186 SAMPLED-DATA CONTROL SYSTEMS 
which is applied to the plant becomes 
e€(t) = 1.58(0) — 0.416(T) — 0.1538(2T) + 0.118(3T) — 0.0798(47) 
+ a) oe 
It is seen that the sequence applied to the plant never exceeds the speci- 
fied limit of 1.5. The price for this limitation is that the settling time 
has been increased from the minimal value of one sample time to two 
sample times and the digital controller has been made more com- 
plicated by requiring an additional storage. 
7.11 “Bypass” Digital Controllers 
One of the important concerns of the designer of a control system is that 
a failure of a component or controller should not result in damaging failure 
of the entire system. In the language of the designer, systems should 
‘fail safe’? when one or more components fail. As an illustration, a 
chemical process being automatically regulated should be inherently 
stable so that failure of the controller would cause no violent behavior. 
Another good illustration is the piloted aircraft which employs an auto- 
matic pilot. For reasons of safety, the aircraft being controlled is 
designed to be inherently stable so that its open-cycle behavior is accept- 
able. In such a situation, failure of the automatic pilot would merely 
cause a drift off course or a change of altitude, but no major instability. 
In this circumstance, where the automatic pilot has failed, the human 
pilot takes over control of the aircraft. In the other extreme is the guided 
missile, which is entirely automatic and which relies on automatic equip- 
ment to pilot and guide it to its target. In this case, any sacrifices that 
are made to produce an inherently stable missile are misdirected since a 
failure of the automatic equipment would result in a failure tc complete 
its mission. In this case, no direct problem of safety exists and a failure 
resulting in destruction of the missile would be acceptable. 
For that class of systems which lie somewhere between the two extremes 
described, a compromise structure can be devised. If it is assumed that 
a digital controller is not as reliable as straight-through continuous 
instrumentation and data-transfer equipment, a compromise can be 
achieved in which the reliability of the continuous system and the 
improved performance of the digitally controlled system are attained. 
The basic block diagram for such a system is shown in Fig. 7.22, where it 
is seen that the digital controller bypasses or is in parallel with a continu- 
ous connection from the error signal and the plant. The command 
signal to the plant H(z) is the sum of the continuous and digital con- 
troller signals. Thus, if the digital controller becomes inoperative and is 
taken out of service, a continuous closed-loop system remains operative. 
