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Maximization of the fuel economy of the lean burn spark ignition (SI) engine strongly depends on precise air-fuel ratio control. A great challenge associated with the air-fuel ratio feedback control is the large variable time delay in the exhaust system. In this paper, a systematic development of an air-fuel ratio controller based on post lean NOx trap (LNT) oxygen sensor feedback using linear parameter-varying (LPV) control is presented. Satisfactory stability and disturbance rejection performance is obtained in the face of the variable time delay. The LPV controller is simplified to an explicit parameterized gain scheduled lead-lag controller form for the ease of implementation. A Ford F-150 truck with a V8 4.6 l lean burn engine was used to demonstrate the LPV air-fuel ratio control design. Both simulation and experimental results demonstrate that the designed controller regulates the tailpipe air-fuel ratio to the preset reference for the full engine operating range.

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This paper represents active multimodal vibration control of a flexible beam structure with piezoceramic (PZT) actuators and sensors using the loop shaping method. With surface-bonded PZT patch actuators and sensors, the flexible beam has both sensing and actuating capacities. Due to its flat auto spectrum in the specified frequency range, the Schroeder wave is used as an excitation signal for the non-parametric identification of the flexible beam structure. The identified open loop model is then used for the closed loop design by using the loop shaping method based on the extended sensitivity charts. A loop shaping compensator is designed to achieve multimodal vibration suppression. Numerical results showed a reduction of 8 decibels for the first mode and 12–14 decibels for the second and third modes. Experimental results closely match the simulation results. Furthermore, the results of loop shaping method are compared with those of the methods of linear quadratic regulator and pole-placement control, which are designed based on state space models via the parametric identification of the flexible beam. Comparisons show that the loop shaping method is easier to design since a parametric identification is not required and requires less control effort while maintaining the effectiveness in vibration suppression.