【正文】 e it is not plete at this writing software will not be discussed in detail in this paper The control algorithm in particular has not been determined but it is likely to be a simple proportional controller and certainly not more plex than a PID Some control design issues will be discussed in Section 4 however 4 The Design Process Although essentially the project is just to build a thermostat it presents many nice pedagogical opportunities The knowledge and experience base of a senior engineering undergraduate are just enough to bring him or her to the brink of a solution to various aspects of the problem Yet in each case realworld considerations plicate the situation significantly Fortunately these plications are not insurmountable and the result is a very beneficial design experience The remainder of this section looks at a few aspects of the problem which present the type of learning opportunity just described Section 41 discusses some of the features of a simplified mathematical model of the thermal properties of the system and how it can be easily validated experimentally Section 42 describes how realistic control algorithm designs can be arrived at using introductory concepts in control design Section 43 points out some important deficiencies of such a simplified modelingcontrol design process and how they can be overe through simulation 41 Mathematical Model Lumpedelement thermal systems are described in almost any introductory linear control systems text and just this sort of model is applicable to the slide dryer problem Figure 4 shows a secondorder lumpedelement thermal model of the slide dryer The state variables are the temperatures Ta of the air in the box and Tb of the box itself The inputs to the system are the power output q t of the heater and the ambient temperature T ma and mb are the masses of the air and the box respectively and Ca and Cb their specific heats μ1 and μ2 are heat transfer coefficients from the air to the box and from the box to the external world respectively Its not hard to show that the linearized state equations corresponding to Figure 4 are Taking Laplace transforms of 1 and 2 and solving for Ta s which is the output of interest gives the following openloop model of the thermal system where K is a constant and D s is a secondorder polynomialK τz and the coefficients of D s are functions of the various parameters appearing in 1 and 2 Of course the various parameters in 1 and 2 are pletely unknown but its not hard to show that regardless of their values D s has two real zeros Therefore the main transfer function of interest which is the one from Q s since well assume constant ambient temperature can be written Moreover its not too hard to show that 1 τp1 1 τz 1 τp2 ie that the zero lies between the two poles Both of these are excellent exercises for the student and the result is the openloop polezero diagram of Figure 5 Obtaining a plete 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 1tp1 1τ z 1τ p2 so that tztp2 ≈ 0 are good approximations Thus the openloop system is essentially firstorder and can therefore be written where the subscript p1 has been dropped Simple openloop step response experiments show thatfor a wide range of initial temperatures and heat inputs K≈ 014 and T ≈ 295 s 42 Control System Design Using the firstorder model of 4 for the openloop transfer function Gaq s and assuming for the moment that linear control of the heater power out