Consider the system of Fig. P6.2-4, with D(z) = 1 . Use the results of Problems 6.2-4 and 6.2-5 if available.

(a) Find the system time constant τ for T = 0.6 s .

(b) With the input a step function, find the time required for the system output c(kT) to reach 98 percent of its final value. Note that this time is approximately four time constants (4τ) .

(c) Repeat parts (a) and (b) for T = 6 s .

(d) Repeat parts (a) and (b) for the analog system, that is, for the system with the sampler/data hold removed.

Problem 6.2-4

Shown in Fig. P6.2-4 is the block diagram of a temperature control system for a large test chamber. This
system is described in Problem 1.6-1. Ignore the disturbance input for this problem.

Problem 1.6-1

A thermal test chamber is illustrated in Fig. P1.6-1(a). This chamber, which is a large room, is used to test
large devices under various thermal stresses. The chamber is heated with steam, which is controlled by an
electrically activated valve. The temperature of the chamber is measured by a sensor based on a thermistor,
which is a semiconductor resistor whose resistance varies with temperature. Opening the door into the
chamber affects the chamber temperature and thus must be considered as a disturbance.

Problem 6.2-5

Consider the temperature control system of Problem 6.2-4 and Fig. P6.2-4.
(a) Let T = 5 s, and solve for the response to the input R(s) = 0.2 s-1. Plot this response on the same
graph with the response found in Problem 6.2-4. Note the effects of increasing T from 0.6 s to 6 s, when
the plant has a time constant of 2 s.
(b) Find c(t) for 0 … t … 6 s. This response can be calculated without the use of the z-transform.

Transcribed Image Text:

R(s) T Controller D(z) 1-E-Ts Volts Disturbance Rd(s) S M(s) Volts 1 Chamber 2.5 s+0.5 2 s+0.5 Sensor 0.04 C(s) C