Abstract
This paper proposes a nonlinear control design methodology using nonlinear model order reduction (MOR) techniques on a practical complex system. As the typical controlled object, we take ultrasonic motor that has strong nonlinearity and needs precise control. In control design phase, Nonlinear Model Predictive Control (NMPC) is applied. In this paper, MOR of Finite Element method is described first. Generally, it is very difficult to apply MOR to a nonlinear finite element model. However, it may be possible by focusing to the character of the model. The key point of this MOR technique is separation with linear space and nonlinear space for system from the composition view point of ultrasonic motor. When the techniques apply to a certain system appropriately, the degree of freedom of the finite element model will be reduced substantially. This model will be called the reduction model, and it has tried to apply this technique to the transient response simulation of ultrasonic motor. A strong nonlinearity appears because ultrasonic motor is driven by the contact friction. We identify the nominal model for the control design from the reduction model. In order to get this nominal model, the conditions of an input and load are changed to a reduction model, and two or more simulations are performed. As a result, the gain constant and the time constant can be found. This gain constant and time constant turn into a nonlinear function whose variables are the input and load. The proposed method tries to carry out speed follow-up control with the application of model prediction control to the model. Finally, the control rule of a nominal model is applied also to reduction model, and the speed servo performance is checked.
