Electronic – Precision Rectifier Help

I know analog guys don't like to hear this, but a small microcontroller could easily meet all of your requirements. It would be easy to modify its operational parameters even after the hardware is built, and it would have by far the lowest overall parts count.

A built-in ADC could digitize the audio (as well as the voltages from your control knobs), individual outputs could drive the LEDs, and a single PWM output could drive your motor (with suitable output buffers, of course).

Consider the simple precision half wave rectifier shown. Let the open loop gain of op-amp be \$A\$.

From the circuit, the voltage at cathode can be calculated as $$V_{anode} = A(V_{in} - V_{cathode})\tag1$$

Now the diode will conduct when $$V_{anode} > V_{cathode} + 0.7V\tag2$$

$$A(V_{in} - V_{cathode}) > V_{cathode} + 0.7V $$ $$V_{in} > \frac{A+1}{A}V_{cathode} + \frac{0.7}{A}$$

For A >> 1, we can write $$V_{in} > V_{cathode} + \frac{0.7}{A}\tag3$$

When the diode conducts, the circuit becomes a voltage follower and \$V_{out}=V_{in}\$. And when the diode does not conduct \$V_{out}=0\$. So the op-amp + diode can be replaced with a diode D1 with cut-in voltage 0.7/A. And as \$A \rightarrow \infty\$, this cut-in voltage \$V_{D_1}\rightarrow 0\$.

^{simulate this circuit – Schematic created using CircuitLab}

Low amplitude voltage can make the precision diode forward biased because of the gain provided by the op-amp. So an ideal operational amplifier can make can make the non-ideal diode an ideal one.

EDIT: (Taken from OP's comment)

So ideally, for \$V_{in} = 0\$, \$V_{out}\$ and the voltage at the output node are both 0, but as soon as \$V_{in}\$ becomes just slightly greater than 0, assuming infinite gain, voltage at the output terminal will overcome \$V_f\$ needed to turn on the diode and the circuit will become a unity gain amplifier.