RealtimeMPC

Background

Constantly increasing emission requirements in the automotive industry creates the need for new solutions in engine development. New technology solutions often add new actuators which provide more degrees of freedom that can be used to minimize emissions and fuel consumption. But the new technology must also work together with existing technology. Multi variable, model-based control is therefore interesting in order to handle the different upcoming challenges.

This CDIO project was performed during the fall of 2020 in a collaboration between students at Linköping University and Volvo Cars Corporation. The goal was to implement a model predictive (MPC) controller for an internal combustion engine to achieve two different drive modes, one with higher fuel efficiency and one with increased performance. The controller together with a simulation environment was successfully created in MATLAB and Simulink.

Implementation

Simulation Environment

A simulation environment was used to test the MPC controller on the plant model containing models of throttle, intake manifold and variable valve time (VVT). The structure of the simulation environment is illustrated in the following figure.

flow_chart Structure of simulation environment.

Actuators and models

The actuators that have been the focus in this project are the throttle together with intake manifold and the variable valve timing (VVT). These two actuators have been modeled to make it possible to control them.

Throttle and Intake manifold

The throttle model controls the air mass flow into the engine using the throttle angle $\alpha_{th}$ , and is described by the following equation: $\Dot{m}_{at} = \frac{p_{bef,th}}{\sqrt{RT_{bef,th}}}A_{eff}(\alpha_{th})\Psi(\Pi)$

Changes in the pressure and temperature in the intake manifold are modeled with the following equations:

$\frac{dp_{im}}{dt} = \frac{R T_{im}}{V_{im}} (\Dot{m}_{at} - \Dot{m}_{ac})$ $\frac{dT_{im}}{dt} = \frac{R T_{im}}{p_{im} V_{im} c_{\textrm{v}}} [\Dot{m}_{at}c_{\textrm{v}}(T_{bef,th} -T_{im}) + R (T_{bef_th} \Dot{m}_{at} - T_{im} \Dot{m}_{ac}) - \dot{Q} ]$

Varaible Valve Time (VVT)

The model that was used for the VVT is a black-box, which means that the model is not based on physical formulas. Based on measurement data from a Volvo engine, functions were made that convert the input signals, the intake manifold pressure and the crankshaft angle, to the desired output which is the air mass flow into the cylinders.

The blackbox model for VVT.

Model Predictive Controller

The investigated real time model predictive controller (MPC) controls the non linear system of the actuators through linearizing and discretizing the system signals. Two alternative methods for linearization are presented and used: current state linearization using Taylor expansion and trajectory prediction linearization using Taylor expansion with Euler’s step method to predict trajectory. The signals are then discretized with Euler’s forward method.

mpc_flow Description of the MPC structure.

For the controller to find an optimal solution the open source QP-solver qpOASES, which supports real time code generation to the engine-test-cell, is used for solving the cost function. The cost function (minimizing u) optimized in the solver and the following constraints is described as follows.

$\min \frac{1}{2}U^{T}M^{T}Q_1MG+Q_2(G^TM^TQ_1(\Tilde{M}(\bar{x}_k,\bar{u}_k,)-R))^TU$

$\alpha_{th,ref} \in [0,1], \quad \theta_{ivo,ref} \in [0,50]$

The control system is created with two settings for engine optimization: Performance and Efficiency, using two different goal functions. Performance is defined as prioritizing cylinder mass flow, and efficiency considers both mass flow and pump losses.

Performance

$\Tilde{M}(\bar{x}_{k}\bar{u}_{k}) = \begin{bmatrix} \dot{m}_{ac}(\Bar{x}_k,\Bar{u}_k) \end{bmatrix}$

Efficiency

$\Tilde{M}(\bar{x}_{k}\bar{u}_{k}) = \begin{bmatrix} \dot{m}_{ac}(\Bar{x}_k,\Bar{u}_k)\\ p_{im} - p_{em} \end{bmatrix}$

Results with performance settings

The project resulted in an real-time MPC that was successfully implemented and run in the Simulation environment. Simulation examples are shown below (without any disturbances):