Rigid Body Attitude Control With Delayed Attitude Measurement

Abstract

Time delay in the evaluation of the attitude of a rigid body can significantly hinder the performance of the attitude control system. In this brief, we propose a dynamically smooth control law that guarantees asymptotic convergence of the rigid body attitude and angular velocity to their desired values in the presence of delayed attitude measurement. We assume that the moment-of-inertia matrix of the body is unknown. The control law includes a matrix gain that is computed by solving a delay-dependent and time-varying matrix differential equation. It is shown that the solvability of the matrix differential equation depends on a uniform controllability condition, which can be verified a priori and based on available information on reference vectors. Finally, the simulation example illustrates the performance of the proposed controller in the case of a satellite system and in comparison with another existing controller.By virtue of the linearity of S(·) with respect to its argument and usingNow, in light of Property 1, we rewrite this equation aswhere the constant and unknown vector s ∈ R 6 consists of the six independent elements of J s = J T s and the regressor

Robust Controller Design for Attitude Dynamics Subjected to Time-Delayed State Measurements

“…In [3], rotation matrices were used to describe attitude, and delays were also considered constant and known. An algorithm to obtain controller parameters was later devised in [2], but also restricting initial orientations. Using quaternion representation, [16] considered both attitude and angular velocity subjected to constant delays; stability conditions rely only on initial velocities and delay magnitude.…”

“…Sufficient conditions that simultaneously guarantee stability and H ∞ performance were given in [23], which also addressed time-varying delays. In fact, to the best of the authors' knowledge, [2] and [23] are the only literature to develop attitude stability analysis under time-varying delays. Nevertheless, the stability analysis for time-varying delays in [2] depends on a proper estimation of the time-delay itself which considerably reduces its applicability, while [23] focused only on the kinematic case, exploiting the structure of the underlying quaternion manifold to derive conditions in form of linear matrix inequalities (LMIs).…”

“…In contrast with [2] which is, in the authors' best knowledge, the only other work to address timevarying delays in the dynamic case, the proposed LMI feasibility conditions are easily verified using any LMI solver, provide directly the controller gains, and enable controller design to be fully performed offline. The controller proposed by [2] is more difficult to implement in practical applications since the controller gains stem from matrix differential equation solutions which must be obtained online in real time by some differential matrix equation solver. At each time this solver requires knowledge on the terminal conditions and the equation must be solved backwards in time.…”

Attitude stabilization of a rigid spacecraft with actuator delay and fault

“…In particular, time delays can arise in feedback due to the time it takes to acquire the information needed for decision-making for control decisions, and to execute these decisions (Sipahi et al, 2011). For example, the thrust profile of a gas jet control system is affected by electrical and mechanical delays in the valve circuits and the time for the propellant to flow through the valve to the thruster (Bahrami and Namvar, 2015). These delays lead undesirable behaviours in some operational conditions, such as chattering and oscillatory motions and even instability in the system.…”

Attitude control of rigid bodies with time-delayed measurements

“…Esta limitação é tratada por controladores adaptativos, que estimam parâmetros de modelo em tempo real, dispensando informação prévia sobre o modelo. Em [15,20], esta estratégia é utilizada no contexto de controle de trajetória considerando apenas medições de atitude atrasadas. Além disto, os resultados obtidos são dependentes do valor exato do atraso, considerado constante, e uma parametrização baseada em matrizes de rotação é utilzada, o que requer mais parâmetros e é mais custosa do ponto de vista computacional quando comparada com quatérnios.…”