Thomasson, A., Llamas, X., and Eriksson, L., "Turbo Speed Estimation Using Fixed-Point Iteration," SAE Technical Paper 2017-01-0591, 2017, doi:10.4271/2017-01-0591.
1In modern turbocharged engines the power output is strongly connected to the turbocharger speed, through the flow characteristics of the turbocharger. Turbo speed is therefore an important state for the engine operation, but it is usually not measured or controlled directly. Still the control system must ensure that the turbo speed does not exceed its maximum allowed value to prevent damaging the turbocharger. Having access to a turbo speed signal, preferably by a cheap and reliable estimation instead of a sensor, could be beneficial for over speed protection and supervision of the turbocharger.This paper proposes a turbo speed observer that only utilizes the conditions around the compressor and a model for the compressor map. These conditions are either measured or can be more easily estimated from available sensors compared the conditions on the turbine side. The observer utilizes an ellipse model for the compressor that outputs pressure ratio as a function of turbo speed and compressor mass flow, alternatively mass flow as a function of pressure ratio and turbo speed. The model is however hard to solve analytically for the turbo speed, which is the state to be estimated. To solve this problem a fixed-point iteration is proposed, where the turbo speed estimation from the previous sample step together with measured mass flow is used to estimate the pressure ratio. The estimation is then compared to the measured pressure ratio and the difference is used to update the turbo speed estimation for the next iteration.The observer is first validated in simulation showing that it converges exactly when the model is perfect. Robustness to model errors and noise is then shown using engine experiments where the observer converges to track the measured turbo speed.