Cascade Control: (Chap 9 in Book and 10 in Edition 2)
Cascade Control: (Chap 9 in Book and 10 in Edition 2)
Cascade Control: (Chap 9 in Book and 10 in Edition 2)
Consider the chemical reactor below. The reactants are preheated in a furnace. Inputs to the furnace: Fuel and Air, Process streams (reactants). Purpose: It is desired to control the reactor temperature TR by acting on the amount of fuel to the furnace. The Figure below represents a FB control of the temperature TR.
Disturbances include air flowrate and fuel flowrate, also the inlet process conditions of the reactants (temperature, flow, concentrations). Other disturbances: outside temperature affects both the furnace and the reactor, impurities in the air stream. The FB block diagram is given below:
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1 Gc1
Now we apply the substitution method to determine the limits of the gain Kc for the FB controller: It gives:
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The bloc diagram of the cascade control of the preheater/reactor system is given next:
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Important: 1. Note an inner loop has been added to the previous primary loop. 2. The inner loop does not envelop the reactor dynamics. 3. The controller Gc2 in the inner loop is not known and must be designed. 4. The controller Gc1 in the outer (primary) loop must designed again, since the overall dynamics of the FB loop has changed.
1 Gc 2
Or
1 Gc 2
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3 1 0.8 (0.2s 1) (3s 1)(s 1) 1 Gc1 0.5 3 1 (4s 1)(s 1) 1 Gc 2 0.5 (0.2s 1) (3s 1)(s 1) Gc 2
1 Gc1
Since we know Gc2 i.e. Kc2, the controller Gc1 is the only unknown. Substitution method gives ultimate values below: Kcu1 7.2 %CO / %TO u1 1.54 rd / min Plots in the Figure below compares the regulation (control) of the reactor temperature with a simple FB controller and a cascade controller. It looks that the cascade control outperforms a one-loop FB controller.
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Important note: This is a two-level cascade Control. The Ziegler-Nichols method (ultimate method) is straightforward. It allows the engineer (yourself) to design a good controller based on the Q-decay. If for some reason the Qdecay cannot be used, then the engineer can try another approach: Minimum Integral Approach (ISE, IAE) or a model based scheme (Dahlins). Another approach is discussed in the text book page 316-317.
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