The construction of the tunnel under the English Channel from France to the Great Britain began...

   

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The construction of the tunnel under the English Channel from France to the Great Britain began in December 1987. The first connection of the boring tunnels from each country was achieved in November 1990. The tunnel is 23.5 miles long and bored 200 feet below sea level. Costing $14 billion, it was completed in 1992 making it possible for a train to travel from London to Paris in three hours. The machine operated from both ends of the channel, bored towards the middle. To link up accurately in the middle of the channel, a laser guidance system kept the machines precisely aligned. A model of the boring machine control is shown in the figure, where Y(s) is the actual angle of direction of travel of the boring machine and R(s) is the desired angle. The effect of load on the machine is represented by the disturbance, Ta(s). Tals) R(s) Gc(s) G(s) Y(s) Controller Plant Angle Desired 1 K+11s Angle s(s + 1) Figure: A block diagram model of a boring machine control system a) Get the transfer function from R(s) to Y(s) b) Get the transfer function from D(s) to Y(s) c) Generate the system response; for K= 10, 20, 50, 100; due to a unit step input - r(t) d) Generate the system response; for K= 10, 20, 50, 100; due to a unit step disturbance d(t) e) For each case find the percentage overshoot(%O.S.), rise time, settling time, steady state of y(t) f) Compare the results of the two cases g) Investigate the effect of changing the controller gain on the influence of the disturbance on the system output The construction of the tunnel under the English Channel from France to the Great Britain began in December 1987. The first connection of the boring tunnels from each country was achieved in November 1990. The tunnel is 23.5 miles long and bored 200 feet below sea level. Costing $14 billion, it was completed in 1992 making it possible for a train to travel from London to Paris in three hours. The machine operated from both ends of the channel, bored towards the middle. To link up accurately in the middle of the channel, a laser guidance system kept the machines precisely aligned. A model of the boring machine control is shown in the figure, where Y(s) is the actual angle of direction of travel of the boring machine and R(s) is the desired angle. The effect of load on the machine is represented by the disturbance, Ta(s). Tals) R(s) Gc(s) G(s) Y(s) Controller Plant Angle Desired 1 K+11s Angle s(s + 1) Figure: A block diagram model of a boring machine control system a) Get the transfer function from R(s) to Y(s) b) Get the transfer function from D(s) to Y(s) c) Generate the system response; for K= 10, 20, 50, 100; due to a unit step input - r(t) d) Generate the system response; for K= 10, 20, 50, 100; due to a unit step disturbance d(t) e) For each case find the percentage overshoot(%O.S.), rise time, settling time, steady state of y(t) f) Compare the results of the two cases g) Investigate the effect of changing the controller gain on the influence of the disturbance on the system output

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a The transfer function from ... View the full answer