The complexity of internal combustion engines has increased dramatically over the last two decades as legislative requirements on vehicle emissions have become ever more rigorous. This trend is set to continue and will increase engine development time and consequently engine cost. One cause of this increased engine development cost is linked to the mainly labor intensive, unsystematic and inflexible engine control design process that exists today. Currently, engine calibration is often reduced to the tuning of multi-dimensional and complicated tables of constants for simple controllers, that do not take into account process interactions and limitations. This problem is further compounded by a deficit of suitably qualified control and calibration engineers in the market.
Honeywell has learned from other industries (such as controlling pulp & paper machines, chemical & petrochemical, refineries and aerospace) that all of the above issues can be eliminated if advanced control methods are utilized. One such method is Model Predictive Control.
Model Predictive Control (MPC) is an advanced optimization based control strategy applicable to a wide range of industrial applications such as chemical plants and internal combustion engines. It is inherently a multivariable strategy that encompasses constraints, handling of actuators, states, process outputs and other variables. For example, it provides a systematic method for the design and tuning of a controller for a diesel airpath system that simultaneously governs both Mass Air Flow (MAF) and Manifold Air Pressure (MAP) while operating below a maximum turbo speed limit.
MPC is truly a model based control strategy. The model is not used exclusively for tuning purposes but also acts as the corner stone of a decision to derive the correct control action to mitigate a hazardous situation in future (e.g. turbo over speeding, smoke forming etc). This is done through the prediction of engine states and outputs based on the engine plant model. Thus, the controller can change its control action to prevent a hazardous situation from occurring. This represents an impossible task for simple controller loops. The performance of the resulting controller is highly sensitive to the quality of the plant models and consequently these models need be as accurate as possible. Nevertheless, it is possible to tune an MPC controller to be robust to model uncertainty.
PRINCIPLES OF MPC
In a MPC framework the control goals, such as the tracking of a reference or the satisfaction of constraints, are formulated as a numerical optimization problem. In most cases this problem is represented as a Quadratic programming or QP problem. For such an optimization problem, the cost function is the additive sum of individual terms that express various control requirements. These terms are multiplied by weighting factors defining the relative importance of each individual control goal. More importantly, controller tuning is reduced to a more intuitive decision process. For example, emphasizing the tracking of MAF or MAP set points in order to eliminate NOx emissions while ensuring operation below the maximum turbo speed limit.
MPC falls into the class of receding horizon control algorithms. This means that the resulting optimization problem from the control design needs to be solved at each sampling interval based on actual measurements. In the past, the computationally demanding nature of algorithms solving receding horizon control problems prevented the application of MPC for embedded systems. The computation power of the CPUs of embedded systems has increased dramatically and substantial effort has been invested into the innovation of fast and reliable solvers. Consequently, this obstacle has been removed. The main contributor to this achievement was discovery that MPC problems can be reformulated to multi-parametric quadratic programming or mp-QP problems. A problem formulated in this manner can be solved off-line once only for a given range of parameters; then at each sampling time the MPC controller is effectively reduced to a look-up table process. This represents a very fast controller implementation solution. It should be noted that this approach is not an approximation but gives exactly the same results as if the optimization problem would have been solved at each sampling interval.