here is a very simple example of AC motor speed control given by changing firing angle of TRIAC with the help of micro controller 89C2051. Varying speed of AC motor by means of changing firing angle of any thyristor is very widely used method. One very nice example is fan regulator in which a fan motor is 1 AC motor used and its speed is varied using DIAC-TRIAC method. Here instead of using DIAC and other components for firing TRIAC here I am using micro controller 89C51 for this purpose.
A zero crossing detector circuit is used here to interrupt 89C2051 after every 10 ms. After getting an interrupt 89C51 will fire TRIAC after some delay from 1 to 9 ms. This will cut the current supplied to motor and so the speed of motor will reduce. Thus by varying the delay after which the TRIAC is triggered one can change the speed of motor.