The paper is devoted to a design problem of PID controllers intended to control altitude of a quadcopter. A linearized quadcopter model found in previous study is used for that purpose. Two novel design approaches are utilized to solve this problem. Both methods reduce design procedure to a matrix optimization problem with a quadratic cost function. The first one was proposed for tracking systems design, and the second one – for bounded external disturbance rejection. The designed PID controllers were tested on a real quadcopter during experimental flights.