**A Virtual In-Cylinder Pressure Sensor Based on EKF and Frequency-Amplitude-Modulation Fourier-Series Method**

#### **Qiming Wang 1,\*, Tao Sun 1, Zhichao Lyu 2 and Dawei Gao 1**


Received: 29 May 2019; Accepted: 10 July 2019; Published: 15 July 2019

**Abstract:** As a crucial and critical factor in monitoring the internal state of an engine, cylinder pressure is mainly used to monitor the burning efficiency, to detect engine faults, and to compute engine dynamics. Although the intrusive type cylinder pressure sensor has been greatly improved, it has been criticized by researchers for high cost, low reliability and short life due to severe working environments. Therefore, aimed at low-cost, real-time, non-invasive, and high-accuracy, this paper presents the cylinder pressure identification method also called a virtual cylinder pressure sensor, involving Frequency-Amplitude Modulated Fourier Series (FAMFS) and Extended-Kalman-Filter-optimized (EKF) engine model. This paper establishes an iterative speed model based on burning theory and Law of energy Conservation. Efficiency coefficient is used to represent operating state of engine from fuel to motion. The iterative speed model associated with the throttle opening value and the crankshaft load. The EKF is used to estimate the optimal output of this iteration model. The optimal output of the speed iteration model is utilized to separately compute the frequency and amplitude of the cylinder pressure cycle-to-cycle. A standard engine's working cycle, identified by the 24th order Fourier series, is determined. Using frequency and amplitude obtained from the iteration model to modulate the Fourier series yields a complete pressure model. A commercial engine (EA211) provided by the China FAW Group corporate R&D center is used to verify the method. Test results show that this novel method possesses high accuracy and real-time capability, with an error percentage for speed below 9.6% and the cumulative error percentage of cylinder pressure less than 1.8% when A/F Ratio coefficient is setup at 0.85. Error percentage for speed below 1.7% and the cumulative error percentage of cylinder pressure no more than 1.4% when A/F Ratio coefficient is setup at 0.95. Thus, the novel method's accuracy and feasibility are verified.

**Keywords:** in-cylinder pressure identification; speed iteration model; EKF; frequency modulation; amplitude modulation
