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Deployment, Station-Keeping, and Retrieval of a Flexible Tether Connecting a Satellite to the Shuttle
Published in Arun K. Banerjee, Flexible Multibody Dynamics, 2022
For these parameters, the open-loop plant equations described by Eqs. (2.78) and (2.79) are found to be unstable with open loop poles at (±7.707, ±j2.398, ±j1.242). The system is, however, controllable, as may be checked by the controllability condition [13] for Eqs. (12) and (13). A full-state feedback controller was generated by using the linear quadratic regulator (LQR) theory [13]. The cost function J was taken as J=∫0∞e2ατ(xTQx+uTRu)dτ
Control Methods
Published in Michael Muhlmeyer, Shaurya Agarwal, Information Spread in a Social Media Age, 2021
Michael Muhlmeyer, Shaurya Agarwal
State variables and state-space forms can be utilized to design a required control method for linear systems in the time domain. The control action u(t) is a function of all or some state variables. When all the states are utilized to build a controller, it is referred to as full-state feedback controller. Generally, as the measurements of all the state variables are not available, we need to build an observer to estimate the states that are not directly measured.
State-Space Design Methods
Published in Arthur G.O. Mutambara, Design and Analysis of Control Systems, 2017
This section addresses the first stage of the full state feedback control design with the assumption that the entire state vector is available for feedback. Estimator design will be discussed in later sections. With the control input u(t) given by Equation 7.93, the state equation of the system in the closed-loop becomes
Station keeping of a subsea shuttle tanker system under extreme current during offloading
Published in Ships and Offshore Structures, 2023
Yucong Ma, Terje Andreas Jevnaker, Yihan Xing
The control system used for the SST hovering, an LQR, was initially designed by Ma et al. (2022a) and then extended by Xing et al. (2022). The control diagram is presented in Figure 8. An LQR is a full-state feedback optimal control method which aims to solve the optimisation problem at hand, i.e. performance versus effort, and thereby find the state feedback controller gain . Defining the performance and effort parameters will be influenced by the desired properties of the subsea shuttle tanker. E.g. one specific gain matrix can be determined by imposing importance on the stability of the subsea shuttle tanker under the offloading process (i.e. a minimal movement is required). This would increase actuator efforts and consequently reduce the energy storage and subsea shuttle tanker range at a higher rate.
H-infinity optimised control of external inertial actuators for higher precision robotic machining
Published in International Journal of Computer Integrated Manufacturing, 2022
Runan Zhang, Zheng Wang, Patrick Keogh
There are options for controller implementation based on optimisation principles. LQR controllers utilise full state feedback in the form of a gain matrix to minimise a quadratic cost function. If full state feedback is not available, a Kalman filter enables feedback and the control is optimal for white Gaussian noise disturbances, hence having flat spectral content. In contrast, synthesis enables controllers to be designed to minimise the maximum of spectral norms of weighted system transfer function matrices. Using appropriate weighting transfer function matrices, it is possible to target specific frequency bands to be minimised in amplitude, and to guarantee closed loop stability for specified uncertainties. Given the dynamic flexibility of serial robots, which may result in the excitation of robot modes by machining forces at specific synchronous and non-synchronous frequencies (not white Gaussian noise), it was considered beneficial to investigate the implementation of controllers for robotic machining.
Semi-active control of primary suspensions to improve ride quality in a high-speed railway vehicle
Published in Vehicle System Dynamics, 2022
Bin Fu, Binbin Liu, Egidio Di Gialleonardo, Stefano Bruni
The Linear Quadratic Gaussian (LQG) is a classic model-based controller, consisting of a Linear Quadratic Regulator (LQR) to calculate the feedback control force, and a Kalman filter (KF) for state estimation. It provides optimal control for the system through full-state feedback. The gain matrix defining state feedback is obtained through the minimisation of a cost function , in which the control targets are defined in the linear-quadratic form. A detailed explanation for the working principle of LQG can be found in [26].