A simple fuzzy control design for powertrain systems with three inertias

Abstract

This paper proposes a simple fuzzy control design for powertrain systems with three inertias. Considering four operating modes of the clutch, the piecewise affine state-space models offers an accurate characterization of the powertrain systems as controlled processes. A class of Takagi-Sugeno fuzzy controllers (T-S FCs) is offered with this regard. The inputs of the T-S FCs are the two variables that define the four operating regimes and they also define a partition of the fifth order state-space model, the control error and the increment of control error. The control error and the increment of control error are usually involved in structures of Mamdani and Takagi-Sugeno PI-fuzzy controllers. The control error is defined considering the wheel speed as the controlled output. Neglecting the affine terms in the piecewise affine state-space models of the process, the frequency domain design is applied to the process models in terms of neglecting the affine terms to obtain four continuous-time PI controllers. The continuous-time PI controllers are next discretized and included in the six rule consequents of T-S FCs. This modal equivalence principle-based design approach offers T-S FCs that exhibit the bumpless interpolation between separately designed linear PI controllers for each operating mode of the clutch. Digital simulation results are presented to illustrate the performance of the fuzzy control system and to compare it with the linear PI-based control system that are successfully used as wheel speed control systems.

Keywords

• piecewise affine state-space models
• PI controllers
• powertrain systems with three inertias
• Takagi-Sugeno fuzzy controllers