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Spacecraft Control Using Magnetic Torques
Published in Yaguang Yang, Spacecraft Modeling, Attitude Determination, and Control Quaternion-based Approach, 2019
This section discusses the attitude control system design using only magnetic torque. We consider linear quadratic regulator (LQR) design method for this problem. Riccati equation plays an important role in the LQR problem [108]. For continuous-time linear systems, the optimal solution of the LQR problem is associated with the differential Riccati equation. For discrete-time linear systems, the optimal solution of the LQR is associated with the algebraic Riccati equation. The numerical algorithms for these Riccati equations have been thoroughly studied since the work of Macfarlane [118], Kleinman [95], and Vaughan [208]. If the linear system is periodic, the optimal solution of the LQR is then associated with the periodic Riccati equation [19]. For continuous-time periodic linear system, algorithms and solutions of the differential periodic Riccati equation have been studied, for example, in [20, 21, 206]. For discrete-time periodic linear system, an efficient algorithm was proposed for the algebraic periodic Riccati equation in [70].
Discrete-Time Optimal Control Systems
Published in Desineni Subbaram Naidu, Optimal Control Systems, 2018
This section is based on [89]. In this section, we use frequency domain to derive some results from the classical control point of view for a linear, time-invariant, discrete-time, optimal control system with infinite-time case, described earlier in Section 5.4. For this, we know that the optimal control involves the solution of matrix algebraic Riccati equation. For ready reference, we reproduce here results of the time-invariant case described earlier in this chapter. For the plant () x(k+1)=Ax(k)+Bu(k),
Continuous‐Time One‐Dimensional Kalman Tracking Filters with Position and Velocity Measurements
Published in K. V. Ramachandra, Kalman Filtering Techniques for Radar Tracking, 2018
In Ref. 6, Ramachandra‐Mohan‐Geetha’s RWA model for a continuous‐time Kalman tracking filter is discussed. Steady state covariances and gains are obtained analytically in this model. As in Ekstrand’s model the first two states of the filter are assumed to be measured continuously and both these measurements are incorporated in the filtering process. The solution is obtained by directly solving the algebraic Riccati equation. The results for the corresponding filter in which measurements of one state alone are available are obtained as a special case of this model. These results are in excellent agreement with those of Fitzgerald [4], discussed in Section 5.3. The solutions are visualized in two graphs.
Nonlinear optimal control of a multi-rotor wind power unit with PMSGs and AC/DC converters)
Published in Journal of Control and Decision, 2023
Gerasimos Rigatos, Pierluigi Siano, Bilal Sari, Masoud Abbaszadeh, Mohamed Assaad Hamida
The performance of the wind power generation system which comprises twin turbines connected to a pair of PMSGs with the generators to be connected next to a pair of AC/DC converters has been further confirmed through simulation experiments. To implement the nonlinear optimal control scheme, the algebraic Riccati equation which appears in Equation (126) had to be solved at each time-step of the control algorithm. The obtained results are depicted in Figure 3–Figure 34. It can be noticed that in all cases fast and accurate tracking of reference setpoints was achieved under moderate variations of the control inputs. The real values of the state vector of the twin-turbine wind power unit are printed in blue, the estimated state variables provided by the H-infinity Kalman Filter are plotted in green, while the associated setpoints are shown in red colour. The variations of the Lyapunov function of the control scheme for the twin-turbine wind power generation unit are depicted in Figure 35–Figure 38.
Robust control strategy for platoon of connected and autonomous vehicles considering falsified information injected through communication links
Published in Journal of Intelligent Transportation Systems, 2022
Anye Zhou, Jian Wang, Srinivas Peeta
We include three baseline controllers for comparison. The first two baselines are the CACC model and the ACC model proposed by Milanés and Shladover (2016). They are deterministic controllers which are formulated without considering the impacts of falsified information. The third one is a graph linear quadratic regulator (gLQR) developed based on the steady-state infinite-time horizon LQR (Lewis et al., 2012), which preserves some robustness in dealing with input disturbances. The control decision of gLQR is determined through minimizing the following objective function: where The objective function of gLQR in Equation (46) seeks to minimize the tracking error and avoid excessively large control decision. Similar to the nominal control decision, also follows the structure of state feedback control strategy: where is the control gain, and is computed through solving the steady-state algebraic Riccati equation:
Experimental Validation of LQR Weight Optimization Using Bat Algorithm Applied to Vibration Control of Vehicle Suspension System
Published in IETE Journal of Research, 2022
T. Yuvapriya, P. Lakshmi, Vinodh Kumar Elumalai
The conflicting control requirements of ASS such as ride comfort and road handling motivate control designer to use the optimal state feedback design using linear quadratic theory for its capability to handle the trade-off between the speed of response and control effort [8]. Some of the advantages of LQR design include guaranteed stability, inherent robustness and methodical approach to extend to multiple-input-multiple-output (MIMO) system. Moreover, solving a quadratic cost function, which constitutes the states and control effort along with their respective input and state penalty matrices, LQR offers an optimal performance by solving the celebrated algebraic Riccati equation (ARE). However, one of the major challenges in the LQR design is the choice of state and input penalty matrices. Since the selection of weighting matrices is time-dependent and there is no standard procedure available for selecting these tuning matrices, often the task is transformed to trial and error approach, which is time consuming as well as tedious [9]. Hence, to address the problem of weight selection of LQR, over the last few years, several researchers have explored the use of nature-inspired optimization algorithms and tested the efficacy on several real world applications ranging from fuel cell [10], synchronous motor [11], inverters [12] to unified power-quality conditioner [13].