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Overview Controlled Systems
Table of Contents
ToggleDescripe and classify controlled systems
In order to check and classify the behavior of the controlled systems, the input signal is preferably a voltage change from 0V to 1V. The step response can be used to determine parameters of the controlled system:
![Evaluate step response of controlled system](https://sp-ao.shortpixel.ai/client/to_auto,q_glossy,ret_img,w_254,h_94/https://learnchannel-tv.com/wp-content/uploads/2018/11/Evaluate-step-response-of-controlled-system.png)
Evaluate step response of controlled system
Proportional Controlled systems
Controlled systems with proportional behavior or P-systems have an end value or steady state value and are therefore also referred to as controlled systems. They can be further distinguished in P- systems with and without delay time and dead time:
PT0-system
A controlled system without delay exists when the controlled variable follows the manipulated variable without a measurable time delay and thus suddenly reaches its steady state. In practice, there is practically no pure P-system. Even a transistor has a delay. However, for simplicity, if the time delay is very small or barely measurable, then the reaction can be idealized.
![Step response and symbol PT0-system](https://sp-ao.shortpixel.ai/client/to_auto,q_glossy,ret_img,w_499,h_163/https://learnchannel-tv.com/wp-content/uploads/2018/11/Step-response-and-symbol-PT0-system.png)
Step response and symbol PT0-system
Parameter to describe this system: Transfer coefficient Kps also referred as gain: KPS = Δx/Δy
P-T1-element (1st order system)
The behavior of a single storage element system (1st order system) can be described by an exponential function:
![P-T1-plant (1st order system)](https://sp-ao.shortpixel.ai/client/to_auto,q_glossy,ret_img,w_615,h_279/https://learnchannel-tv.com/wp-content/uploads/2018/11/P-T1-plant-1st-order-system.gif)
P-T1-plant (1st order system)
Parameter: Transfer coefficient Ks , Time constant T
The e-function is described by: x = Ks * y * (1 – e –t/T)
The time constant T is a measure for how fast the steady-state condition can be reached. Graphically it can be determined using the slope tangent at the starting point. This tangent cuts the straight line of the maximum value. Now draw a straight line vertically to the time axis.
The time constant is the time that the controlled value x needs to reach 63,2% of the final value (maximum, steady-state). Practically, the steady-state is reached after about 5T.
Multiple storage element ( P-Tn)
![step response and symbol of PTn system](https://sp-ao.shortpixel.ai/client/to_auto,q_glossy,ret_img,w_605,h_166/https://learnchannel-tv.com/wp-content/uploads/2018/11/step-response-and-symbol-of-PTn-system.png)
step response and symbol of PTn system
If a controlled system has several stages which store energy, then you call it a PTn - system. Here you see an example: A tin bath (PT2-system) consisiting of 2 separate elements: the heating resistors and the tin itself - both elements store energy in form of heat.
![Closed-loop control - Multiple storage element ( P-Tn)](https://sp-ao.shortpixel.ai/client/to_auto,q_glossy,ret_img,w_460,h_171/https://learnchannel-tv.com/wp-content/uploads/2018/11/Closed-loop-control-Multiple-storage-element-P-Tn.png)
Closed-loop control - Multiple storage element ( P-Tn)
How to determine the parameter via the step-response you see here:
![Step response of PTn-system](https://sp-ao.shortpixel.ai/client/to_auto,q_glossy,ret_img,w_416,h_276/https://learnchannel-tv.com/wp-content/uploads/2018/11/Step-response-of-PTn-system.png)
Step response of PTn-system
Parameter: Tg balancing time, Tu delay time