单片机温度控制英文文献及翻译(3)

the one from Q(s), since we’ll assume constant ambient temperature) can be written

Moreover, it’s not too hard to show that 1=tp1 <1=tz <1=tp2, i.e., that the zero lies between the two poles. Both of these are excellent exercises for the student, and the result is the openloop

pole-zero diagram of Figure 5.

Obtaining a complete thermal model, then, is reduced to identifying the constant K and the three unknown time constants in (3). Four unknown parameters is quite a few, but simple

experiments show that 1=tp1 _ 1=tz;1=tp2 so that tz;tp2 _ 0 are good approximations. Thus the

open-loop system is essentially first-order and can therefore be written

(where the subscript p1 has been dropped).

Simple open-loop step response experiments show that,for a wide range of initial

temperatures and heat inputs, K _0:14 _=W and t _ 295 s.1

4.2 Control System Design

Using the first-order model of (4) for the open-loop transfer function Gaq(s) and assuming for the moment that linear control of the heater power output q(t) is possible, the block diagram of Figure 6 represents the closed-loop system. Td(s) is the desired, or set-point, temperature,C(s) is the compensator transfer function, and Q(s) is the heater output in watts.