Identification and Control of a Linear Time-Periodic Test Bench Using Harmonic Transfer Functions and LQR Controllers

The increased need for accurately modeling the input-output characteristics of linear time-periodic (LTP) systems necessitates novel identification and control algorithms as well as new test benches for their experimental validation. This paper introduces a simple-to-build test bench for the identification and control of LTP systems. We mechanically coupled the shafts of two DC motors and fed back the angular velocity to the second motor with a time-periodic modulation. This allowed us to imitate a time-periodic load for the first DC motor, thereby yielding an experimental LTP plant. We used Matlab/Simulink target hardware support to implement the entire software in Simulink, which greatly simplifies input design, data collection, and analysis as compared to embedded programming. We used constant-frequency sinusoidal signals for the data collection on the experimental test bench. Subsequently, we estimated the harmonic transfer functions and identified the parameters of a state-space model of the proposed LTP system. We then designed a time-periodic controller in order to regulate the output of the LTP system. We designed a reference-tracking controller along with a Linear Quadratic Integrator (LQI) to improve the system performance. We validated our results through experiments on the physical LTP system plant.