Design of a fuzzy logic controller for a target tracking system

Abstract

A fuzzy logic controller has been developed to track a single non-maneuvering target. The fuzzy controller simplifies the problem by analyzing the azimuth and elevation movements independently. The performance of the controller has been optimized primarily for error and secondarily for computation time. The resulting system is a multi-input single-output, single closed loop proportional controller with the platform drive motor voltage as the feedback variable. Results are summarized from experiments with heuristic rulebase learning programs and membership function shape. Small improvements in error reduction can be made by changing the membership functions but the most significant improvements come through improved rulebase learning. I IntroductionThe primary goal for this Single Target Tracking (STT) Fuzzy Logic Controller (FLC) is to demonstrate a reduced tracking error compared to previously designed fuzzy logic controllers. This reduced tracking error is derived via a rulebase learning program. This tracking error will be evaluated and compared with both a traditional tracking system (Kalman filter) and an early fuzzy tracking system to demonstrate some reduction in error. The new FLC reduces the tracking error when compared to early fuzzy controllers but is only comparable to the traditional system in an ideal environment. The reduced tracking error of the FLC becomes evident in the presence of input signal noise.The STT FLC assumes a radar system is supplying the target position with a sampling rate of 40Hz. The target position is in x-y-z Cartesian coordinates and transformed into a-p-r spherical coordinates for the FLC. The linear trajectories, either constant velocity or constant acceleration, move through Cartesian 3 space but the tracking software uses polar 2 space coordinates. The polar third dimension of range is not used by the controller. The fuzzy controller further simplifies the problem by analyzing the azimuth and elevation movements independently. The data returned is the azimuth and elevation position offset angles. Discrete time target position angles are calculated as offsets from the tracking platform in degrees. This work represents an extension to that of Pacini and Kosko[l], through rulebase learning and expanded training and testing data sets with more comprehensive testing.The controller from Figure 1 has three input variables and one output variable. The controller software calculates two of the inputs: the error, between the platform orientation and the target position (in degrees) and the first derivative of the error with respect to time. The controller uses a unit delay element in a single closed loop from the output to feedback its final input, the voltage applied to the platform servomotors. The performance of the controller has been optimized primarily for error and secondarily for computation time.The FLC further assumes the tracking platform is able to move from 0 to 180 degrees and 0 to 90 degrees in azimuth and elevation space respectively. The FLC output voltage for eith...