Tracking or rejecting rotational-angle dependent signals using time varying repetitive control

Rotational-angle is a natural clock for the internal combustion engine. Many of the engine control problems involve controlling actuators or mechanisms to track or reject signals that are periodic in the rotational-angle domain. However a periodic signal in the rotational-angle domain becomes cyclic but aperiodic in the time domain as the rotational speed changes. This phenomenon poses a great challenge for achieving asymptotic tracking or disturbance rejection. To take advantage of the fact that the signal is periodic in the rotational-angle domain, we can transform the actuator dynamics into the rotational-angle domain and design the controller correspondingly. However the linear time invariant (LTI) actuator model becomes linear time varying (LTV) after the transformation. Time varying repetitive control is then proposed to drive the time varying plant to track or reject periodic signals. The periodic signal internal model is embedded in the time varying feedback loop to ensure asymptotic performance. Simulation results demonstrate the effectiveness of the proposed algorithms.