Is it possible to create a transfer function in Matlab with unknown constants

Is it possible to create a transfer function in Matlab with unknown constants for example:

G = tf([1 2],[4 K 2 T]);

[Dyuman Joshi]

Do you wish to substitute (scalar) values for K and T?

[Askic V]

In general, control system toolbox and tf function doesn't support symbolic variables.

Answer 1

[Walter Roberson]

No.

What is possible is to create control systems with tunable parameters. A tunable parameter always has a specific value at any given time, but the set up allows the parameter to be changed easily and supports automatic tuning procedures.

In order to process with a variable that does not have a specific value then you need to use the symbolic toolbox and laplace transforms.

Answer 2

[Sam Chak]

Hi @Dario

Not exactly sure what you meant by the unknown constants of K and T.

Equivalent state-space model

If they are tunable parameters, then you can create an equivalent state-space model:

K   = 3;                    % parameter 1
T   = 1;                    % parameter 2
A   = [0  1  0;
       0  0  1;
      -T/4 -2/4 -K/4];      % state  matrix
B   = [0; 0; 1];            % input  matrix
C   = [2/4 1/4 0];          % output matrix
D   = 0;                    % direct matrix
sys = ss(A, B, C, D);       % state-space model
G1  = tf(sys)               % convert to transfer function

G1 =
 
          0.25 s + 0.5
  -----------------------------
  s^3 + 0.75 s^2 + 0.5 s + 0.25
 
Continuous-time transfer function.

G   = tf([1 2],[4 K 2 T])   % original transfer function

G =
 
           s + 2
  -----------------------
  4 s^3 + 3 s^2 + 2 s + 1
 
Continuous-time transfer function.

G2  = minreal(G)            % minimal realization of G

G2 =
 
          0.25 s + 0.5
  -----------------------------
  s^3 + 0.75 s^2 + 0.5 s + 0.25
 
Continuous-time transfer function.

It is clear that the state-space that produces has the same transfer function as .

Uncertain systems

If K and T are uncertain parameters with known nominal values, then you can consider this approach:

T    = ureal('T', 1, 'PlusMinus', 0.5);
K    = ureal('K', 3, 'Range', [2, 4]);
usys = tf([1 2], [4 K 2 T])

Uncertain continuous-time state-space model with 1 outputs, 1 inputs, 3 states.
The model uncertainty consists of the following blocks:
  K: Uncertain real, nominal = 3, range = [2,4], 1 occurrences
  T: Uncertain real, nominal = 1, variability = [-0.5,0.5], 1 occurrences

Type "usys.NominalValue" to see the nominal value and "usys.Uncertainty" to interact with the uncertain elements.

bodemag(usys)