Decoupled torque-AFR control by Frobenius H∞ feedback and a λ estimator

A novel λ -normalised air-fuel ratio (AFR)estimator for port-fuel injected (PFI) spark-ignition (SI) internal combustion (IC) engines is proposed. The estimator has an algebraic NARMAX structure which is developed by identification from dynamometer based engine test data. The estimated λ signal has significantly less time delay than the measured λ signal. A slow acting PID trimming loop is implemented to remove long time-scale drift between estimated and measured λ. Two robust linear controllers are designed each to provide a 2 x 2 MIMO feedback system to regulate λ and to allow tracking of torque demand. Both a mixed-sensitivity (MS) maximum singular value H_∞ controller and a MS Frobenius norm H_∞ controller are implemented and evaluated experimentally. The Frobenius norm H_∞ controller, allows the use of an intuitive Hadamard element-by-element weighting selection. This is implemented to decouple the torque and AFR paths. Both controllers are otherwise found experimentally to have similar robustness and performance, but the Frobenius norm H_∞ controller achieves a superior decoupling.