So you want to rotate a motor at nearly three times its rated speed. Depending on how well the motor is built, it will fail immediately or later.
Then you build a 200W recitifier. This is the standard Diode Bridge, condensator setup.
And a 200W Pulse width sine generator. The tools for that are listed on Atmels AVR site. They have example code to do just that. You should be able to glean the code from some of the examples on
http://www.atmel.com/dyn/products/app_notes.asp?family_id=607#Application_Example_and_Algorithms
Wouldnt it be cheaper to get a faster motor in the first place?
Assumption: Some mechanism exists to sense RPM, either through an encoder attached to the motor shaft, or via back-emf sensing.
An approach to achieve better results that what the question describes, for low RPM operation of a motor, is to use a PID controller algorithm thus:
- Motor is provided maximum rated power at start-up, as specified in the motor datasheet
- As the RPM sensed approaches the desired set-point, the power is systematically reduced my modifying the triac trigger phase
- Once the RPM set-point is achieved, the PID controller continues to sustain that RPM by increasing or decreasing power to compensate for loading effects
- If load drives the motor to stall, or beyond acceptable power ratings, the controller initiates a controlled fail-safe spin-down of the motor, and also triggers an alarm indication.
From the Wikipedia article linked above, this graph might help explain this process visually:
Depending on the acceptability of overshoots (or not) and desired system behavior, the Proportional (P), Integral (I) and Derivative (D) values of the PID algorithm need to be tuned. The diagram above specifically covers tuning the I value: For absolutely no overshoot of RPM, but with greater time to reach set-point, the red line on the graph shows the preferred behavior, as achieved with a Ki = 0.5.
On the other hand, the black trace, with Ki = 2, achieves (and overshoots) the set-point fastest, and then over/undershoots the set-point in diminishing cycles till it settles down.
There exist excellent motor controller ICs which incorporate both back-EMF sensing (if applicable to your type of motor) and PID controlling, in one package.
Also, assuming the OP has limited experience in designing such systems, off-the-shelf PID controllers for motors are available for a variety of power ratings. These allow a set-point to be interactively set, along with tuning parameters or constraints.
There are also several projects by hobbyists out there, designing and implementing PID AC motor control using microcontrollers or microcontroller boards. For instance, see this YouTube video, for one such Arduino-based PID controller for AC motors.
Links to details are provided in the description text of that video.
Best Answer
No need to scale. You need to limit your PID controller output wit 0% and 99%, and find out what factors work best. There is I*R, all kinds of interference, acceleration, so voltage is not strictly related to speed. Actually sometimes it may seem like there is no relation at all. So you do PI or PID, and tune it. Best practice is to also use SI units everywhere, but not mandatory.
By the way, and this is very important. You must build motion profile. Which in case of velocity control means you have to gradually raise the velocity according to acceleration. Otherwise you will get overshoots and very unstable behavior, or poor control if you will lower your gain to calm system down.