How to write the feedback command here.

hello here my question is that

Use “feedback” command in Matlab to find the closed loop transfer function of the compensated

system.

i know that in feedback command i have to compare the systemA and system B but i am not sure how can i do taht. also how can i write the (s+4) and (s+5) in command because i tried many ways to write them but i am not getting the result.

[Sam Chak]

Hi @Hardik

You can show your code and let's see what can be fixed. I suspect you used the 'zpk' command.

help zpk

 ZPK  Constructs zero-pole-gain model or converts to zero-pole-gain format.
 
   Construction:
     SYS = ZPK(Z,P,K) creates a continuous-time zero-pole-gain (ZPK) model 
     SYS with zeros Z, poles P, and gains K. SYS is an object of class @zpk.
 
     SYS = ZPK(Z,P,K,Ts) creates a discrete-time ZPK model with sampling
     time Ts (set Ts=-1 if the sample time is undetermined).
 
     S = ZPK('s') specifies H(s) = s (Laplace variable).
     Z = ZPK('z',TS) specifies H(z) = z with sample time TS.
     You can then specify ZPK models directly as expressions in S or Z, 
     for example,
        z = zpk('z',0.1);  H = (z+.1)*(z+.2)/(z^2+.6*z+.09)
 
     SYS = ZPK creates an empty zero-pole-gain model.
     SYS = ZPK(D) specifies a static gain matrix D.
 
     You can set additional model properties by using name/value pairs.
     For example,
        sys = zpk(1,2,3,'Variable','p','DisplayFormat','freq')
     also sets the variable and display format. Type "properties(zpk)" 
     for a complete list of model properties, and type 
        help zpk.<PropertyName>
     for help on a particular property. For example, "help zpk.IODelay" 
     provides information about the "IODelay" property.
 
   Data format:
     For SISO models, Z and P are the vectors of zeros and poles (set
     Z=[] when there are no zeros) and K is the scalar gain.
 
     For MIMO systems with NY outputs and NU inputs,
       * Z and P are NY-by-NU cell arrays where Z{i,j} and P{i,j}
         specify the zeros and poles of the transfer function from
         input j to output i
       * K is the 2D matrix of gains for each I/O channel.
     For example,
        H = zpk( {[];[2 3]} , {1;[0 -1]} , [-5;1] )
     specifies the two-output, one-input ZPK model
        [    -5 /(s-1)      ]
        [ (s-2)(s-3)/s(s+1) ]
 
   Arrays of zero-pole-gain models:
     You can create arrays of ZPK models by using ND cell arrays for Z,P
     and a ND double array for K. For example, if Z,P,K are 3D arrays
     of size [NY NU 5], then
        SYS = ZPK(Z,P,K)
     creates the 5-by-1 array of ZPK models
        SYS(:,:,m) = ZPK(Z(:,:,m),P(:,:,m),K(:,:,m)),   m=1:5.
     Each of these models has NY outputs and NU inputs.
 
     To pre-allocate an array of zero ZPK models with NY outputs and NU
     inputs, use the syntax
        SYS = ZPK(ZEROS([NY NU k1 k2...])) .
 
   Conversion:
     SYS = ZPK(SYS) converts any dynamic system SYS to the ZPK
     representation. The resulting SYS is of class @zpk.
 
   See also ZPK/EXP, ZPKDATA, ZPK, SS, FRD, DYNAMICSYSTEM.

    Documentation for zpk
       doc zpk

    Other uses of zpk

       control/zpk              idParametric/zpk    rffilter.rffilter/zpk
       dsp.AllpassFilter/zpk    mpc/zpk             signal/zpk
       DynamicSystem/zpk

Answer 1

[Sam Chak]

Hi @Hardik

These are the basic commands. You can find more examples in the documentations related to commands. Search MathWorks Support or Google for better results related to the Keywords.

s   = tf('s');
G1  = 20/(s + 1)

G1 =
 
   20
  -----
  s + 1
 
Continuous-time transfer function.

G2  = (s + 20)/((s + 2)*(s + 5))

G2 =
 
      s + 20
  --------------
  s^2 + 7 s + 10
 
Continuous-time transfer function.

G12 = series(G1, G2)

G12 =
 
        20 s + 400
  -----------------------
  s^3 + 8 s^2 + 17 s + 10
 
Continuous-time transfer function.

% closed-loop transfer function
Gcl = feedback(G12, 1)

Gcl =
 
         20 s + 400
  ------------------------
  s^3 + 8 s^2 + 37 s + 410
 
Continuous-time transfer function.

pole(Gcl)   % can check eigenvalues

ans = 
  -8.9705 + 0.0000i
   0.4852 + 6.7432i
   0.4852 - 6.7432i

step(Gcl)

% check bode plot to see why the closed-loop system is unstable
margin(G12)