Gasoline engines. Diesel engines. Hybrid fuel cell vehicles. Model Predictive Control in automotive systems R. Scattolini, A.

Transcription

1 Model Predictive Control in automotive systems R. Scattolini, A. Miotti Dipartimento di Elettronica e Informazione Outline Gasoline engines Diesel engines Hybrid fuel cell vehicles

2 Gasoline engines 3 System description Engine model and validation (VW Lupo) Design of the engine static maps Design of a predictive control scheme State and unknown parameters observers Feedback linearization + MPC Conclusions Air path scheme 4 Throttle EGR VVT AIR FLOW METER Measurable variable ECU SPEED SENSOR Actuators PRESSURE SENSOR

3 A multivariable system 5 Driver Accelerator ECU Advance Fuel Brake pedal Gear Throttle EGR VVT Air supply system Engine Torque Engine speed Vehicle dynamics Vehicle speed Manifold pressure Input air flow Lambda sensor Emissions [NO X, CO, HC] System characteristics 6 Multivariable system Strongly non linear Heavily coupled Few measurements available on-board No measurements of performance variables (torque, emissions)

4 Dynamic model and assumptions 7 Lumped-parameter, time-based, nonlinear, Mean Value Model (MVM) Uniform thermodynamic properties; Homogeneous mixtures of air and combustion (ideal) gas; Stoichiometric combustion of air and fuel; Heat transfer effects neglected; Flow through restrictions modeled as isentropic compressible flow. Throttle 8 Algebric Model w th is the flow through throttle Measured by means of an air flow meter From experimental data the parameter ka th (α) has to be identified (also as function of N). Problem: The downstream pressure p th is unknown p th =p man

5 Intake manifold 9 w air w egr 3 state variables m m T air egr man w eng w air : from throttle equation w egr : from EGR model w eng : flow coming in the engine x egr : egr percentage coming in engine Assumption: Ideal gas law Mass equations m air = w air w eng mair m + m air eng, m egr = w air w eng m air m egr + m eng Energy equation T man R = V c c man pair man vman w eng ( c T man pair w air T (1 x air egr + c ) c pegr pegr w w egr eng T T egr man x egr ) Static maps 1 volumetric efficiency; EGR valve; torque; emissions; engine temperature.

6 Vehicle dynamics 11 Transmission ratio shaft/wheels : τ t = τ c τ p J at is the total momentum of inertia Re : Effective wheel radius M : Mass of the vehicle Jr : Inertia of e wheel Power at shaft Engine losses Road Load Air path validation (1) 1 Manifold pressure [Pa] Intake manifold pressure Air flow [kg/h]

7 Validation of the vehicle model 13 Engine speed [rpm] Vehicle speed [km/h] Mathematical model 14 The model, ignoring some additional dynamics and transport delays, takes the form x = f ( x, u) y = h( x, u) where T x = m m man air egr, u N α = VVT EGR, y = Torque NO x HC CO Main problems: some state and output variables are not measured. Many static functions are derived from data and do not have an explicit mathematical form.

8 Design of an industrial control scheme 15 driver: pedal request α o Static engine map Torque request Γ o Static control maps u Engine N Computed with the simulator Built with the simulator by solving a suitable optimization problem Design of the static control maps 16 For any point (Γ,N) on a prescribed grid, the engine simulator has been used to solve the following (static) optimization problem min α, EGR, VVT λ ( Γ 1.85α Γ) N = EGR 5 α 1.15α VVT + λ NOx + λ CO + λ HC N 4 3 4

9 Control maps 17 Table data Γ o Column breakpoints Table and breakpoints data for block: PROVA_VVT_ottimnt/Mappa VV T Ottimizzazione Throttle /farf nt 5 α o rpm Row breakpoints 4 Annotations denote column breakpoints Table data Column breakpoints Table and breakpoints data for block: PROVA_VVT_ottimnt/Mappa VV T Ottimizzazione /EGR nt 5 EGR Row breakpoints Annotations denote column breakpoints Design of an MPC regulator 18 Designed on a linear identified model (N = 5 rpm, Γ = 3 Nm) MPC regulator Torque Torque request Γ o Static control maps u δu Air path Torque Fuel cons. NOx CO HC N

10 MPC design 19 State estimator + MPC state feedback control law Ny = 4 (prediction horizon), Nu = 1 (control horizon) : Performance index J = J 1 + J J 1 = N p o [ µ 1( Γ (( h + l) Tc ) Γ( ( h l) Tc )) ] + l= 1 J = N p [ µ NO (( h + l) T ) + µ δα ( ht ) µ δegr( ht ) ] + l= 1 x c 3 c 4 c Constraints δα min δα ( htc) δα max δegr min δegr( htc) δegr max Experiments With MPC Without MPC Set point 1 11 With MPC Without MPC Set point Vehicle speed [Km/h] 4 18 Vehicle speed [Km/h] Time [s] Time [s] 5 Low speed With MPC Without MPC 8 6 High speed With MPC Without MPC 4 Torque error [Nm] 5 Torque error [Nm] Time [s] Time [s]

