Find the correct state values[A] for a State-Space Modell

Hi,

I'm trying to implement a Regulation on a given System. I am trying to regulate a Temperature with a Lift going up and down in a vat. My task is to generate a modell. I am not quite sure what the States actually are, i was thinking that i have two possible states (too high temperature, too low temperature) or ( Lift too low- lift too high), but like this i cannot really think of what variables i can use for the State-Space Modell. Does somebody maybe have an example of how to fill the Array? Like what values can be used for the [A] State nxn Matrix?

[Sam Chak]

Hi @Marc Hammerschmidt

The states are probably the Temperature , the position and the velocity of the Lift.

To fill the matrices in the linear state-space model, you need to refer to the dynamical equations.

The Temperature should be a first order equation and the motion of the Lift should be a second order equation.

which can be rewrriten as

Please provide them.

Answer 1

[Sayan]

Hi @Marc Hammerschmidt,

I understand from your query that it is required to build a state-space model for a lift system to regulate its speed and temperature. This can be done by determining the parameters that come under consideration while designing the system and finding the states that can completely define the characteristics of the system. You can follow the steps mentioned below.

• If a DC series motor is used to regulate the speed of the lift, the "angular speed" of the motor is one state that is required to define the system.
• The "temperature" is also one state that is required to define the system. You can find the temperature coefficient of the material to determine the temperature change. The datasheet of the motor can be useful to find the relation between rotational speed and its temperature to find the state space equation.
• The "angular position" of the motor can be another state of the state-space system.
• After determining the coefficients of each state in the state-space equation, you can use MATLAB to find the results.
• If you are using a MATLAB script, use the "ss" function to build the system. This is shown in the below code snippet.

sys=ss(A,B,C,D)%Here "A","B","C","D" are the matrices required to implement the state-space model

• If you are using Simulink the State-Space block can be used to implement the state-space model.

Further information on state-space ,"ss" function and "State-Space" block acn be found in the following MATLAB documentation:

1. state-space:https://www.mathworks.com/discovery/state-space.html
2. "ss" function:https://www.mathworks.com/help/releases/R2022a/control/ref/ss.html
3. "State-Space" block:https://www.mathworks.com/help/releases/R2022a/simulink/slref/statespace.html

Hope this helps in answering the query.