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An LQR Approach of Automatic Transmission Upshift Control Including Use of Off-going Clutch within Inertia Phase
ISSN: 0148-7191, e-ISSN: 2688-3627
To be published on April 14, 2020 by SAE International in United States
The paper first demonstrates, based on control trajectory optimization results, that using the off-going clutch during the inertia phase along with the main, oncoming clutch can improve the performance an automatic transmission (AT) upshift control in terms of faster and/or more comfortable shift, while sacrificing transmission efficiency and control simplicity to some extent. The use of linear quadratic regulation (LQR) in upshift control is beneficial from the standpoint of optimality of multi-input control action, and the possibility to set a trade-off between the aforementioned conflicting criteria. The proposed LQR cost function includes two conflicting criteria related to driving comfort and clutch thermal energy loss, while the third criterion related to shift duration is determined by imposing a linear profile of oncoming clutch slip-speed reference, shown to be nearly-optimal based on control trajectory optimization. A special emphasis is on proper implementation of nonlinear energy loss term through linear LQR cost function cross term and using a clipped optimal control approach to provide that the clutches (described as torque source elements) can only dissipate energy. The LQR approach is applied for a fifth-order powertrain model and different control scenarios ranging from the use of single clutch towards using both clutches and engine torque reduction. Pareto frontiers obtained by applying the LQR approach for different sets of cost function weighting coefficients are discussed and compared with multi-objective genetic algorithm-based control parameter optimization results. The analysis points out that the LQR approach can reproduce Pareto frontiers obtained by multi-objective optimization. Thus, apart from being used in realistic closed-loop control, the LQR approach can be exploited for computationally efficient (off-line) optimization purposes.