Apply Your Knowledge 
20.9 To control three controlled variables you need to adjust the minimum of 
Controllability 
20.10 To control three controlled variables, you can adjust a maximum of 
Controllability 
20.11 For the 2x2 system in Figure 20.8, what is true if no interaction exists? 
Interaction 
20.12 For the 2x2 system in Figure 20.8, if all the steadystate gains are nonzero ( K_{ij} <> 0), the system is controllable. 
Controllability 
20.13 The test for controllability (det(K) = 0) is 
Controllability 
20.14 For the process boiling water in the figure, how should the pressure and temperature be controlled 
Controllability 
20.15 The following design will control the pressure and flow of a fluid in a pipe. 
Controllability 
20.16 The following design will control the two flow rates of a fluid in a pipe. 
Controllability 
20.17 The following design is adequate for splitting the two flows 
Controllability 
20.18 The CSTR in Example 13.12 has the steadystate gain matrix below. Which of the multiloop control designs will function correctly, i.e., could yield zerooffset, stable control? 
Interaction
& 
20.19 We want to design controllers for temperature and composition in the nonisothermal CSTR shown below. What is the minimum number of process reaction curve experiments that we must perform? 
Modelling 
20.20 The pressure and temperature can be controlled to independent values by the flash drum control system in the figure. 
Controllability 
