Modelling of Control System

1. Problem Statement Consider a single cylindrical water tank with cross-sectional area A, inlet flow controlled by a valve/pump, and constant outflow. The desired water level (setpoint) is maintained using feedback from a level sensor. The system operates as a closed-loop controller to regulate the height h despite disturbances in outflow rate. 2. Tasks / Questions (a) Conceptual Understanding i. Classify the water level control system as open-loop or closed-loop. Justify your answer by explaining the role of the level sensor and feedback path. Draw simple diagrams comparing a generic open-loop water level system (e.g., manual valve adjustment without sensor) and the closed-loop version. ii. Identify the major components (e.g., controller, actuator/valve/pump, plant/tank, and sensor) and explain the feedback mechanism. Discuss at least two advantages of closed-loop operation over open-loop in this scenario (e.g., disturbance rejection). (b) Modeling & Analysis i. Construct the complete block diagram representation of the closed-loop water level control system. Include blocks for the controller (e.g., comparator and amplifier), actuator (valve/pump), plant (tank dynamics), and feedback sensor (assume unity gain for simplicity). Label inputs (desired level, disturbance outflow) and output (actual level). ii. Perform step-by-step block diagram reduction to obtain the simplified closed-loop transfer function (relating output level to desired set point and disturbances). Show all intermediate diagrams. iii. Alternatively, draw the signal flow graph for the same closed-loop system. Identify forward paths, loops, and non-touching loops. Apply Mason's gain formula to compute the overall transfer function and verify it matches the block diagram reduction result.