Engine system with inferential sensor

1. An engine system comprising:

an engine;

one or more sensors each configured to sense one or more parameters related to operation of the engine; and

a controller in communication with the engine and the one or more sensors, the controller comprises a first virtual sensor and a second virtual sensor; and

wherein:

the first virtual sensor is configured such that during operation of the engine the first virtual sensor determines one or more initial conditions for the second virtual sensor based at least in part on values of the one or more parameters sensed by the one or more sensors by solving a differential algebraic equation to determine the one or more initial conditions;

the second virtual sensor is configured such that during operation of the engine, the second virtual sensor determines values for one or more output parameters of the engine; and

the controller is configured to send control signals to the engine to control operation of the engine, the controller is configured to determine the control signals based, at least in part, on the values for one or more output parameters of the engine determined by the second virtual sensor.

2. The engine system of claim 1 , wherein the second virtual sensor solves a differential algebraic equation to determine the values for one or more output parameters of the engine.

3. The engine system of claim 1 , wherein the first virtual sensor incorporates an air-path state estimator configured to estimate one or more of an intake manifold temperature of the engine, intake manifold pressure of the engine, exhaust manifold pressure of the engine, an amount of fuel per stroke of the engine, intake manifold gas composition of the engine, in-cylinder charge mass, in-cylinder charge temperature, in-cylinder charge pressure, in-cylinder charge composition, residual mass temperature, and residual mass composition.

4. The engine system of claim 1 , wherein the second virtual sensor incorporates a NOx concentration module.

5. The engine system of claim 4 , wherein the second virtual sensor solves a differential algebraic equation obtained from a physics based model of the engine to determine an output of the NOx concentration module.

6. The engine system of claim 1 , wherein:

the first virtual sensor incorporates an air-path state estimator; and

the second virtual sensor incorporates a NOx concentration module that solves a differential algebraic equation obtained from a physics based model of the engine to determine an output of the NOx concentration module.

7. The engine system of claim 1 , wherein the controller comprises:

an off-line portion; and

an on-line portion configured to incorporate the first virtual sensor and the second virtual sensor; and

wherein the off-line portion is configured to determine one or more differential equations for one of the first virtual sensor and the second virtual sensor.

8. The engine system of claim 7 , wherein the controller comprises a plurality of control units and a first control unit of the plurality of control units incorporates the off-line portion and a second control unit of the plurality of control units that incorporates the on-line portion and is in communication with the first control unit.

9. The engine system of claim 7 , wherein:

the first virtual sensor and the second virtual sensor are configured to estimate one or more parameters related to the operation of the engine; and

the off-line portion of the controller is configured to derive an ordinary differential equation (ODE) model of the one or more parameters estimated by one or both of the first virtual sensor and the second virtual sensor into a differential algebraic equation (DAE) model of the one or more parameters estimated by one or both of the first virtual sensor and the second virtual sensor.

10. The engine system of claim 1 , further comprising:

one or more turbochargers; and

wherein the first virtual sensor solves one or more of the following:

a differential equation of pressure between components in a volume of the engine;

a differential equation of temperature between components of the engine;

a differential equation of a mass fraction of a gas species in the engine; and

a differential equation of a turbocharger speed of one or more turbochargers.

11. A method of controlling operation of an engine system, the method comprising:

receiving values of one or more sensed parameters from a physical sensor, the one or more sensed parameters are related to an operation of an engine;

using a first differential algebraic equation to calculate one or more initial conditions of an in-cylinder gas based, at least in part, on the values of one or more sensed parameters received from the physical sensor;

using a second differential algebraic equation to calculate one or more values of a parameter output from the engine based, at least in part on the one or more initial conditions of the in-cylinder gas;

determining one or more control signals to control operation of the engine, the one or more control signals are determined based, at least in part on, the one or more values of a parameter output from the engine that are calculated; and

sending the one or more control signals to the engine.

12. The method of claim 11 , wherein the sending the one or more control signals includes sending control signals to an on-board diagnostics system configured to monitor operation of the engine.

13. The method of claim 11 , wherein the one or more initial conditions of the in-cylinder gas incorporate one or more of an intake manifold pressure of the engine, an intake manifold temperature of the engine, an exhaust manifold pressure of the engine, an amount of fuel per stroke of the engine, one or more gas compositions in an intake manifold of the engine, in-cylinder charge mass, in-cylinder charge temperature, in-cylinder charge pressure, in-cylinder charge compositions, residual mass temperatures, and residual mass compositions.

14. The method of claim 11 , wherein the first differential algebraic equation and the second differential algebraic equation are configured in an off-line portion of a controller of the engine system.

15. The method of claim 14 , wherein in the off-line portion of the controller:

the first differential algebraic equation is determined by converting a first ordinary differential equation configured to model engine parameter values to a same or lower number of differential equations including the first differential algebraic equation; and

the second differential algebraic equation is determined by converting a second ordinary differential equation configured to model engine parameter values to a same or lower number of differential equations including the second differential algebraic equation.

16. The method of claim 11 , wherein using the first differential algebraic equation to calculate one or more initial conditions of an in-cylinder gas includes solving one or more of the following:

a differential equation of pressure between components in a volume of the engine;

a differential equation of temperature between components of the engine;

a differential equation of a mass fraction of a gas species in the engine; and

a differential equation of a turbocharger speed of one or more turbochargers of the engine system.