求解一类反控制方程周期解

本文运用迭代方法研究了非线性自治方程dudt=f(u,λ),u(0)=u(T),的周期解及其在反控制方程x=yy=z2中的应用。

Attitude controller for reentry vehicles using state-dependent Riccati equation method

To get better tracking performance of attitude command over the reentry phase of vehicles, the use of state-dependent Riccati equation (SDRE) method for attitude controller design of reentry vehicles was investigated. Guidance commands are generated based on optimal guidance law. SDRE control method employs factorization of the nonlinear dynamics into a state vector and state dependent matrix valued function. State-dependent coefficients are derived based on reentry motion equations in pitch and yaw channels. Unlike constant weighting matrix Q, elements of Q are set as the functions of state error so as to get satisfactory feedback and eliminate state error rapidly, then formulation of SDRE is realized. Riccati equation is solved real-timely with Schur algorithm. State feedback control law u(x) is derived with linear quadratic regulator (LQR) method. Simulation results show that SDRE controller steadily tracks attitude command, and impact point error of reentry vehicle is acceptable. Compared with PID controller, tracking performance of attitude command using SDRE controller is better with smaller control surface deflection. The attitude tracking error with SDRE controller is within 5°, and the control deflection is within 30°.

Trajectory planning and tracking control for underactuated unmanned surface vessels

The trajectory planning and tracking control for an underactuated unmanned surface vessel(USV) were addressed.The reference trajectory was generated by a virtual USV,and the error equation of trajectory tracking for underactuated USV was obtained,which transformed the tracking and stabilization problem of underactuated USV into the stabilization problem of the trajectory tracking error equation.A nonlinear state feedback controller was proposed based on backstepping technique and Lyapunov's direct method.By means of Lyapunov analysis,it is proved that the proposed controller ensures that the solutions of closed loop system have the ultimate boundedness property.Numerical simulation results are presented to validate the effectiveness and robustness of the proposed controller.

Impulsive orbit control for spacecraft around asteroid

An impulse feedback control law to change the mean orbit elements of spacecraft around asteroid is presented. First, the mean orbit elements are transferred to the osculating orbit elements at the burning time. Then, the feedback control law based on Gauss’s perturbation equations of motion is given. And the impulse control for targeting from the higher circulation orbit to the specified periapsis is developed. Finally, the numerical simulation is performed and the simulation results show that the presented impulse control law is effective.

Trajectory tracking control for underactuated unmanned surface vehicles with dynamic uncertainties

The trajectory tracking control problem for underactuated unmanned surface vehicles(USV) was addressed, and the control system took account of the uncertain influences induced by model perturbation, external disturbance, etc. By introducing the reference, trajectory was generated by a virtual USV, and the error equation of trajectory tracking for USV was obtained, which transformed the tracking problem of underactuated USV into the stabilization problem of the trajectory tracking error equation. A backstepping adaptive sliding mode controller was proposed based on backstepping technology and method of dynamic slide model control. By means of theoretical analysis, it is proved that the proposed controller ensures that the solutions of closed loop system have the ultimate boundedness property. Simulation results are presented to illustrate the effectiveness of the proposed controller.

Extraction kinetics of zinc by new extractant in ammoniacal system

The controlling step and the extraction reaction rate equation of zinc extraction from Zn（II）-NH3 solution by using a newly synthesized organic compound, 2-acetyl-3-oxo-dithiobutyric acid-myristyl ester as the zinc extractant, were clarified. The effects of agitation speed, specific interfacial area, temperature, extractant concentration and Zn ion concentration on the extraction rate are studied in constant interfacial area cell. The results show that the extraction rate depends on interfacial chemical reaction and diffusion by using this new extraetant to extract zinc, and the apparent activation energy of this extraction reaction is measured as 28.2 kJ/mol, which demonstrates that the extraction reaction is controlled by the mixed-controlled reaction rate. The apparent reaction orders a and b are measured as 1 and 0.38, and the constant k0 is 138.70. So, when extraction conditions are controlled as [HR]=20%-50%, T=0-30℃, N=120-177 r/min and S=72.6-127.5 m-1, the solvent extraction reaction rate can be depicted as v/（mol . m-2 . s-1 ） = 138.7. exp（ - 28 206/8.314T ）. [Zn 2＋ ]r ·[HR ]o0.38.

Effects of first-order chemical reactions on the dispersion coefficient associated with laminar flow through the lungs

This paper aims to look into the determination of effective area-average concentration and dispersion coefficient associated with unsteady flow through a small-diameter tube where a solute undergoes first-order chemical reaction both within the fluid and at the boundary. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer, and an irreversible component due to absorption into the wall. To understand the dispersion, the governing equations along with the reactive boundary conditions are solved numerically using the Finite Difference Method. The resultant equation shows how the dispersion coefficient is influenced by the first-order chemical reaction. The effects of various dimensionless parameters e.g. Da （the Damkohler number）, a （phase partitioning number） and F （dimensionless absorption number） on dispersion are discussed. One of the results exposes that the dispersion coefficient may approach its steady-state limit in a short time at a high value of Damkohler number （say Da 〉 10） and a small but nonzero value of absorption rate （say P 〈0.5）.