Question 3 (5 points) \begin{tabular}{|l|l|}\hline In Listen \\ In proportional control, the controller's output is constant and equal to 1.5 . If the \\ controller's proportional gain is 0.8 , the setpoint temperature is \( 75^{\circ} \mathrm{F} \), and the actual \\ temperature is \( 72^{\circ} \mathrm{F} \), what's the controller's output? \end{tabular}

In proportional control, the control output is calculated using the formula: \( \text{Output} = K_p \times (\text{Setpoint} - \text{Actual}) \), where \( K_p \) is the proportional gain. With a setpoint of \( 75^{\circ} \mathrm{F} \) and an actual temperature of \( 72^{\circ} \mathrm{F} \), the error is \( 75 - 72 = 3 \). Thus, the output becomes \( 0.8 \times 3 = 2.4 \). Proportional control is widely utilized in various industries for temperature regulation, speed control, and pressure systems. The beauty of this method lies in its simplicity; it adjusts the output directly proportional to the error. However, while it can effectively minimize the offset, relying solely on proportional control can lead to a steady-state error, especially in systems with a constant disturbance.