Control/Design Interactions in Precision Machines - Part 1: Modeling
Pradeep K. Subrahmanyan, RAPT Industries, Inc.

There are increasing requirements on precision and speed in the industry today. In order to meet the required performance criteria, it is no longer sufficient to close a control loop around a plant. Instead, the dynamics of the machine needs to be modeled well along with the disturbances the machine is subjected to. This course is targeted towards the practicing mechanical and control designers and introduces them to the basics of modeling to create generalized plants which are used in modern control design.

The first part of this 2-part course focuses on modeling systems and creating the concept of a generalized plant. Modeling of dynamic systems for modern control design is covered - this includes nominal models, uncertainty models and disturbance models all of which come together to create a generalized plant model. Concepts are developed using single degree of freedom (DOF) systems, extended to multiple DOF lumped parameter systems specifically focusing on the creation of transfer functions from modal analysis. Finite element modeling of continuous systems is introduced very briefly and the use of commercial CAD packages to generate modal models that can be used in controls design is discussed.

Considerations for modeling uncertainty in the models are presented - both structured and unstructured uncertainty are introduced for mass/spring/damper systems and tied to modal analysis. Corroboration of physical models by experiment is critical and system identification techniques are presented with case studies. Use of system identification to create both nominal models as well as uncertainty representations is discussed.

Representation of disturbance spectra is then introduced along with an introduction to fundamental relationships between the time and frequency domain thus enabling error budgets to be translated into frequency domain specifications. Shaping filters are introduced as a means to model disturbances such as ground vibrations, payload motions, etc. when subject to white noise input. The course ends with a discussion on model order reduction.

Throughout the discussion, relevant examples are worked out to generate models that can be used for further analysis and control synthesis in part 2 of the 2-course series.

Prerequisites: Course attendees need to have a fundamental background in dynamic systems. Most concepts will be developed based on second-order mass-spring damper systems. Frequency responses will be introduced and used as the fundamental tool to develop the concepts in the course, and it will help to have an introductory course in control systems that covers the basics of root-locus techniques and Bode plots. Prior experience with modeling of continuous systems and/or finite element programs is a plus.