Matematika i Matematičeskoe Modelirovanie (Jan 2019)
Simulation of Observer Based Tracking Control for the Longitudinal Dynamics Model of a Vertical Takeoff and Landing Aircraft
Abstract
The article describes a method for constructing a nonlinear finite-horizon tracking control for the output of a weakly nonlinear dynamic system obtained by the author earlier and also presents the results of numerical experiments, which have used this method to control the output of the longitudinal dynamics model of a vertical takeoff and landing aircraft. The article aim is to demonstrate a performance capability of the method for non-weakly non-linear systems, as well as to evaluate the effectiveness of the obtained control in comparison with linear analogues.The method is based on the approximate solution of a matrix Riccati-like differential equation with state dependent coefficients. In the English literature, such a constructing approach to control is called a SDRE technique. The latter has become quite widespread in practical applications due to the relative ease of implementation. The disadvantage of the SDRE technique is that there is the need to numerically solve the Riccati-like matrix equation in the course of operation for each new system state, which may come up against the limited computational resources. To overcome this drawback, a number of methods for approximate solution of this equation were developed, including that of for the finite-horizon tracking problem.A feature of the method under study is an approach to the approximate equation solution based on the formal asymptotic small- parameter expansion of this solution in case of system nonlinearity. A numerical-analytical procedure for constructing the control was obtained. In contrast to the known results, with such an approach there is no need to perform a number of computationally expensive operations in the control process. This allows potential application of this method for problems with highly limited computational resources, for example for the problem of an autonomous robotic control.The article considers several scenarios where initial conditions of the aircraft dynamics model differ from each other. It is shown that in most cases, the obtained nonlinear controls exceed the linear analogues by the quadratic quality criterion considered.
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