Chapter 9, Problem 38P

Figure P9.5 shows a two-tank system. The liquid inflow to the upper tank can be controlled using a valve and is represented by $F_0$ . The upper tank's outflow equals the lower tank's inflow and is represented by $F_1$ . The outflow of the lower tank is $F_2$ . The objective of the design is to control the liquid level, $y\left(t\right)$ , in the lower tank. The open-loop transmission for this system is $\frac{Y\left(s\right)}{F_0\left(s\right)}=\frac{a_2{a}_3}{s^2+\left(a_1+a_4\right)s+a_1{a}_4}$(Romagnoli, 2006). The system will be controlled in a loop analogous to that of Figure P9.l, where the lower liquid level will be measured and compared to a set point. The resulting error will be fed to a controller, which in turn will open or close the valve feeding the upper tank.

a. Assuming $a_1=0.04,a_2=0.0187,a_3=1$ , and $a_4=0.227$ , design a lag compensator to obtain a step-response steady-state error of 10% without affecting the transient response appreciably.

b. Verify your design through MATLAB simulations.

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