Model Embedded Control: A Method to Rapidly Synthesize Control- lers in a Modeling Environment
Edward Tate, Michael J. Sasena, Jesse Gohl, Michael M. Tiller · 2008
One of the challenges in modeling complex systems is the creation of quality controllers. In some projects, the effort to develop even a reasonable prototype controller dwarfs the effort required to develop a physical model. For a limited class of problems, it is possible and tractable to directly synthesize a controller from a mathematical statement of control objectives and a model of the plant. To do this, a system model is decomposed into a controls model and a plant model. The controls model is further decomposed into an optimization problem and a ‘zero-time’ plant model. The zero-time plant model in the controller is a copy or a reasonable representation of the real plant model. It is used to evaluate the future impact of possible control actions. This type of controller is referred to as a Model Embedded Controller (MEC) and can be used to realize controllers designed using Dynamic Programming (DP). To illustrate this approach, an approximation to the problem of starting an engine is considered. In this problem, an electric machine with a flywheel is connected to crank and slider with a spring attached to the slider. The machine torque is constrained to a value which is insufficient to statically overcome the force of the spring. This constraint prevents the motor from achieving the desired speed from some initial conditions if it only supplies maximal torque in the desired direction of rotation. By using DP, a control strategy that achieves the desired speed from any initial condition is generated. This controller is realized in the model using MEC. The controller for this example is created by forming an optimization problem and calling an embedded copy of the plant model. Furthermore, this controller is calibrated by conducting a large scale Design of Experiments (DOE). The experiments are processed to generate the calibrations for the controller such that it achieves its design objectives when used for closed loop control of the plant model. It is well understood that Modelica includes many language features that allow plant models to be developed quickly. As discussed previously, the development of quality control strategies generally remains a bottleneck. In this paper we show how existing features along with appropriate tool support and potential language changes can make a significant impact on the model development process by supporting an automated control synthesis process.