|Budget Amount *help
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1986: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1985: ¥1,200,000 (Direct Cost: ¥1,200,000)
In this project, we studied the nonlinear system theory based on the variational approach and named as a "Variational System Theory", and its applications to the real control processes. Applying the method introduced by L.I.Rozonoer to the nonlinear system with controls appearing linearly and the C -structure, we derived several equivalent necessary and sufficient conditions of complete invariance and output controllability. Combining these conditions with those of stability and functional independence, we have obtained the design procedures of canonical form, nonlinear observers, decoupling, disturbance decoupling, inverse systems, and model following control systems. Especially, our model following control system has enough flexibility for the further theoretical investigations and the practical applications.
In the different but related projects of our group, we studied the design of multistep discretizing controller for continuous time control law, approximate digital expressions of
continuous time nonlinear systems, and carried out a preliminary investigation on the computer aided design of nonlinear control systems. Incorporating the results obtained in these projects with our design procedures of nonlinear systems, we studied the control problem of a robot Rhino XR-1 along the continuous path and obtained the expected results both in the numerical simulations and in the practical experiments, where the static and dynamic characteristics of the robot are identified experimentally for the three degrees of freedom. This result seems to show the applicability of our theory.
If the state space of a nonlinear system is a differentiable manifold, our invariance theory can be applied only to the local expressions of its dynamical behaviour. Therefore, it is necessary to study how to combine the control laws designed for each local expressions. With the aim of solving this difficulty, we studied the attitude control problem of an artificial satellite. Applying our design procedures and the expression via quarternion numbers, we obtained successful results in stabilizing problems, which gave us a hint to study the problem in general. Less