A boost controller does exactly that, controls your boost level. How, by controlling the amount of manifold pressure getting to the turbo wastegate.
If you wish to increase your boost pressure (typically 7psi), the boost controller must modify the pressure
signal to the wastegate actuator.
There are two types of boost controllers; mechanical and electronic. 
Mechanical (gated) boost controllers  are easy to fit, simple in operation and require little maintenance.
Electronic boost controllers are a far more sophisticated, offering a host of boost settings mapped against different triggers. Electronic boost controllers require 
special fittment and programming. They do give you the ultimate control over the boost curve with  features designed for one thing, that one thing we all want, performance.
This programmable control means that you can increase the performance and response from your engine without raising the boost pressure. Electronic Boost controllers
 also allow the user to control 3 different aspects of the boost curve; maximium boost pressure (set point), spool up rate of the turbocharger (gate pressure) 
and reaction time of the controller (sensitivity).


How does a boost controller work?
There are 2 main parts of a boost control system on a turbo engine: the wastegate with actuator and the boost controller.
As far as waste gates go two types exist internal and external. Internal wastegates are found on the vast majority of turbo cars, where a flap-type valve is built
 into the  turbocharger exhaust housing and is opened by a remote diaphragm actuator. AN external waste gate usually  a poppet-style valve attached directly to
 a diaphragm.
The wastegate does as it name suggestsand wastes the exhaust gas bypassing the turbine wheel and limits the amount of boost. The  actuators
  are controlled by the boost pressure so as boost pressure increases it overcomes the spring pressure and opens the wastegate.
The boost control device is designed to reduce the pressure reaching the actuator, which it does by ‘bleeding off' a specific amount of air from the supply hose.
 This can be done electronically through the ECU by pulsing a solenoid-type valve in the supply hose, or mechanically by placing a ‘controlled leak' in the supply
External Waste Gate

Standard boost control

Without a boost controller, air pressure is fed from the compressed side of the turbo directly to the wastegate actuator via a vacuum hose.
This air pressure can come from anywhere on the intake after the turbo, including after the throttle body.
This air pressure pushes against the force of a spring located in the wastegate actuator this opens the wategate and allows exhaust gas to bypass the turbine wheel.
In this simple configuration the springrate and preload determine the maximum boost.Springs are classified by the boost pressure they typically achieve, such as
a "7 psi spring".

Car Modifications Part

Electronic boot control
Electronic boost control uses a solenoid or a stepper motor controlled by an electronic controller. The principle is still the same as a manual bleed valve, the amount of air pressure applied to the waste gate actuator is controlled or bleed off.
At the component level, boost pressure can either be bled out of the control lines or blocked outright. Either can achieve the goal of reducing pressure pushing against the wastegate. In a bleed-type system air is allowed to pass out of the control lines, reducing the load on the wastegate actuator. On a blocking configuration, air traveling from the charge air supply to the wastegate actuator is blocked while simultaneously bleeding any pressure that has previously built up at the wastegate actuator.
Electronic boost control allows closed loop operation. A closed loop system relies on feedback from the MAP sensor. With an open loop system boost control is determined by inputs like TPS and RPM.
Most systems will be closed loop. The boost control will often be pulse width modulated to control the solenoid opening time. The solenoid contains a needle valve that can respond quickly to requested changes. By varying the pulse width the solenoid is commanded to open for a percentage of the time. This alters the amount of pressure to the wastegate thus controlling boost pressure. 
This level of control allows different boost levels to be achieved at different speeds or in different gears.
Variable geometry turbochargers are a completely different story.

 Variable Vane Turbo

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