User:DanielMartensson/sandbox

The developments behind this project are built on to work with both MATLAB and GNU Octave.

Matavecontrol is using most of the time built in functions and for-loops to compute transfer functions, state space models and other types of matrices.

GNU Octave and MATLAB share the same basic built in functions such as eig, ode45, inv etc.

• The function are.m is using ode45 to solve Algebraic Riccati Equations
• The function tf.m is using struct and cellarrays to do string handling
• The function lyap.m is using kronecker product to find the solution to the Lyapunov equation
• The function pid.m is creating a transfer function as a PID-controller.
• Matavecontrol is using functions such as "or" and "and" insted of "||" or "&&".

Matavecontrol works with both discrete time models and continuous time models. Control System ToolBox from MathWorks is separating functions depending if it's discrete time or continuous time. For example "dlyap.m" and "lyap.m" or "dare.m" and "care.m".

Matavecontrol has the same name on the functions as Control System ToolBox has. But insted Matavecontrol have included the discrete time and continuous time functions in the same function. Matavecontrol requrie that the user always create a transfer function or a state space model to begin with. That model can then be used in almost all functions.

Here is some examples how to use Matavecontrol.

>> G = tf([1 2], [1 0.4 5], 3) % 3 is the delay - Optional
G =

  scalar structure containing the fields:

    num =

       1   2

    den =

       1.00000   0.40000   5.00000

    delay = 3
    tfnum =  s + 2
    tfdash = ---------------
    tfden =  s^2 + 0.4s + 5
    type = TF
    sampleTime = 0

Creating a state space model.

>> sys = ss(1, [0 1; -2 -3], [0; 1], [1 0], [0]) % Here is the delay 1 a requriment, but C, D are opional
sys =

  scalar structure containing the fields:

    A =

       0   1
      -2  -3

    B =

       0
       1

    C =

       1   0

    D = 0
    delay =  1
    type = SS
    sampleTime = 0

Here is an example how to find the solution to the Algebraic Riccati Equation. In this case, sys, is a continuous model. Which result that are.m choosing the continuous Algebraic Riccati Equation. If sys was discrete, then are.m is choosing discrete Algebraic Riccati Equation.

>> Q = [1 0; 0 1], R = 5
Q =

   1   0
   0   1
  
R = 

   5

>> X = are(sys, Q, R) % Find the solution to Algebraic Riccati Equation
X =

   1.24690   0.24690
   0.24690   0.24690

>>

How to interprent the help text. Here we can se that t should only be a real number such as 10, 11 or 24.2. G symbols a transfer function and sys symbols a state space model.

>> help step

 Simulate continuous time model of a state space model or transfer function
 Input: G, sys, t(optional)
 Example 1: step(G, t)
 Example 2: step(G)
 Example 3: step(sys, t)
 Author: Daniel Mårtensson, 2017 September