Design an MPC controller for the reactor/flash unit plant and test it using a simulation of the linearized model of this plant. For purposes of this exercise, first design and implement a PI controller for the reactor level using the reactor outflow rate W3 as manipulated variable (see Exercise 24.S). Also, include a flash unit holdup of 500 kg and implement a PI controller for the liquid level with the flash unit outflow rate w4 as manipulated variable (see Exercise 24.6).
The following manipulated and controlled variables are to be used in the 4 × 4 MPC:
Manipulated Variables Controlled Variables
A feed stream flow (w1) Production ram (w4)
B Iced stream flow (w2) Composition of A in the product stream
(w4A) Purge stream flow (w6) Recycle lank holdup (HT) Recycle line flow (w8) Composition of D in recycle stream (x8D) Your design must meet the following control objectives:
(i) The product should contain approximately 9% C; the remaining impurity is A.
(ii) The desired p
roduction rate of product w4 to the downstream unit should meet the specifications:
nominal value ±1% on long-term basis (days),
nominal value ±3% on short-term basis (hours).
(iii) The reactor should be operated with approximately constant conversion (unspecified) as production rate varies within expected limits. The nominal reactor temperature TR is fixed,
(iv) Important quality constraint mass fraction of A in the product stream (x4A) must be less than 0.011.
(v) For the purposes of this design, the only manipulated variable constraint is that flows are required to be positive.
Once the controller has been designed, evaluate its performance for the following set-point and disturbance sequences (each one separately).
(a) Disturbance response to a + 01)3 change in x2D,
(b) Set-point response to a 5% change in the production rate (w4)
(c) Same as (a), but with the rate constant k increased by 20%
(d) Set-point response to a 20% change in the production rate (W4)