State estimationCarleman linearizationKronecker productIt?Stochastic differential ruleFokker-Planck equationtwo-tank systemThe two-tank problem is often considered as a challenging benchmark problem of process control, owing to its non-linear nature and non-minimum phase behavior. Non-linearity arises due...
Look at the barometer problem where the "hole diameter is infinite". Solving for h, you will see the water should be at 10m. If you do see only a 5m height, something is wrong; the valve is closed, or maybe it is because there is air trapped inside. Now calculate the amount of ...
The singular perturbation solution to a general optimal control problem consisting of the optimization of a final-time function of the "slow" variables, subject to inequality control constraints in the inner control region, and a free-time terminal manifold for the fast-slow differential equations, ...
In this section, the efficacy of the aforementioned controller design approach for PCCS has been verified through simulation on CSTR differential equations (Eqs. (1,2,5)). The proposed method is compared with different structures like series cascade control structure and parallel control structure (...
Necessary conditions for optimality and a method of steepest ascent based on second variations arc derived for the deterministic optimal control problem in systems described by non-linear differential-difference equations. The algorithm is used to determine tho optimal time-varying proportional gain for ...
These criteria are based on approximations to the governing differential equations (boundary value problem). The approximate criteria are shown to be in good agreement with the exact criteria obtained by solving the boundary value problem. It is not necessary to solve the boundary value problem to ...
The results indicate that the multidimensional modal method is a very good tool for solving liquid nonlinear sloshing dynamics and will be developed to investigate more complex sloshing problem in our following work. 展开 关键词: circular cylindrical tank, nonlinear free sloshing, multidimensional modal...
(2007). In this way, the whole dynamic problem becomes a computationally efficient set of first-order differential equations. The identification of a state space model is performed using the toolbox provided by Perez and Fossen (2009), which automatically selects a proper order, hereafter called...
In addition, due to the length of the cylindrical tank, if this tank wants to be mounted into the commercial aircraft, the sloshing problem needs to be solved to keep the weight balance. Therefore, the weight of the cylindrical tank is greater than tank in sphere shape for same capacity. ...
The fluid–structure coupling model is applied to the simulations of the elastic plate subjected to hydrodynamic pressure in the benchmark problem of dam break (see Fig. 11.17) and the violent sloshing flow with a hanging baffle. Khayyer et al. [27] improved FSI model by incorporating the ...