A process to be controlled has two controlled variables Y1 and Y2, and three inputs that can be used as manipulated variables, U1, U2, and U3. However, it is desired to use only two of these three manipulated variables in a conventional multiloop feedback control system. Transfer functions for the process are shown below. Which multiloop control configuration will 364 Chapter 18 Multiloop and Multivariable Control result in the smallest amount of steady-state interaction between inputs and outputs? Justify your answer. Y (s) = - 3 - U (s) - 0 5 U (s) + 1 U (s) 1 2s + 1 1 (s + 1)(s + 3) 2 s2 + 3s + 2 3 2 4 Y2(s) = -10U1(s) + s + 1 Uz(s) + (s + 1)(3s + 1

Chapter 6 - Power function y=bx^m gives a straight line when plotted on a log-log axis - Exponential function y=be^(mx) also y=b(10)^(mx) gives a straight line when plotted on a semilog plot where the y axis is logarithmic. - Exponential functions never pass through the origin - Power function can pass through origin only if M>0 - P=polyfit(x,y,n) returns n+1 terms - Least square criterion: minimizes the sum of the squares of the residuals (sort of like a line of best fit) - Polyfit is based on the least square method