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PID Controller Modelling and Optimization in Cr Systems with Standard and Reduced Accumulators

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Abstract

The proportional-integrative-derivative (PID) controller and the pressure control valve of a Common Rail system are modelled by taking into account electronic, electrical, hydraulic and mechanical aspects. A fully predictive model of the injection apparatus is realized and validated by means of comparison with experimental data. The effects of the PID parameters on the injection system dynamics are illustrated and discussed on the basis of model results, which refer to steadystate and transient working conditions. The influence of the accumulator size on the rail pressure time history is investigated when the rail volume is dramatically reduced (up to 2.5 cm3). In particular, the effect of the large rail pressure drop that occurs at the end of the main injection for Minirail layout solutions is examined when after injections are implemented. An objective is to try to determine possible suitable values of the PID controller parameters and of the pressure-sensor sampling-frequency for rails of reduced size.

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Abbreviations

A :

restricted flow-area

C :

geometric constant of the magnetic circuit

CR :

common rail

D :

diameter of the valve seat; derivative part

ET :

energizing time

F :

force

G :

system transfer function; mass flow-rate

I :

electric current; integrative part

K :

gain

M :

mass

P :

proportional part

PCV :

pressure control valve

PID :

proportional-integrative-derivative control

PWM :

pulse width modulation

V :

volume

S :

surface

f :

frequency

k :

spring stiffness

m :

valve armature mass

n :

engine speed

p :

pressure

x, ẋ, ẍ :

valve displacement, velocity and acceleration

α :

valve-seat cone semi-angle

β :

valve damping coefficient

Δp :

pressure drop

θ :

flux-force angle

μ :

flow coefficient

after :

after injection

d :

derivative part

fl :

flux forces

i :

integrative part

inj :

injected

p :

proportional part

mag :

magnetic

main :

main injection

nom :

nominal value

pc :

pressure control

tot :

total

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Authors and Affiliations

  1. Energy Department, Politecnico di Torino, Corso duca degli Abruzzi 24, Torino, 10129, Italy

    Alessandro Ferrari, Antonio Mittica, Pietro Pizzo & Zhiru Jin

Authors
  1. Alessandro Ferrari
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  2. Antonio Mittica
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  3. Pietro Pizzo
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  4. Zhiru Jin
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Correspondence to Alessandro Ferrari.

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Ferrari, A., Mittica, A., Pizzo, P. et al. PID Controller Modelling and Optimization in Cr Systems with Standard and Reduced Accumulators. Int.J Automot. Technol. 19, 771–781 (2018). https://doi.org/10.1007/s12239-018-0074-4

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  • DOI: https://doi.org/10.1007/s12239-018-0074-4

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