Auto Tuning Equations
(c) 2009 Delta Computer Systems, Inc. 20091211
In the formulas below
%lambda is the location of the closed loop poles when critically damped
%mu is the location of some of the closed loop poles when over damped
%nu is the output filter frequency
The above values are in radians per second to they must be divided by 2*%pi
to convert to a frequency.
T0P1 PI CD
Calculate the controller gains for a type 0 first order system.
The poles are critically damped.
This solution should only be used when %lambda>=MinLambda.
If not then is OD solution.
| (%i1) |
remvalue(all)$ /* Forget definitions */ Gp: K*%alpha/(s+%alpha); /* System transfer function */ Gc: Ki/s+Kp; /* Simple PI controller */ CLTF: Gc*Gp/(1+Gc*Gp)$ /* Closed loop transfer function */ CE: expand(denom(ratsimp(CLTF)))$ /* Characteristic equation */ DIFCE: expand(CE-(s+%lambda)^2)$ /* %lambda is the desired pole locations */ solve(coeff(DIFCE,s,0),Ki)$ 'Ki=Ki: rhs(%[1]); /* remove from list and use only the rhs */ solve(coeff(DIFCE,s,1),Kp)$ 'Kp=Kp: rhs(%[1]); solve(Kp,%lambda)$ 'MinLambda=rhs(%[1]); |
