Cascade control design – locating the secondary measurement Water flows through four tanks in series and is heated. You must control the temperature leaving Tank 4 (primary loop), while a major disturbance enters as a second stream into Tank 2. Where should the secondary (inner-loop) measurement be placed to implement the best cascade scheme?

Introduction / Context:
Cascade control improves disturbance rejection by measuring and controlling an intermediate variable close to the disturbance source or actuator. In a series of heated tanks, the objective is to maintain the outlet temperature from the last tank. However, a secondary stream enters earlier in the train, adding a thermal disturbance that propagates downstream.

Given Data / Assumptions:

• Primary controlled variable: temperature at the outlet of Tank 4.
• Major disturbance: second stream temperature or flow entering Tank 2.
• Secondary loop should be faster than the primary loop and measure near the disturbance.

Concept / Approach:
In cascade architecture, the inner loop is positioned where it can “see” and suppress the disturbance before it reaches and degrades the primary controlled variable. Placing the secondary sensor at Tank 2 allows quick correction (e.g., adjusting steam or heat input) before the error propagates to Tanks 3 and 4. A sensor in Tank 3 would react later; Tank 4 would reduce to single-loop control. Tank 1 is upstream of the disturbance and offers no advantage.

Step-by-Step Solution:

Verification / Alternative check:
Block-diagram representations show that moving the inner measurement upstream decreases the effective dead time and reduces the load seen by the primary temperature loop, improving phase margin and settling time.

Why Other Options Are Wrong:

• Tank 4: Collapses to single-loop control; disturbance is felt too late.
• Tank 3: Better than Tank 4 but still reacts after Tank 2 has mixed.
• Tank 1: Upstream of disturbance; provides little benefit.

Common Pitfalls:
Placing the inner loop too slow or far from the disturbance; cascade requires a significantly faster secondary loop to be effective.

Final Answer:
Tank 2