When I try to lower engine rpm by retarding the throttle control to idle the engine speed does not change?

First do a throttle body cleaning. There are many ways to do it. Here is one of them.

https://www.youtube.com/watch?v=Gisr5dK0WDg

What Colorado do you have ? 2 wheel or 4 wheel drive ? Sport ,sport LS 3.5L , Z71, Z71 LS. etc. what size engine ? an does it have electronic throttle control ? I have factory service info an it is not showing that code .
DTC P0506

Circuit Description

The throttle actuator control (TAC) motor is controlled by the powertrain control module (PCM). The DC motor located in the throttle body drives the throttle plate. In order to decrease idle speed, the PCM commands the throttle closed reducing air flow into the engine and the idle speed decreases. In order to increase idle speed, the PCM commands the throttle plate open allowing more air to pass the throttle plate. If the actual idle RPM does not match the desired idle RPM within a calibrated time, this DTC sets.

DTC Descriptor

This diagnostic procedure supports the following DTC:
DTC P0506 Idle Speed Low
DTC P0507

Circuit Description

The throttle actuator control (TAC) motor is controlled by the powertrain control module (PCM). The DC motor located in the throttle body drives the throttle plate. In order to decrease idle speed, the PCM commands the throttle closed reducing air flow into the engine and the idle speed decreases. In order to increase idle speed, the PCM commands the throttle plate open allowing more air to pass the throttle plate. If the actual idle RPM does not match the desired idle RPM within a calibrated time, this DTC sets.

DTC Descriptor

This diagnostic procedure supports the following DTC:
DTC P0507 Idle Speed High
Cleaning the throttle body mite take care of it !
Cleaning Cleaning An Electronic Throttle Body Safely

The idle speed is not supposed to be adjustable. It is controlled by the computer.
What you may have is a vac leak, or the throttle cable may not be adjusted correctly.
If the throttle plate is completely closed, and there are no vac leaks, the idle air control valve is supposed to control idle speed by regulating how much air enters the intake.

Instructions

1. • 1 Park your RSV 1000R on a well-ventilated, level area, using its kickstand.
     
   • 2 Start the engine and let it idle in place until the temperature gauge built into the instrument cluster indicates a minimum internal temperature of 180 degrees Fahrenheit. This is the motorcycle's ideal operating temperature.
     
   • 3 Take note of the engine idle speed, using the tachometer needle, while the engine is running. Ideally, the engine should idle steadily at 1,250 rpm.
     
   • 4 Adjust the engine idle speed to 1,250 rpm, using the idle adjuster screw hidden between the lower right edge of the fuel tank and the upper edge of the right middle fairing panel. Turn the idle adjuster screw clockwise to increase the engine idle speed, or counterclockwise to decrease the engine idle speed, using a small flat screwdriver if your RSV 1000R's frame (VIN number) precedes ZD4MEE009YS000292. A plastic knob allows the engine idle speed to adjusted by hand on RSV 1000R models with a frame (VIN) numbers starting from ZD4MEE009YS000293.
     
   • 5 Rev the engine two to three times and observe the tachometer. The engine should return to a 1,250 rpm idle. Adjust the engine idle speed as needed, using the method described, then rev the engine again. Problems may exist within the throttle control, fuel-injection system or engine, if the engine idle speed will not hold steady at 1,250 rpm. Contact your local Aprilia service facility for assistance.
     
   • 6 Stop the engine, once you have obtained a steady 1,250 rpm idle speed.
     

Engine stalls or RPM fluctuates at idle up and down.

This problem is commonly caused by a dirty automatic idle speed control valve and throttle valve but always run a OBD2 fault code as well as the cleaning procedure. Buy a can of throttle valve cleaner (do not use carburetor spray cleaner!) from NAPA or Carquest (made by CRC chemicals) and spray it into the air intake while the engine is running, use up about 1/2 the can, engine will try to stall hold the speed up, shut it down and let it soak for 30 minutes, restart and blow out the remaining fluid, shut it down and disconnect the negative battery cable for 5 Min's to reset the base idle control

This problem is commonly caused by a dirty automatic idle speed control valve and throttle valve. Buy a can of throttle valve cleaner (do not use carburetor spray cleaner!) from NAPA or Carquest (made by CRC chemicals) and spray it into the air intake while the engine is running, use up about 1/2 the can, engine will try to stall hold the speed up, shut it down and let it soak for 30 minutes, restart and blow out the remaining fluid, shut it down and disconnect the negative battery cable for 5 Min's to reset the base idle control

unfortunately no ! Your best bet take it to the dealer . The P0420 always ends up being the catalytic converter ! P2104 isn't throttle air control . P2112 - Throttle Actuator Control (TAC) System - Stuck Closed. Description: This powertrain control module (PCM) fault status indicates the throttle plate is at a lower angle than commanded. Possible Causes:

• Binding throttle body, stuck closed.
• Damaged PCM.

