Design of Piecewise Linear LQ Control by Multivariable Circle Criterion for Dynamic Positioning System

A model of servomechanism used for high-powered actuators in mechanical systems consists of a position feedback loop around the cascade connection of a saturation function with an integrator. The saturation function constrains the position change rate and so for a position demand rate faster than the maximum rate of the actuator servosystem, the time lag of the actuator response behind the demand results in the actual plant input different from the controller output and may exhibit undesirable behavior such as excessive overshoot and further the control system may become unstable. This paper clarifies a design of piecewise linear LQ control (PLC) whose control gain switching variable is an input of the saturation function in the actuator servomechanism and which makes the controlled system stable even under drastic disturbances. In design procedures the permissible maximum absolute value of the input to the saturation function as a reciprocal number of the permissible minimum sector bound is decided by the multivariable circle criterion enabling to ensure the local absolute stability of the total system according to each level of LQ controller gain groups determined beforehand. In control procedures the gain switching function selects a control gain group by monitoring the inputs of the saturation functions, for example the gain switching function selects the smaller gain group when the input absolute value to the saturation function exceeds the permissible maximum absolute value decided for the used control gain group. Evaluation of the design method is made by computer simulation for dynamic positioning (DP) system by PLC using the controller gain switching function, which holds the position and heading of a ship under wind disturbances by controlled thrusters and the results as expected are obtained