Math framework for decision making in intelligent electromechanical actuators
Significant progress has been made in the science of designing sophisticated electromechanical actuators to serve the ever growing needs of complex motion. There are many controllable parameters that can be managed in an actuator in real time to obtain significant operational benefits. However, normally only one parameter (usually current) is managed in real time. The focus has not been managing the available resources to maximize performance but on traditional control for stability. Actuators are very nonlinear and the operation of an actuator is full of uncertainties. The nonlinearity is trivialized by using simplified linear control. The uncertainties are also neglected. Actuators are often discarded before they have been fully utilized for lack of reliable knowledge with regards to the actual condition (degradation) of the actuator. Here we strive for the best operational decision or course of action. Optimization is definitely one way to tackle this problem. But that approach, for the most part, is not transparent to the end user who might like to have some assurance that the decisions suggested by these optimization algorithms are not flawed. The objective of this report is to develop a math framework for decision making in actuators to overcome the previously cited obstacles. The framework should allow for human involvement in the decision making process. It should use test data models (as opposed to simple physics based models) for maximum utilization of actuator capabilities and representation of the nonlinearities. The model should be updatable as new information about the actuator is obtained from a sensor suite. The framework should be capable of handling uncertainties in the parametric model, the in-situ sensor data and the decision process itself. It should allow the generation and full utilization of decision making criteria for performance maximization, condition based maintenance, fault tolerance, layered control and force motion control. Based on the above requirements a framework was developed in this report that requires the following math techniques; Bayesian causal network modeling of actuators, design of experiments for data collection, Bayesian regression for model fitting, Sensor data fusion techniques for accurate modeling, combining maps to obtain decision surfaces and applying norms on the decision surfaces We show that Bayesian causal network modeling is the best suited for our task. It offers the advantage of isolating only those parameters that are important during the operation of the actuator. Also it enables the inclusion of uncertainties and propagation of uncertainties to other parameters through causal links. We demonstrate how Bayesian regression techniques make it straightforward to update the model when new data becomes available and how this in turn helps condition based maintenance. Using the actuator Bayesian causal network we then generate 3 dimensional decision surfaces. We illustrate eight different ways of arriving at these decision surfaces from primary performance maps (maps that were generated through experiments). The illustrations were done using data gathered on a test bed built specifically for the purpose of developing the decision making framework. The test bed is modular and has a controller architecture that allows for different types of actuators (with any type of prime mover; switched reluctance motors, brushless DC motors, brushed DC motors and stepper motors) to be tested on it. We then proceed to develop norms mathematically. They are applied to the decision surfaces and their physical meaning is brought out through example scenarios. The framework was demonstrated on a simple actuator model and found to work satisfactorily for performance maximization and condition based maintenance. In future, the framework needs to be further developed to treat specific decision making situations relating to fault tolerance, layered control and force/motion control.