MATLAB: Hi how to solve below eqation in matlab command window in tf command

pid

how to put this below equation in command windows. here s2 means s to the power 2

H(S)=((s2 * Kd )+ (S * Kp) + Ki)/ s2(1+Kp) +s(1 +kp) +Ki

i want to pass numratoe to num and denominator to den varible
finally a=tf(num,den)

Best Answer

The tf function expects the num and den to be matrices that hold the coefficients to the numerator and denominator. In your case it would look like this:

num = [Kd , Kp , Ki];
den = [(1+Kp) , (1+kp) , Ki];
a = tf(num,den)

Related Solutions

MATLAB: How to extract values of Kp, Ki, Kd and D of a PID transfer functio

s=tf('s');
PID=(29.24)+(15.51/s)-(840.334/(s+35))
syms Kp Kd Ki N
NPID_num=[Kp+N*Kd Kp*N+Ki N*Ki];
NPID_den=[1 N 0];
eqn1=PID.Numerator{1}(1)==NPID_num(1);
eqn2=PID.Numerator{1}(2)==NPID_num(2);
eqn3=PID.Numerator{1}(3)==NPID_num(3);
eqn4=PID.Denominator{1}(2)==NPID_den(2);
solx=vpasolve([eqn1 eqn2 eqn3 eqn4]);
Kp=subs(Kp,solx.Kp)
Kd=subs(Kd,solx.Kd)
Ki=subs(Ki,solx.Ki)
N=subs(N,solx.N)

What I did is a simple equation solving. I defined the unknown parameters as symbolic and then obtain the numerical values with the vpasolve function. Note that at the end, the symbolic controller parameters are replaced with their numerical values. After that, in the PID Controller block in Simulink, write Kp, Ki, Kd and N to the parameters repsectively. Hope this helps.

MATLAB: How come m-file and simulink generate different results with same PID controller design

how come there is a delay

It is not a delay. In your model you have the reference signal stepping at 1 second - default value of "Step time" field in Step block. To have the step happen at 0, double-click Step block, and change "Step time" to 0 in block dialog.

and the peak amplitube exceeds 1 that step response generated by m-file doesnt?

The response you see from plot command is correct. The reason why your Simulink model produces a response that look different (the overshoot, not the step time issue addressed above) is because you are using pure derivative block. This is not a good idea, and in real life you never want to differentiate a noisy measurement signal. The recommended approach is to replace a pure derivative s with a derivative plus a lowpass filter: s * N/(s+N). Make N a large number, 1,000, and you will see Simulink model provide essentially the same response as step command.

would also like to know how to tell some characteristics like rise time, settling time from the plot generated by scope?

You cannot do it directly in the scope. The best way would probably be to save the simulation results to worskspace, and then use stepinfo function. You can even include a callback to your model to do this automatically when simulation ends.

Finally, some suggestions on working with PID controllers.

In MATLAB, you can use pid objects. For example, to create the controller you have and plot closed-loop step response:

>>s=tf('s');

>>sys=1/(s^2+10*s+20);

>>C1=pid(350,300,50);

>> C2=pid(350,300,50,0.001); % use lowpass filter for derivative term with N=1,000

>>step(feedback(C1*sys,1)); % plot closed loop step response

>> hold on; step(feedback(C2*sys,1),'r'); %observe essentially unchanged response

In Simulink, use PID Controller block. Parameterize with C2.Kp, C2.Ki, C2.Kd, 1/C2.Tf, and you will see the same response as from step command.

HTH.

Arkadiy

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Related Solutions

MATLAB: How to extract values of Kp, Ki, Kd and D of a PID transfer functio

MATLAB: How come m-file and simulink generate different results with same PID controller design

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