Multiple Nonlinearity SDP Modelling and Control
Lancaster University, Master of Philosophy, 2009
Supervisor: C.J. Taylor, W. Tych
Abstract
In order to find new ways to improve construction operations and to meet ever increasing demands on robotic excavation, better understanding and analysis of the operations involved are required.The dynamic nature of robotic excavation is investigated using a novel multiple nonlinearity modelling and control methodology, i.e. the multiple State Dependent Parameter (SDP) approach. Here, a new method of estimating the state dependent parameters based on a Generalised Random Walk (GRW) model is used. Spline methods are combined with Linear Polynomial Modelling (LPM) and the Kalman Filter (KF) to introduce another method of SDP modelling termed Stochastic Splines. The test bed used to evaluate and refine the control algorithm developed was the 1/5th scale Lancaster University Computerized Intelligent Excavator (LUCIE). A comprehensive modelling study was conducted by looking at several different model structures and SDP parameterizations.
Based on the representation of the nonlinear dynamical system in this quasi–linear SDP form, in which the parameters vary as functions of more than one state variable, a Proportional–Integral–Plus (PIP) control law was designed using linear techniques such as pole assignment. However, the SDP–PIP state feedback gains are updated at each sampling instant, in order to maintain closed–loop stability and performance requirements in the nonlinear case. A discrete time Smith Predictor (SP) is utilized so that the delay present in every engineering system is external to the control loop and hence the linear design response is maintained. The response of the SDP–PIP closed–loop system is compared with a linear closed–loop system using the same assigned poles.