🔍 Key Concepts

• Identify which op-amp block in figure B is labeled Derivative and how it fits into a PID (Proportional–Integral–Derivative) controller • Recall that in a PID controller, proportional, integral, and derivative terms each have a distinct mathematical relationship to the error signal • Understand how a capacitor placed in series or in feedback with an op-amp input affects whether the circuit is performing integration or differentiation of the input signal

💭 Think About

• Look at U4 in figure B: how is it labeled, and what component (R or C) is directly associated with it? What does that label suggest about its function in the PID loop? • Compare the wording of each answer choice to the standard definitions of proportional, integral, and derivative control actions. Which one matches the purpose of a derivative stage? • Which stage (U1, U2, U3, U4) would logically be responsible for simply forming the basic error signal, and which would be applying time‑related operations (past errors or rate of change)?

✅ Before You Answer

• Verify which op-amp in figure B is explicitly labeled Differential amplifier, which one is Proportional, which is Integral, and which is Derivative • Match the phrase "sum of all past error signal voltages multiplied by time" with the definition of the integral term, and "difference between process variable and set point" with the definition of the error term • For U4, confirm that its associated capacitor C_D and resistor R_3 are arranged in a way typical for a derivative circuit that responds to the rate of change of the input error signal