Analyzing the Robustness of Two-Scale Command Shaping for Reducing Powertrain Vibration During Engine Restart

Abstract

This paper analyzes the robustness of a two-scale command shaping strategy for reducing vibrations in hybrid electric vehicle (HEV) powertrains during engine restart. Propagation of HEVs through the automobile market depends on their perceived quality and performance. In this work, a two-scale command shaping strategy addresses the drivability of the vehicle by focusing on the reduction of noise, vibration, and harshness (NVH) issues associated with restarting the internal combustion engine (ICE) during a mode transition. The strategy tailors the electric machine (EM) torque profile, which consists of a linear and time-varying component, to significantly mitigate the powertrain and chassis vibrations for a smoother ICE startup. The time-varying EM torque component is calculated by applying a perturbation technique for separating the scales of an analytical ICE model, which isolates the ICE nonlinear response. Command shaping is then applied to the linear problem governed by the remaining scale. Simulations confirm that the two-scale command shaping strategy is a straightforward technique for reducing powertrain and chassis vibrations during ICE restart. In real-time implementation, inaccuracies or variations in system parameters and initial conditions arising from the operating condition or from general wear during a vehicle’s life cycle will occur. Therefore, successful implementation of the two-scale command shaping strategy relies upon the robustness of the perturbation technique and command shaping to these variations. This paper validates the perturbation technique’s robustness to variations in the ICE parameters and initial conditions. Robust command shaping methods are also explored to decrease the impact of system parameter variations on the efficacy of command shaping. Improving the overall robustness of the two-scale command shaping strategy will increase the applicability to consumer HEVs by ensuring its performance under variations in system parameters.

Two-scale command shaping for feedforward control of nonlinear systems

“…As shown previously, applying the shaping process results in After application of T1(t), the undesirable oscillations from the nonlinear behavior of the crankshaft is reduced to an acceptable level without application of command shaping. However, oscillations still persist in the frame, which was also observed in previous analyses found in Chapter 3 and [7,40,90]. Including the command shaping process to form the complete TSCS input, while focusing on the frame's flexible modes, mitigates the remaining vibrations shown in Figure 5-4.…”

“…When implementing the TSCS strategy in a real-time application, uncertainty in system parameters may decrease the strategy's effectiveness. The effect of variations in the driveline and chassis parameters can be mitigated by using robust command shaping strategies, such as ZVD, EI, and perturbation-based EI input shapers, since these variations affect only the vibration frequencies observed in the driveline and chassis [7,9,[40][41][42].…”

“…In real-time implementation, TSCS will likely suffer from inaccuracies and variations in the ICE parameters, or modes of the powertrain and chassis systems. Robust command shaping can compensate for vibration mode variations [40]. However, robust command shaping cannot mitigate the effect of variations in the ICE parameters since these variations impact the indicated torque of the ICE, which acts as an excitation.…”

“…As shown in Chapter 3, the torque from the EM in the TSCS strategy for the experimental apparatus is expressed as 125 𝑇 𝑀 = 𝑇 0 𝑆ℎ𝑎𝑝𝑒𝑑 (𝑡) + 𝜀𝑇 1 (𝑡) (5.6) where 𝑇 0 𝑆ℎ𝑎𝑝𝑒𝑑 denotes the component of the input defined utilizing command shaping applied to the zeroth-order problem and T1 the time-varying component used to mitigate nonlinear behavior of the ICE [7,40,[90][91]. ε in Eq.…”

“…where 𝜃 𝐸0 is the solution of the zeroth-order equation governing the linear motion of the ICE crankshaft. Equation (5.7) is one of the two components required to completely define the EM torque in the TSCS strategy; the other component is given by command shaping the zeroth-order, or linear, dynamics of the apparatus [7,40,[90][91].…”