Discrete-Time Model Reference Tracking Control for A Class of Combined Spacecraft: A High-Order Fully Actuated System Approach

This paper studies discrete-time high-order fully actuated (HOFA) model reference tracking (MRT) control for a class of combined spacecraft simulators (CSSs) with disturbances. Firstly, a discrete-time second-order fully actuated system modeling of the CSS system is carried out and generalized to a general discrete-time HOFA system (HOFAS) with disturbances, and the MRT control problem is formulated. Then, by designing a discrete-time HOFA MRT controller consisting of feedback and feedforward components, a linear closed-loop system with an arbitrarily assignable eigenstructure can be obtained. The convergence of the tracking error is proved by introducing the Sylvester equation condition and final value theorem of discrete-time sequence. Further, using the arbitrariness of the eigenstructure configuration, the control performance can be improved via a multi-objective optimization design. Finally, the MRT control of CSS system with disturbances is successfully realized using the proposed technique and comparative simulations are carried out, thus verifying the effectiveness and advantages of the technique.
Note to Practitioners
—This paper is inspired by MRT tasks for practical CSS systems and also contributes to the advancement of HOFAS theory in the discrete-time domain. Traditional researches on MRT control of discrete-time systems are basically carried out under the framework of the first-order state-space approach which are suitable for solving state vectors rather than control vectors, and thus it is difficult to handle the control problems of complex nonlinear systems. Moreover, converting the original higher-order system to a first-order one and then completing the associated control design would significantly increase the computational effort and complexity. Instead, this paper directly investigates the MRT control of discrete-time HOFASs and designs the HOFA MRT controller, which can easily handle nonlinearities and enable the system output to track the output of the reference model, and produce a closed-loop system with an arbitrarily assignable eigenstructure. Possible application areas include many discrete-time fully actuated systems in a practical or mathematical sense, including spacecraft control, robot or intelligent vehicle control, and UAV control, etc. As long as their discrete-time HOFA models can be established by physical modeling or model transformation, the techniques proposed in this paper are applicable.