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Vatsa3322 edited this page Jan 19, 2026 · 3 revisions

Welcome to the Simulation-on-Antenna-Azimuth-Positioning-via-PID-Control-System wiki!

image

The viewpoint for 3D graph[Link for reference]

I Referred Control System Engineering book by Norman S. Nise. All Configuration are taken from his book

Requirements:-

  1. Rotate in Azimuth
  2. Reach desired Angle
  3. Stop exactly at desired angle
  4. Reject disturbances and friction

Objective:- Given a desired angle, rotate antenna smoothly, quickly and accurate to that angle

System Modelling:-

The system is naturally a feedback system, This feedback system tells azimuth position of antenna. Therefore we definitely need feedback mechanism to exactly track the angle. We derive transfer function which tells us about stability, oscillation etc. properties of the systems.

  1. What are the components included, or what does our system is equipped with:

    (i) Two potentiometer are included. One at input and one at output

    (ii) A pre-amplifier, power amplifier, load , motor

    (iii) Block Diagram and Schematic of System(from text book):

    image image

  2. We can reduce motor & load and gears into one one subsystem, by cascading property:

    Motor and Load contant K(m) = (Kt) / Jm*Ra

    Jm = Ja + Jl,

    In our case k(t)=0.5 N-m/A , Ra = 8ohm , Ja = 0.02 kg-m^2 , Jl = 0.01 kg-m^2 , am=1.71

    that gives us km i.e; k(m)=2.083 N-m/A , Jm=0.03 kg-m^2

    Transfer Function for motor and load is (2.083) / s(s+1.71)

    gear constant K(g) is 0.1

    that reduces our overall transfer function to (0.2083) / s(s+1.71)

    K(pot) is 0.318

    pre-amplifier and power amplifier are obtained using Routh-Hurwitz criteria

    K= 31.6 is choose for better output values, but K can range from 0-262

    Now overall transfer function for system reduces to

    T(s) = (6.63 * K) / (s^3 + 101.71s^2 + 171s +6.63 K)

  3. Controller :

    Without Controller , System reach only via plant dynamics, High overshoot, slow settling point.

    Types of Controllers used in Antenna positioning:

    1. PID
    2. State-Feedback(pole placement method)
    3. LQR(Linear Quadratic Regulator)
    4. LQG(Linear Quadratic Gaussian)
    5. Fuzzy Logic Controller
    6. Self-Fuzzy Logic Controller
    7. Discrete PID

  4. How PID Works : PID works on poles, zeros, Time Constants Kp, Ki, Kd

    Proportional (P):

    1. Reacts to current error

    2. Causes High Overshoot

    Integral (I):

    1. Reacts to accumulated error

    2. Eliminate Steady-state error

    3. Can slow system

    Derivative(D):

    1. Reacts for rate for error

    2. Adds Damping to integral

  5. ** Ziegler - Nicholas tuning method:**

    (i) Set Ki and Kd to zero

    (ii) Increase Kp until the system shows sustained oscillations.

    (iv) Record

     Kc :- value at constant amplitude  oscillations 

 Tu :- Time between two consecutive peaks

    (v) Compute PID gains using Z-N formulas

     Kp = 16.4, Ti = 0.15, Td = 0.25, you can follow this [paper](https://www.researchgate.net/publication/326628443_Antenna_Azimuth_Position_Control_System_using_PID_Controller_State-Feedback_Controller_Approach) for reference

You can play with these values, How system response for various input like ramp, sine inputs.

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