Diagnostic Aids: Application Key On Engine Off Key On Engine Running Continuous Memory All GO to DV1
P2104 - Throttle Actuator Control (TAC) System - Forced Idle Description: The TAC system is in the failure mode effects management (FMEM) mode of forced idle. Possible Causes:

• Open or short in multiple accelerator pedal position (APP) sensor circuits.
• Damaged APP sensor.
• Damaged powertrain control module (PCM).

Diagnostic Aids: This DTC is an informational DTC and can be set in combination with a number of other DTCs which are causing the FMEM. Diagnose other DTCs first. Application Key On Engine Off Key On Engine Running Continuous Memory All GO to QE1
P0506 - Idle Air Control (IAC) System RPM Lower Than Expected For Vehicles With Electronic Throttle Control (ETC) Description: This DTC is set when the powertrain control module (PCM) detects an engine idle speed that is less than the desired RPM. Possible Causes:

• Air intake restriction.
• Exhaust restriction.
• Engine mechanical fault.
• Damaged electronic throttle body (ETB).
• Damaged PCM.

Diagnostic Aids: This DTC is informational only and it may be accompanied by other DTCs. Diagnose other DTCs first. If other DTCs are not present inspect the intake air system for air restrictions and damage. If no concerns are present, clear the DTC and retest. For All Others Description: This DTC is set when the powertrain control module (PCM) detects an engine idle speed that is less than the desired RPM. Possible Causes:

• IAC circuit open.
• Air inlet is plugged.
• B+ or VPWR to IAC solenoid open.
• Damaged or incorrect IAC valve.
• IAC valve stuck closed.
• VPWR to IAC solenoid open.
• IAC circuit shorted to PWR.

Diagnostic Aids: Disconnect the IAC valve and look for little or no change in engine RPM as an indication of a stuck or damaged valve. Application Key On Engine Off Key On Engine Running Continuous Memory Vehicles With Electronic Throttle Control (ETC) Refer to the Description, Possible Causes and Diagnostic Aids for the DTC. All others GO to KE1

Idle Speed Control (ISC) Motor OPERATION Eagle Throttle Body Fuel Injection (TBI) System NOTE: The Eagle TBI system is used only on 2.5L Premier engines. The Idle Speed Control (ISC) motor is mounted to the throttle body and controlled by the PCM. The throttle lever rests against the initial adjustment screw of the actuator (plunger). The idle speed is not adjustable. The initial adjustment screw is only used to establish the initial positioning of the actuator when the ISC motor has been replaced. The actuator extends or retracts to control engine idle speed and to set throttle stop angle during deceleration. Based on inputs from the various engine control system sensors and switches to the PCM supplies current to the ISC motor to adjust the actuator position for the particular operating conditions.
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P0506 - Idle Air Control (IAC) System RPM Lower Than Expected

What does that mean?
This P0506 code is one that's sometimes triggered on vehicles that have electronic throttle control. That is, they don't have a regular throttle cable from the accelerator pedal to the engine. They rely on sensors and electronics to control the throttle. In this case, the P0506 DTC (diagnostic trouble code) is triggered when the PCM (powertrain control module) detects an engine idle speed that is lower than the desired (pre-programmed) RPM.

Potential Symptoms: Most likely the only thing you'll notice is the idle speed is lower than normal so it will likely be rougher. There are potentially other symptoms as well. Of course, when trouble codes are set, the MIL (malfunction indicator lamp, a.k.a. the check engine light) illuminates.

Causes: A P0506 DTC trouble code may be caused by one or more of the following:
* A vacuum leak
* An air restriction in the intake air path or exhuast
* A faulty positive crankcase ventilation (PCV) valve
* Damaged/failed/dirty throttle body
* Internal engine problem
* Failed PCM

Possible Solutions:
This DTC is more of an informational code, so if there are any other codes set, diagnose them first. If there are no other codes, inspect for vacuum leaks, restrictions, and damage. If there are no symptoms other than the DTC itself, just clear the code and see whether it returns.

Other related DTCs: P0507

The problem is in the idle air control motor. It is mounted on the throttle body with two bolts, you can pull it off and make sure it is not caked with carbon also check where it mounts on the throttle body and make sure it is not caked with carbon.