%__________________________________________________________
%
%??tank_DKiteration.m
%
%??Perform?an?H_infinity/mu?synthesis?design?for?a?process
%??tank?system.???The?main?purpose?of?this?code?is?to
%??demonstrate?the?use?of?the?software?for?robust?H_infinity
%??control?design.
%
%??Requires?version?3.0?（Sept/2004）?of?the?robust?control
%??toolbox.
%
%??Roy?Smith??23/May/2006
%
%__________________________________________________________


%??The?system?consists?of?a?water?tank?with?controlled?hot?and
%??cold?water?inlet?flows.??An?outlet?flow?is?located?at?the
%??bottom?of?the?tank.???The?measured?variables?of?interest
%??are?the?level?and?temperature?of?the?water?in?the?tank.

%??The?tank?system?and?the?perturbation?model?is?described?in:
%
%???“Model?validation?for?robust?control:?an?experimental?process
%???control?application“??Roy?S.?Smith??Automatica?Vol.?31?
%???No.?11?pp.?1637-1647?1995.

%??_________________________________________________________

clear?all

%??Nominal?model:

%??Physical?constants:??（scaled?dimensionless?units）

A1?=?91.4;??????%?tankcross-sectional?area
alpha?=?1.34;???%?exit?flow?gain
beta?=?0.6;?????%?exit?flow?bias
th?=?1.0;???????%?hot?water?temperature
tc?=?0.0;???????%?cold?water?temperature

act_tc?=?0.05;??%?actuator?time?constant

%??Nominal?operating?point:

h1nom?=?0.47;
t1nom?=?0.5;

%??Linearized?model?with?
%?????input?variables:??[fh;?fc]
%?????state?variables:??[E;?f1]
%?????output?variables:?[h1;?t1]

A_tank?=?[-（1+beta/h1nom）/（A1*alpha）?beta*t1nom/（A1*h1nom）;
??????0???-1/（A1*alpha）?];
????
B_tank?=?[th/A1??????????tc/A1;
?????1/（A1*alpha）??1/（A1*alpha）];
???
C_tank?=?[0????????alpha;
?????1/h1nom?-t1nom*alpha/h1nom];

D_tank?=?[0?0;
?????0?0];
???
P_tank?=?ss（A_tankB_tankC_tankD_tank）;

%???Actuator?model.

%???We?use?a?model?of?the?form:??exp（-theta*s）*k/（tau*s?+?1）
%???with??0.8?<=?k?<=?1.2??1.5?<=?tau?<=?2.5?and?0.5?<=?theta?<=?1.0.
%???A?second?order?Pade?approximation?models?the?delay.

s?=?tf（‘s‘）;
P_act?=?（s^2?-?8*s?+?21.3）/（（2*s+1）*（s^2+8*s+21.3））;

%???Examine?the?frequency?response.

omega?=?logspace（-42250）;
P_tank_f?=?frd（P_tankomega）;
P_act_f?=?frd（P_actomega）;

figure（1）
subplot（211）???????????
loglog（abs（P_tank_f（11））abs（P_tank_f（12））...
???????abs（P_tank_f（21））abs（P_tank_f（22））...
???????abs（P_act_f））;
axis（[min（omega）max（omega）1e-510]）
grid
legend（‘h1?<-?fh‘‘h1?<-?fc‘‘t1?<-?fh‘‘t1?<-?fc‘‘P_{act}‘）
xlabel（‘Frequency?[rad/sec]‘）
ylabel（‘Magnitude‘）

r2d?=?180/pi;

subplot（212）
semilogx（r2d*unwrap（angle（P_tank_f（11）））r2d*unwrap（angle（P_tank_f（12）））...
???????r2d*unwrap（angle（P_tank_f（21）））r2d*unwrap（angle（P_tank_f（22）））...
???????r2d*unwrap（angle（P_act_f）））
grid
xlabel（‘Frequency?[rad/sec]‘）
ylabel（‘Phase?[deg]‘）
title（‘Nominal?model‘）

%???--------------?Perturbation?weights?---------------------

%???Actuator?model??（see?Laugh