Control/Design Interactions in Precision Machines - Part 2: Synthesis
Pradeep K. Subrahmanyan, RAPT Industries, Inc.

Following the models developed in part 1, a controller can be designed - such a controller is governed by some fundamental constitutive laws and may or may not be capable of delivering the performance required. In case performance requirements are not met, the mechanical and control designers work in an iterative fashion to come with a design that meets specifications - repeatability is used as the figure of merit.

The constitutive laws governing a control system design are introduced. Actuator and sensor placement is discussed along with an introduction to controllability and observability from a modal standpoint. Issues behind collocation and non-collocation of actuators and sensors are discussed, along with design limitations imposed by non-minimum phase plants. These limitations are illustrated through two case studies. One case study is a disk drive actuator design - the various parameters available to the mechanical designer and the limitations on the controls designer are studied. Plant and disturbance models are set up for the disk drive actuator and the effect of design choices on final performance is illustrated through simulations. The other case study is a stage design with a mirror for interferometry - the choice of feedback (encoders on the stage motors vs. laser interferometry) is studied and performance limits illustrated through simulation.

The modern control approach is then discussed with a very brief introduction to structured singular values and its application to modern control design. While this part of the course is not intended to cover modern control theory(that has been well implemented with commercially available toolboxes such as the Matlab control systems toolbox), an overview of the underlying manipulations is presented so the user can create the right inputs to the software. It is very quickly seen that the real ingenuity is in the design of the plant and in understanding the relevant physics.

In many cases mechanical design problems such as passive vibration isolation can be introduced as control/filtering problems where the design of the controller in effect leads to the design of optimal passive mount (stiffness and damping). Practical techniques to get around some of these limitations using innovative mechanical designs (dynamic vibration absorbers, constrained layer damping) are also presented. Control performance is modeled through frequency response analysis and the repeatability of the precision machine under closed-loop control is derived.

Prerequisites: While this course can be taken independently, participants will significantly benefit from being exposed to the concepts of generalized plants and model order reduction developed in part 1. As before, a background in dynamical systems and modal analysis is preferred. Course attendees need to have a fundamental background in dynamic systems. It will help to have an introductory course in control systems that covers the basics of root-locus techniques and Bode plots.