MATLAB: How to properly excite state-space models with time-delay using step-function

Control System Toolboxssstate-spacesteptime delay

Hi,

I have constructed the following state-space presentation with a time-delay:

C = pid(1,0.1);
G = tf(2.5,[105 1],'InputDelay',5);
sys = feedback(ss(G),C);
step(sys);

The result is decaying to zero, however the steady state value for a unit step input should be 1 for the given system? Am I missing something here?

Best regards, Aapo Keskimölö

Best Answer

Now I get it, your C PID should be in series with your model G and the feedback is the constant 1

sys=feedback(G*C,1)
step(sys)

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MATLAB: Do state space and its equivalent transfer function models yield different step responses

Hi there,

Examine the state-space model sys_ss:

>> sys_ss

Note that it has a non-unity E matrix. This happens because your H, a pure derivative, is improper. The connect command represents that block as a two-state ss with a non-unity E matrix - a descriptor ss. When connect builds the interconnected system, it preserves those states, so it yields a descriptor system.

And that means that your call to ss2tf, which only uses A,B,C, and D, is missing part of the dynamics of the system. sys_tf doesn't represent the same dynamics as sys_ss.

This is one of the reasons that ss2tf is not a great command to use when converting from ss to tf form. Try this instead:

>> sys_tf = tf(sys_ss)

This time when you plot the step responses, they match up. Also, tf removes those two extra states.

You can also reduce and simplify sys_ss into explicit form (E = 1) using the 'explicit' option of the ss command:

>> sys_ss_ex = ss(sys_ss,'explicit')

Now all of the system dynamics are described by A,B,C, and D.

For more information about explicit and descriptor state-space models, see the reference page for ss.

>> doc ss

Hope this helps!

MATLAB: Pid tunnig with non unity feedback

Try the following approach:

s=tf('s'); %needed to define transfer function in s domain
G=1/3*s+4;H=1/(0.1*s+1); %if feedback is not unity, then it has to be considered in open loop, as G*H
C=pidtune(G*H,'PID',1) 
sys=(C*G)/(1+C*G*H)
step(sys)

Best Answer

Related Solutions

MATLAB: Do state space and its equivalent transfer function models yield different step responses

MATLAB: Pid tunnig with non unity feedback

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