1. Analysis of achievable control performance for a heat exchanger
Heat exchanger serves the purpose of transfering heat from one liquid to another: the cooling liquid with flow rate q=1±1 kg/s is used to cool the hot liquid with temperature T0=100±10∘C so that its temperature at the output is T=60±10∘C. Temperature measumement introduces time delay of 3 sec. The variation in the temperature  T0 can be viewed as the major disturbance acting on the system. This is a linear (linearized) model in incremental variables

ΔT(s)=8(60s+1)(12s+1)Δq(s)+0.6(20s+1)(60s+1)(12s+1)ΔT0(s)

Scale the model first. Is it ever possible to control the system with an acceptable performance?

2. Minimization of peaks in sensitivity and complementary sensitivity functions using conventional design methods
For a system with the transfer function

G(s)=s−4(s−1)(0.1s+1)

try to minimize the peaks in sensitivity functions using conventional methods (learnt at previous courses)? Can you go bellow 1.67?

3. Balancing inverted pendulum
Situation: you are balancing a long stick, say, the broom stick, on your palm. First you are trying to balance it watching the far tip of the stick, second you are observing the palm.

G1(s)=−gs2(Mls2−(M+m)g);G2(s)=ls2−gs2(Mls2−(M+m)g)

For specific values of length l=1 m an equal masses of palm and stick M=m, conduct an analysis of this problem as regards bandwidth requirements.

4. Analysis of a suitable control configuration for a Fluidic Catalytic Crack
Based on Skogestad, 2nd ed., Exercise 6.17, page 257. Consider a linear model of a Fluidic Catalytic Crack (FCC) system described by a matrix of transfer functions

⎡⎣⎢⎢y1y2y3⎤⎦⎥⎥=⎡⎣⎢⎢⎢16.8(920s2+32.4s+1)−16.7(75.5s+1)1.27(−939s+1)30.5(52.1s+1)31(75.8s+1)(1.58s+1)54.1(57.3s+1)4.3(7.28s+1)−1.41(74.6s+1)5.4⎤⎦⎥⎥⎥(18.8s+1)(75.8s+1)⎡⎣⎢⎢u1u2u3⎤⎦⎥⎥

Acceptable control systems includes two automatic loops and one manual. The third input is disturbance, hence we have a 2x2 system. Possible variants are

Y1=[y1y2];Y1=[y2y3];Y1=[y1y2−y3]

Which of these three do you prefer? For the one that you chose, perform a thorough analysis of achieveble performance. Why is 3x3 system difficult to control?

Naposledy změněno: středa, 10. května 2017, 17.13