11 Results 1 Cost on emissions Cost on torque error Static maps MPC weight on torque error MPC weight on torque + emissions Static maps MPC weight on torque error MPC weight on torque + emissions Exp Exp Exp Exp State feedback linearization State feedback law Simplified model Constraints on fictitious inputs v

12 Nonlinear observers 3 STATES ARE NOT MEASURABLE SLIDING MODE NONLINEAR OBSERVER The most uncertainty parameter is the volumetric efficiency NONLINEAR INPUT OBSERVER Linear MPC + F.L. + nonlinear observer 4 1/s Torque req. p o man Linear MPC Feedback linearization W th, W egr engine p man,,no x Nonlinear state observer Main problem: constraints handling

13 Pressure transient 5 Perturbed model Turbocharged Diesel engines 6 Engine description Engine model Model analysis and validation Control problems Classical control structures Advanced control design

14 Air path 7 Intake manifold Exhaust manifold Turbocharger Dynamic model 8 Dynamic equations m + 1 = wc1 w1e wegr Mass balances in the manifolds ṁ = w1e wegr wt +w fuel Energy balances 1 T = (w c1 (Tc1c pair T c ) w T R + w (T c m 1c vair 1 T = (w1e (Teng cpair T cvair) wtt R+ wfuel(t engc pegr T cvegr)-w m c 1 1 vair 1e 1 egr egr pegr vair egr T c 1 T R-K vegr conv )) (T -T amb )) N tc = P turbine P N tc I compressor tc Turbocharger 1 p γ Pturbine = w tcpegrtη t 1 p p Pcompressor = w c1cpairtamb p γ 1 γ 1 γ 1 η c

15 Dynamic model - 9 Variables to be determined: Recirculating gas flow rate (w egr ) EGR valve opening (KA egr ) Gas flow rate to the engine (w 1e ) Volumetric efficiency (η vol ) Engine temperature (T eng ) Compressor air flow (w c1 ) Compressor efficiency (η c ) Turbine efficiency (ηt) Static map Turbine flow rate (w t ) Turbine flow rate 3

16 Model characteristics 31 Inputs Engine speed (N) Fuel flow rate (w fuel ) EGR VGT Outputs Intake manifold pressure (p 1 ) Compressor air flow rate (w c1 ) Control variables EGR VGT Step responses VGT step variations, EGR constant N=5 [rpm] W fuel =1.6 [g/s] Different magnitudes N=3 [rpm] W fuel =1.6 [g/s] Change of signo N= [rpm] W fuel =.3 [g/s]

17 Step responses - 33 EGR step variations, VGT constant N=5 [rpm] W fuel =1.6 [g/s] N=3 [rpm] W fuel =1.6 [g/s] N= [rpm] W fuel =1 [g/s] Static gains 34 VGT-MAP VGT-MAF EGR-MAF EGR-MAP

18 Control design Feedforward control PI + feedforward (limited operating range - N=5[rpm] w fuel =1.6[g/s]) H + feedforward (limited operating range - N=5[rpm] w fuel =1.6[g/s]) Feedforward Torque/fuel EGR= VGT=constant rpm Control design - 36 Feedforward + PI control

19 Nonlinear control design 37 State observer (sliding mode observer + unknown input observer) + Feedback linearization + linear MPC or Nonlinear MPC + interpolation Nonlinear MPC Solve off-line (MUSCOD) a dynamic optimization problem for a great number of initial conditions in the operating space (torque, rpm). Use the results to find a suitable interpolation (NN RBF - ) of the state-feedback control law 3. Use it in conjunction with a state observer map o,,maf o Interpolated N-MPC EGR, VGT Diesel engine map,,maf Nonlinear state observer

20 Hybrid fuel cell vehicle 39 A vehicle with a fuel cell stack and a battery A detailed simulation model has been developed A low level scheme controls the fuel cell acting on the compressor command and on the anode and cathode valves The high level MPC controller manages the power fluxes, i.e. the power absorbed by the motor and the one provided by the fuel cell The main constraints are related to the battery charge (SOC) Control strategy 4 Power request High level control i Batt i FC P mot = P FC + P Batt Low level control

21 High level control 41 Constraints: δp δi min mot min FC SOC min δp δi mot FC SOC max ( k) δp mot max ( k) δi FC ( k) SOCmax Power Request P mot FC Current P mot = P FC + P Batt High level control System to be controlled P mot FC System Power I FC + Battery SOC Performance index: N 1 o o J = [ q ( Power ( k) Power( k) ) + q ( SOC ( k) SOC( k) ) + r P ( k) r I ( k) ] i= 1 1 mot + FC Constraints: δp δi min mot min FC SOC min δp δi mot FC SOC max ( k) δp mot max ( k) δi FC ( k) SOCmax

22 High level control - 43 Sampling time:.5 s Two tunings: Low use of the battery High use of the battery Simulations Battery low use Battery high use P mot = P FC + P Batt

23 Simulations - 45 Battery low use Battery high use P mot = P FC + P Batt