. A model of the idle-speed control system (shown) of a vehicle is being developed. The...

  

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. A model of the idle-speed control system (shown) of a vehicle is being developed. The throttle position controls the air flow rate into the manifold. The engine develops torque as a result of air intake into the cylinders (from the manifold) for combustion of the fuel supplied to the cylinders. Use the following variables: q;(t): air mass flow entering the manifold; q.(t): air mass flow leaving the manifold; 9m (t): mean air mass retained in the manifold T(t): engine torque; w (t): engine speed; J: engine inertia TD: induction to power stroke delay The following govern the physics of this system: a) The air mass flow rate entering the manifold is directly proportional to the throttle position (constant gain K₁) -ie; dat) != K₁0 (t) dt Air Idle speed control motor dq;(t). dt To manifold air mass flow rate entering the manifold dao(t); air mass flow rate leaving the manifold dt Ta: disturbance torque, assumed constant e(t): throttle angle measured from fully closed position C: viscous damping coefficient for engine drag b) The mean air mass is determined from qm(t) = f( √ (da; (t) __ dao(t)) dt dt dt c) The air mass flow rate leaving the manifold is directly proportional to the mean retained air mass dqo(t) in the manifold (constant gain K₂) and the engine speed (constant gain K3) - i.e.; dt K₂9m (t) + K₂w (t) d) The engine torque is directly proportional to the mean air mass retained in the manifold (constant gain K4) delayed by TD - i.e.; T(t) = K49m(t-TD) e) The engine torque is related to the engine dynamics as per jªw() + Cw (t) + T₁ (t) = T(t) dt 1.1 Draw a block diagram of the above system with the throttle angle 8(t) as the input and the engine speed w(t) as the output. Show the transfer function of each block. [6] 1.2 Determine the transfer function (6), where (s) = L(w(t)) and Ⓒ (s) = L(0 (t)) 1.3 Is the characteristic equation a polynomial in s? Did you anticipate this? Why?| [2] [2] . A model of the idle-speed control system (shown) of a vehicle is being developed. The throttle position controls the air flow rate into the manifold. The engine develops torque as a result of air intake into the cylinders (from the manifold) for combustion of the fuel supplied to the cylinders. Use the following variables: q;(t): air mass flow entering the manifold; q.(t): air mass flow leaving the manifold; 9m (t): mean air mass retained in the manifold T(t): engine torque; w (t): engine speed; J: engine inertia TD: induction to power stroke delay The following govern the physics of this system: a) The air mass flow rate entering the manifold is directly proportional to the throttle position (constant gain K₁) -ie; dat) != K₁0 (t) dt Air Idle speed control motor dq;(t). dt To manifold air mass flow rate entering the manifold dao(t); air mass flow rate leaving the manifold dt Ta: disturbance torque, assumed constant e(t): throttle angle measured from fully closed position C: viscous damping coefficient for engine drag b) The mean air mass is determined from qm(t) = f( √ (da; (t) __ dao(t)) dt dt dt c) The air mass flow rate leaving the manifold is directly proportional to the mean retained air mass dqo(t) in the manifold (constant gain K₂) and the engine speed (constant gain K3) - i.e.; dt K₂9m (t) + K₂w (t) d) The engine torque is directly proportional to the mean air mass retained in the manifold (constant gain K4) delayed by TD - i.e.; T(t) = K49m(t-TD) e) The engine torque is related to the engine dynamics as per jªw() + Cw (t) + T₁ (t) = T(t) dt 1.1 Draw a block diagram of the above system with the throttle angle 8(t) as the input and the engine speed w(t) as the output. Show the transfer function of each block. [6] 1.2 Determine the transfer function (6), where (s) = L(w(t)) and Ⓒ (s) = L(0 (t)) 1.3 Is the characteristic equation a polynomial in s? Did you anticipate this? Why?| [2] [2]