Standard feedback control block diagram (conceptual): identify the incorrect statement about variable/transfer-function labeling in a simple single-loop system (controller, process, measuring element, feedback).

Introduction / Context:
In textbook single-loop diagrams, signals and transfer functions have conventional labels: the controller C(s) (or Gc), the process G2(s) (or Gp), the measuring element H(s), the set point R (or X1), the load/disturbance X, the controlled output Y (or C), and the manipulated variable m (or u). Understanding these conventions helps avoid misinterpretation when writing closed-loop transfer functions.

Given Data / Assumptions:

• Simple unity-feedback style diagram with controller, process, and measuring element.
• Common notation: C(s) for controller TF, G2(s) for process TF, H(s) for sensor TF.
• Output variable often denoted C or Y; manipulated variable often denoted m or u.

Concept / Approach:
The manipulated variable (MV) is the actuator output that drives the process (e.g., valve position, flow). In common notation, C usually designates the controlled variable (CV), not the MV. Therefore, a statement claiming “Manipulated variable is represented by C” is incorrect in the standard labeling scheme.

Step-by-Step Solution:

Verification / Alternative check:
Any standard process control text shows CV labeled y or c, MV labeled u or m; controller is Gc(s). The mismatch highlights the incorrect statement.

Why Other Options Are Wrong (or Not Chosen):

Common Pitfalls:
Confusing the symbol C for “controller” vs. “controlled variable.” Context (function C(s) vs. signal C) matters.

Final Answer:
Manipulated variable is represented by C.