Question

At this point in the course, you have enough information necessary to build a robust analog feedback control system known as a PID (short for Proportional, Integral, Derivative controller). This circuit is often used to control HVAC systems for temperature settings, cruise control in automobiles, speed governors on wind turbines, and even trim adjustments for aircraft autopilot features (to name a few applications) A signal voltage is measured within the physical system we are trying to control to tell us the current state of the system property we want to modify. Using this signal, we can compare it to a reference signal (or voltage) that corresponds to the voltage value the system should be reading at a known state. If the sensor voltage (signal voltage) and our reference voltage (value we manually adjust) are not equal we will want the circuit to add some power to the system to make them equal We can compare the values using a simple subtracting Op-Amp, which will output a voltage related to the difference of the two values. Then we send this voltage to three parallel gain stages; the proportional, integral, and derivative. Each one will adjust how quickly the signal changes to the desired signal for the system setting we prefer. If you are curious why we use these three relations, feel free to research this further. Using this circuit, we now have an automatic controller that just makes adjustments to a system automatically as needed! The following circuit is a PID controller for temperature control. We compare our desired voltage reference to the measured voltage at the temperature sensor to generate a input signal to the PID controller: R5 R5 C1 PID Controller R6 R5 Съ R5 R5 Heating Element 04 R4 Temperature Sensor What is the corresponding gain relation for this circuit, in terms of Vsensor and the given resistor/capacitor terms? d(Vsensor) sensoT sensoT R2C2 sensorR12V 4R1C dt ensor.12V Ro.12V 12V) dt + V (0)+ R2C2 Ro 12V .Vsensor R d(Vsensor) sensoT ー·Kensor 4

Answer 1

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