This is a presentation of one useful PC application providing very easy Control System Analysis and Synthesis. It is suitable even for the users with a limited knowledge of the Control System Theory.

1. Control Systems Analyzer and
Synthesizer
Computer Aided Design with CSAS Application

2. General Control System Diagram
First-order system has a typical transfer function:
𝐺𝑃 𝑠 =
𝐾
𝑠𝜏𝑖 1 + 𝑠𝜏
Second-order astatic system has a typical transfer function:
𝐺𝑃 𝑠 =
𝐾
1+𝑠𝜏1 1+𝑠𝜏2
e(t)
Set Point
(reference input)
Controller
Controlled
System
r(t) u(t) y(t)
+
- Output

3. • The second-order system is typical for any continuous process, which
requires a continuous input driving to maintain a desired output level
(temperature, flow, speed).
• The first-order system can represent servomechanism, which require
an input driving only for a limited time period, while a desired output
value (position) is not reached.
• The CSAS software package can automatically detect which type (out
of those two systems) is being analyzed, and its typical parameters,
i.e. the time constants, τ1 and τ2 or τi and τ will be calculated.

4. System Analysis
System Analysis is based on analyzing data stored in the data file (.txt), which the customer has to be
generate from the analyzed system (plant). To do so, to the system has to be applied a known step function at its
input, and the system output values have to be periodically sampled and saved to a text file. Such a way you will
log a transfer function of the open system, which will be very likely a “S” shaped curve as shown below.
Tu Tn t [ms]
G(t)
1.0

5. The proper analysis and interpreting of the time periods Tu and Tn can provide the actual time constants of the
analyzed system. The number of samples should be adequately large, practically 3-5 times more than the “estimated”
time constant (τu + τn) of the system with a total number of samples to be around 1000. As the first value in this data
(text) file should be the step function value (amplitude).

6. When you launch the CSAS application and push the “Data Loading and Analysis” button, a “File dialog” for
selecting a .txt data file will appear. You need to select a folder and then the file, which contains the logged data.
Immediately after the selected data file (.txt) has been opened, CSAS will display the following Window:
At, first, the Window title will show you a type of the analyzed system (Second order system or First order Astatic).

7. The diagram below shows a result of the first-order astatic system analysis. Output of such a system (if running
open, without a closed feedback), would tend to grow forever, which is practically not possible (like in servomechanisms).
In such cases the user should apply a lower step function (let’s say 10%, or even less) and let the system run until the full
output range (100%) is not reached.

8. Closed Loop Control System Synthesis
Once the controlled system parameters are known, the CSAS application can synthetize the closed loop
control system and find the optimal controller parameters. After pressing the “Control System Synthesis” button, the
application will start calculation of all controlling parameters (Kp, Ki, Kd and additional parameters for enhanced
controlling), which should provide an optimal control process of a given system. The PID parameters are selected such a
way, that they will cancel poles of the controlled system, as this can be seen in the following equation describing open
loop transfer function. The first order astatic system synthesis is based on the same idea, just the integral part of the
controller won’t be used.
   
  2
2
1
2
1
2
1
1
s
s
K
s
s
K
K
s
K
K
K
s
G
s
G I
D
I
P
I
p
c



 













Following is the window, which will appear after the “Control System Synthesis” button pressing:

9. The picture above shows the transfer functions of several “variants” of the previously analyzed (second order) system, this
time when running as the closed loop system: Ideal PID, Real PID and Optimal (PID + Feedforward)

10. When the controlled system is a first-order astatic, the closed loop system synthesis ends with a different picture:
As an optimal controller is suggested a “Bang-Bang” (time optimal) control system, consisting of two non-linear blocks.

11. The user can manually adjust all the control parameters by selecting the “Manual Tuning” and to see
immediately results of any parameter change.
For further information about the CSAS application, please contact Peter Galan at: petergalan@rogers.com