Using the Euler method known as "Backward Euler Approximation" to obtain the approximation of a continuous PID system in a discrete PID system, considering where Ts is the sampling period.

a) Obtain the difference equation that represents the system. b) Sketch the block diagram of the discrete PID system. c) Obtain the transfer function .

1-2-1 -S= Ts H[z] C[Z] E[Z] 1-2-1 -S= Ts H[z] C[Z] E[Z]