Non-square internal model control for mode transition of hybrid electric vehicles with multiple time delays

Mode transitions of multi-mode hybrid electric vehicles need careful coordination among the engine torque, motor torque, and clutch transmitted torque. However, the three torques have different actuation delays which make it difficult to ensure mode transition performance. A non-square internal model controller (IMC) is proposed in this paper for mode transition during which the input number is greater than the output number and each input has a different actuation delay. At first, the Moore-Penrose generalized inverse matrix is introduced to solve the inverse of the non-square matrix and make the IMC applicable. Secondly, the all-pole method is adopted to approximate the three delay models. Based on these specialized techniques, the tracking controller and anti-disturbance controller of the IMC are derived. Experiment results verify the effectiveness of the proposed controller.