Question 1

Control of Drone using Root Locus Tool Considers a quadcopter whose height about the ground is measured using an altimeter. When hovering the motors are maintained at a constant rate, such that thrust force balances the gravity acting on the quadcopter.

Take F(t) to be the amount of additional thrust, and need to make changes in height. The quadcopter weighs 750 grams and has air resistance proportional to 0.3 of its velocity. For each of the four motors, the transfer function between voltage/thrust is given by 0.4. Use the information given to write down the differential equation for the quadcopter, for movement in the vertical direction, and hence the transfer function for f(t)and h(t).

• Plot the unit step response of the quadcopter, for the first 15 seconds.

The quadcopter is fitted with an altimeter that measures the height of the ground.

1. Sketch a diagram of the closed-looped system for the speed control in order to maintain height at a set point, and write down the closed-loop transfer function.

2. Plot the system response.

3. Find the feedback gain that results in a step response that is less than 2% overshoot, and note down the rise time. Provide a plot and state the gain. a. Design a simple controller such that the step response of 2% overshoot is obtained. Note down the rise time, pole positions, and the feedback gain.

Question 2

The quadrotor helicopter shown in Figure la is an example of a real system. The idealized model of the system is shown in Figure lb. As your first task, you are required to obtain:

(a) State-space model for the idealized system

(b) Build a Simulink model for the quadrotor helicopter using state-space equations and

(c) Simulate the built model and record the output. Hint: the system has 3 degrees of freedom, so to model the system, we need 6 state variables.