Use of symbolix toolbox to derive PI controller Kp,Ki

I'd like try to use Symbolic toolbox to derive closed loop transfer function of control system:

to help design PI controller as of standard 2nd order system compring charasterictic polynomial with that of a standard second order

to get out:

Please advice how to achive it with Symbolic toolbox?

[Jack Daniels]

[Jack Daniels]

to have s^2 clean and with no variable

[Jack Daniels]

How to get out (derive) Kp and Ki?

Answer 1

[Star Strider]

You can get there, however you have to force iit —

syms K_P K_I L R s xi omega_0 real
G_PI = (K_P*s + K_I) / s

G_PI = 

G_RL = 1 / (L*s + R)

G_RL = 

FB = G_PI * G_RL / (1 + G_PI * G_RL)

FB = 

FB = simplify(FB, 500)

FB = 

●

[FBn,FBd] = numden(FB)

FBn = 

FBd = 

LHS = FBd

LHS = 

RHS = s^2 + 2*xi*omega_0*s + omega_0^2

RHS = 

[LHSc,Lsv] = coeffs(LHS,s)

LHSc = 

Lsv = 

LHSc(1)

ans = 

L

LHSc = LHSc / LHSc(1)

LHSc = 

[RHSc,Rsv] = coeffs(RHS,s)

RHSc = 

Rsv = 

K_Psln = isolate(LHSc(2) == RHSc(2), K_P)

K_Psln = 

K_Isln = isolate(LHSc(3) == RHSc(3), K_I)

K_Isln = 

.

[Jack Daniels]

Looks great! I gonna try it:)

BTW you have nice formatted output - do you use a Live editor or other way to have nicely formatted output?

[Star Strider]

Thank you!

I believe the online version (here) uses its version of the Live Editor. (I don’t usually use the Live Editor in my own projects, although sometimes it’s preferable.)

You can get LaTeX formatted results of any symbolic expression using the latex function, however you then have to use a LaTeX interpreter (for example using the text function with Interpreter='LaTeX') to view it correctly.