In this paper, the dominant pole assignment problem, the dominant eigenstructure assignment problem and the robust dominant pole assignment problem for linear time-invariant positive systems with state feedback are considered. The dominant pole assignment problem is formulated as a linear programming problem, and the dominant eigenstructure problem is formulated as a quasiconvex optimisation problem with linear constraints. The robust dominant pole assignment problem is formulated as a non-convex optimisation problem with non-linear constraints which is solved using particle swarm optimisation (PSO) with an efficient scheme which employs the dominant eigenstructure assignment technique to accelerate the convergence of the PSO procedure. Each of the three problems can be further constrained by requiring that the controller has a pre-specified structure, or the gain matrix have both elementwise upper and lower bounds. These constraints can be incorporated into the proposed scheme without increasing the complexity of the algorithms. Both the continuous-time case and the discrete-time case are treated in the paper.
This paper studies the control theory and the methods of the silicon micromachined resonant accelerometers(SMRAs). According to the structure and movement of the resonant accelerometer, the model of its dynamics and the equations of motion are deduced. The model of the closed-loop control is set up with the phase lock loop (PLL). The principle of PLL is expounded in detail. The requirements for phases and gains of the sinusoidal self-drive-oscillation are met by PLL. The average method is to take the average of slowly changing variables within a cycle to find the solutions of nonlinear equations. Using the average method, it analyzes the PLL’s phase control methods in depth and derives the system stability condition. The simulation results verify the correctness of the stability condition. It provides a guiding theory for the realization of SMRA’s precision control.
Combined with the system state equation and the measurement equation, a new method of cascade Kalman filter is proposed and applied to the correction of gravity anomaly distortion. In the signal processing procedure, according to the self-correlation sequences of the measurement gravity signal, the relation of the gain matrix K and the self-correlation sequences could be obtain, and the gravity signal at current time can be calculated by the gain matrix K. Emulations and experiments indicate that both the cascade Kalman filter method and the single inverse Kalman filter method are effective in alleviating the distortion of the gravity anomaly signal, but the performance of the cascade Kalman filter method is better than that of single inverse Kalman filter method.
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