electronic trainer build kit
Motor control would be an easy one to see and physically interact with. Choose a motor with tachometer, and the control loop can change the supply to the motor in order to keep the speed constant. The kiddies can try to grab the motor spindle to slow it down, but your circuit will increase motor power to always keep the speed constant.
You can shoot for PID if you want to, but I have to say that you yourself should know the control method front to back before attempting to build a project to teach others about it. Let's move on to the dirty details of one simple control method.
A lot of tachometers are just a simple disc spinning with the motor. The disc has holes punched in it that an LED shines through. A photodetector outputs a pulse each time a hole passes by, so the frequency of the pulses changes as the motor speeds up and slows down.
Simplest control would be to take those square-wave pulses and use an R-C filter to generate an analog signal proportional to motor speed. Then, you just need an integrator (built using LM13600 or even op-amp type II compensation) to integrate the difference between desired speed (a fixed 1v or something) and the current motor speed (the filtered tach signal).
Now you have an integrated error voltage that can be used to control the motor speed. If motor is too slow, error voltage will rise at a rate proportional to the difference between desired and actual speed. If motor is too fast, error voltage will fall. If motor speed is exactly right, error voltage will neither rise nor fall to keep the motor at exactly the same driving point.
Driver could be a constant-current circuit (just use a V to I converter from the error voltage) or even PWM control.
For PWM, compare the error voltage to a sawtooth ramp, and close a switch in series with the motor when the compare is high. If the error voltage is higher, we will give larger ON pulses to the motor and vice versa. Your PWM can run at 50kHz or so to void making an audible noise.
The motor will be very inductive, so you don't need a seperate inductor in the pwm stage.
I used this scheme to control the speed of a motor for a gemstone faceting machine. It worked fine, you could really press down hard on the grinding wheel and watch the PWM increase but the motor speed stayed dead on at wherever you set the "speed" potentiometer.
Good luck!