An X-4 quadrotor flyer is designed as a small-sized

Chapter 9, Problem 51

(choose chapter or problem)

An X-4 quadrotor flyer is designed as a small-sized unmanned autonomous vehicle (UAV) that flies mainly indoors and can help in search and recognizance missions. To minimize mechanical problems and for simplicity, this aircraft uses fixed pitch rotors with specially designed blades. Therefore, for thrust it is necessary to add a fifth propeller. A simplified design of the thrust control design can be modeled as in Figure P9.1 with G(s) = \(G_c(s) P(s)\) where

P(s) = \(\frac{1.90978\left(\frac{s}{0.43}+1\right)}{\left(\frac{s}{9.6}+1\right)\left(\frac{s}{0.54}+1\right)}\)

represents the dynamics of the thruster rotor gain, the motor, and the battery dynamics. Initially, the system is designed using a proportional compensator given by \(G_c(s)\) = 3 (Pounds, 2009).

a. Calculate the resulting steady-state error for a unit step input.

b. Design a lag compensator to yield half the steady state error of the proportional compensator, without appreciably affecting the system’s transient response.

c. Use MATLAB to simulate the original design and the lag compensated design. Verify your results.