Controls Theory


Overview


Control theory deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a control model for controlling such systems using a control action in an optimum manner without delay or overshoot and ensuring control stability.

Fundamentally, there are two types of control loops:

  • Open loop control – the control action from the controller is independent of the process output.
  • Closed loop (feedback) control – the control action from the controller is dependent on feedback from the process in the form of the value of the process variable (PV). 

A control system possessing monitoring feedback, the deviation signal formed as a result of this feedback being used to control the action of a final control element in such a way as to tend to reduce the deviation to zero.


Summer Projects


Cruise Controller 


AIM


Designing cruise controller to reach  desired velocity by ​Implementing the concept of PID controller .

  • With constant input velocity .
  • With variable input velocity and constant slope.         

Working in Brief


Dynamics:

1.  If the inertia of the wheels is neglected, and it is assumed that air drag (which is proportional to the car’s speed at low speeds) is what is opposing the motion of the car, along with rolling friction and on a slope downwards gravity, then the problem is reduced to a simple first order system.
2.  The motion of the car can be written as, 

m.vdot + b.v = u
​where,
      a. b is air drag coefficient and
      b. is mass of the car
      c. u is the Input Force provided by the car to move the car at the desired velocity.

PID Tuning of Drone


AIM

Tuning of a 2-D quadcopter model using a PID controller to reach a certain desired setpoint and / or follow a planned trajectory.

Working in Brief :

A planar quadrotor is a simplified case of a general 6-DOF quadrotor that is restricted to the y-z plane.

Additional conditions :

​1. Saturating the controller so that the maximum and the minimum thrust forces allowed are given by maxF and minF respectively.

2. The tuning parameters must give the system a rise time of about 2secs and maximum overshoot of less than 5%.

3. Plot the subplots of z vs t, y vs t and phi vs t.

Controller design:


Software



Concepts used


  •  Laplace transform, transfer functions
  •  Linearization
  •  LTI systems on state space form 

GitHub Repository  : Drone