Causal inversion of non-minimum-phase systems for hardware-in-the-loop transmission testing

Hardware-in-the-loop transmission testing requires precise speed and torque tracking of the actuators that emulate the engine and vehicle dynamics. System-inversion-based feedforward controllers offer a solution, but they do not work for non-minimum-phase systems. Preview filters can provide stable approximate inversion of non-minimum-phase systems, but they require future values, which are not available in hardware-in-the-loop tests. This article develops a simple but effective controller to enable preview filters to provide causal inversion within the frequency range of interest. Causality is achieved by adding manual delays to the measured response signal either in a closed-loop or open-loop configuration, followed by system identification in the frequency domain. The proposed controller was initially validated experimentally for precise speed and torque tracking of uncoupled actuators. Then additional compensators were designed to deal with two dynamometers, which are coupled through a transmission system. The effectiveness of the proposed coupled controllers is demonstrated experimentally by using the dual actuator hardware-in-the-loop transmission test facility and commercially supplied models for the engine, driver and vehicle.