The optimal guidance law of an autonomous four-rotor helicopter, called the Quadrotor, using linear quadratic regulators (LQR) is presented in this paper. The dynamic equations of the Quadrotor are considered nonlinear so to find an LQR controller, it is necessary that these equations be linearized in different operation points. Due to importance of energy consumption in Quadrotors, minimum energy is selected as the optimal criteria.
In this paper consensus in second-order multi-agent systems with a non-periodic sampled-data exchange among agents is investigated. The sampling is random with bounded intersampling intervals. It is assumed that each agent has exact knowledge of its own state at all times. The considered local interaction rule is PD-type. The characterization of the convergence properties exploits a Lyapunov-Krasovskii functional method, sufficient conditions for stability of the consensus protocol to a time-invariant value are derived. Numerical simulations are presented to corroborate the theoretical results.
The current paper presents the determination of a closed-loop guidance law for an orbital injection problem using two different approaches and, considering the existing time-optimal open-loop trajectory as the nominal solution, compares the advantages of the two proposed strategies. In the first method, named neighbouring optimal control (NOC), the perturbation feedback method is utilized to determine the closed-loop trajectory in an analytical form for the non-linear system. This law, which produces feedback gains, is in general a function of small perturbations appearing in the states and constraints separately. The second method uses an L1 adaptive strategy in determination of the non-linear closed-loop guidance law. The main advantages of this method include characteristics such as improvement of asymptotic tracking, guaranteed time-delay margin, and smooth control input. The accuracy of the two methods is compared by introducing a high-frequency sinusoidal noise. The simulation results indicate that the L1 adaptive strategy has a better performance than the NOC method to track the nominal trajectory when the noise amplitude is increased. On the other hand, the main advantage of the NOC method is its ability to solve a non-linear, two-point, boundary-value problem in the minimum time.
Micro electro-mechanical systems (MEMS) are increasingly being used in measurement and control problems due to their small size, low cost, and low power consumption. The vibrating gyroscope is a MEMS device that will have a significant impact on stability control systems in the transportation industry. This paper investigates the application of a modified model reference adaptive control for MEMS gyroscope. Using this adaptive control algorithm, an estimation of the angular velocity and the damping and stiffness coefficients in real time is easily computable. Changing the conventional model reference input makes it feasible to utilize a low pass filter to remove unwanted oscillations caused by high adaptation gain. This new adaptive control technique enables quick compensation for large changes in the system dynamics, providing consistent estimation of gyroscope parameters including angular velocity and large robustness to parameter variations and external disturbances. The asymptotic stability of the mentioned adaptive controller is guaranteed using the Lyapunov direct method. Numerical simulation is presented to verify the effectiveness of the proposed control scheme.
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