Using the PID Tuner to read excel data

I am trying to use the PID tuner for this excel sheet to automatically tune this values for less than 20% overshoot I am struggling to find a code to be able to read the imported values from this time series data to tune my controller. Is there anyone that can help provide a code that was used to read the values from this excel sheet for the PID tuner to use?

Answer 1

[Sam Chak]

Hi @Brandon

The PID tuner can only tune single-input, single-output (SISO) linear time-invariant (LTI) dynamical system objects. In the continuous-time domain, LTI systems are described using ordinary differential equations (ODEs) with constant coefficients, but they are often expressed in the form of state-space representation (using matrices). In the frequency domain, SISO LTI systems are described as transfer functions after performing a Laplace transform on the ODEs.

However, the data in the attached .csv file is merely a sequence of measured currents over successive intervals of time. Can we generally derive a complete mathematical model from the raw measured output signal alone? The answer is no! Modeling dynamical systems using a data-driven approach requires knowledge of both input and output signals, as well as the system's structure and parameters.

Measured current signal:

T   = readtable('Controlled Current test.csv', VariableNamingRule="preserve");
x   = T{:,1};
y   = T{:,2};
plot(x, y), grid on
ylim([0, 200])
title('Controlled Current test')
xlabel('Time (s)');
ylabel('Current (amp)');

If you have both input and output signals, you can use the ssest() command from the System Identification Toolbox to estimate a state-space model using time-domain or frequency-domain data.

Example:

% load input/output data
load sdata1 tt1

% estimated number of states
nx  = 4;

% estimate a 4th-order state-space model
sys = ssest(tt1, nx, 'DisturbanceModel', 'none')

sys =
  Continuous-time identified state-space model:
      dx/dt = A x(t) + B u(t) + K e(t)
       y(t) = C x(t) + D u(t) + e(t)
 
  A = 
            x1       x2       x3       x4
   x1  -0.7457   -3.646  -0.2348   -0.748
   x2    5.826   -2.426   -2.445   -2.131
   x3  -0.5061    1.008   0.3814   -23.58
   x4  -0.4342   0.9482    17.45   -1.883
 
  B = 
             u
   x1   0.2455
   x2  -0.4267
   x3  0.05298
   x4  0.08337
 
  C = 
           x1       x2       x3       x4
   y    65.83    31.99    1.339  -0.3672
 
  D = 
      u
   y  0
 
  K = 
       y
   x1  0
   x2  0
   x3  0
   x4  0
 
Parameterization:
   FREE form (all coefficients in A, B, C free).
   Feedthrough: none
   Disturbance component: none
   Number of free coefficients: 24
   Use "idssdata", "getpvec", "getcov" for parameters and their uncertainties.

Status:                                         
Estimated using SSEST on time domain data "tt1".
Fit to estimation data: 70.76%                  
FPE: 1.749, MSE: 1.658                          
 

% compare the simulated model response with the measured output
compare(tt1, sys)

% plot zero initial condition response of the estimated system
figure
step(sys, 5), grid on

% PID controller design
opt = pidtuneOptions('PhaseMargin', 60, 'DesignFocus', 'reference-tracking');
[C, info]  = pidtune(sys, 'PIDF', opt)

C =
 
             1            s    
  Kp + Ki * --- + Kd * --------
             s          Tf*s+1 

  with Kp = 0.266, Ki = 0.709, Kd = 0.0235, Tf = 0.00107
 
Continuous-time PIDF controller in parallel form.

info = struct with fields:
                Stable: 1
    CrossoverFrequency: 8.2095
           PhaseMargin: 60.0000

% closed-loop system
Gcl = minreal(tf(feedback(C*sys, 1)))

Gcl =
 
  From input "u" to output:
      56.82 s^5 + 4270 s^4 + 7.677e04 s^3 + 2.1e06 s^2 + 1.906e07 s + 4.793e07
  --------------------------------------------------------------------------------
  s^6 + 999.7 s^5 + 9096 s^4 + 4.933e05 s^3 + 3.362e06 s^2 + 2.795e07 s + 4.793e07
 
Continuous-time transfer function.

% plot the simulated response of compensated system (not the actual measured signal)
figure
step(Gcl, 5), grid on

stepinfo(Gcl)

ans = struct with fields:
         RiseTime: 0.2046
    TransientTime: 1.6445
     SettlingTime: 1.6445
      SettlingMin: 0.8467
      SettlingMax: 1.0141
        Overshoot: 1.4106
       Undershoot: 0
             Peak: 1.0141
         PeakTime: 0.3981