A four stroke four cylinder Diesel engine is going to be simulated by using the first order ordinary differential equation below. ?N 60 ?t 2- N is the engine rotational velocity [rpm], T, and , are engine and load torques respectively and ? is the engine moment of inertia. Engine torque is found by: 17 = V2n where = ? = 45 MJ/kg 1 ?7 ? , = Ty? N ?y?=4 (number of cylinders) V, is the displacement volume of the engine, pm, is the mean effective pressure, p, is the mean fuel pressure, pm, is mean friction pressure, m, is the mass of the fuel in a cylinder during a cycle and H, is the fuel calorific value. v is taken 1 for two stroke engines and 2 for four stroke engines. ? , is the mass flow of the fuel. The initial condition of the engine rotational velocity is 1500 rpm. V. = 0.0016 m3 , I, = 0.2715 kgm?, e = 0.38 and Pm, =100 kPa Draw a block diagram of the model with ? ? and 7, as the inputs and Nand To as the output. Simulate the Diesel engine performance for a constant load torque of 85 Nm and a smoothly increasing mass flow of the fuel, for a smoothly increasing torque (from 70 Nm to 100 Nm in 10 seconds) and a constant mass flow of the fuel (hint: use the "Ramp" block of Simulink for T? ). Control Design a PID controller to control the engine rotational velocity by using the mass flow of the fuel as the input variable to the system. Simulate the controller performance for a constant load torque of 85 Nm and make the engine rotational velocity reach 2000 rpm. Show and comment on the results by plotting N t - I, graphs for each simulation (t: time). (hint: use "Clock" and "To Workspace" blocks of Simulink and "plot" command of Matlab. )