畢業(yè)設(shè)計(jì)單片機(jī)溫度控制英文文獻(xiàn)(編輯修改稿)
2025-01-07 08:17 本頁面
【文章內(nèi)容簡介】 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 output q t is possible the block diagram of Figure 6 represents the closedloop system Td s is the desired or setpoint temperatureC s is the pensator transfer function and Q s is the heater output in watts Given this simple situation introductory linear control design tools such as the root locus method can be used to arrive at a C s which meets the step response requirements on rise time steadystate error and overshoot specified in Table 1 The upshot of course is that a proportional controller with sufficient gain can meet all specifications Overshoot is impossible and increasing gains decreases both steadystate error and rise time Unfortunately sufficient gain to meet the specifications may require larger heat outputs than the heater is capable of producing This was indeed the case for this system and the result is that the rise time specification cannot be met It is quite revealing to the student how useful such an oversimplified model carefully arrived at can be in determining overall performance limitations 43 Simulation Model Gross performance and its limitations can be determined using the simplified model of Figure 6 but there are a number of other aspects of the closedloop system whose effects on performance are not so simply modeled Chief among these are 178。 quantization error in analogtodigital conversion of the measured temperature 178。 the use of PWM to control the heater Both of these are nonlinear and timevarying effects and the only p
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