analysis and control synthesis is proposed. This unified framework combines two seemingly diversified methods in systematic gain-scheduling, LPV control theory, and extends the applicability of full block S -procedure to a general class of LPV systems. An example is used to demonstrate the proposed general LPV design approach, and to show its relative merits compared to other systematic gain-scheduling control techniques.