Problems 1–5 require analytical solutions, Problems 6 and 8 are SIMULINK problems.

1: | Design an IMC for the following process model:
Assume that the all-pass factorization technique is used. Assuming the model is perfect, sketch the transient response of y(t) to a step setpoint change in r(t). |

2: | Consider the following IMC block diagram. Find the closed-loop transfer functions relating the load [l(s)] and the setpoint [r(s)] to the output [y(s)]. Assume that the model is not perfect. |

3: | A biochemical reactor with several components ... |

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