PID Controller Tuning Optimization with Genetic Algorithms for a Quadcopter

Abstract

Abstract-This paper is focused on the dynamic of mathematical modeling, stability, nonlinear gain control by using Genetic algorithm, utilizing MATLAB tool of a quadcopter. Previously many researchers have been work on several linear controllers such as LQ method; sliding mode and classical PID are used to stabilize the Linear Model. Quadcopter has a nonlinear dynamics and unstable system. In order to maintain their stability, we use nonlinear gain controllers; classical PID controller provides linear gain controller rather than nonlinear gain controller; here we are using modified PID control to improve stability and accuracy. The stability is the state of being resistant to any change. The task is to maintain the quadcopter stability by improving the performance of a PID controller in term of time domain specification. The goal of PID controller design is to determine a set of gains: Kp, Ki, and Kd, so as to improve the transient response and steady state response of a system as: by reducing the overshoot; by shortening the settling time; by decrease the rise time of the system. Modified PID is the combination of classical PID in addition to Genetic Algorithm. Genetic algorithm consists of three steps: selection, crossover, and mutation. By using Genetic algorithm we correct the behavior of quadcopter.

Design of Robust & Predictive Controller for Altitude Stabilization and Trajectory Tracking of a Quad-Copter

“…Newton Euler's method provides the basis to derive the rotational equations in the body frame as [13,14]: Ω is the relative speed of the rotor and i Ω is the angular velocity of i th rotor. The orientation parameters of the quadcopter are approximated and can be found as [1,4]:…”

“…Where 1q U is input for the system hovering and altitude, 2q U , 3q U and 4q U are the inputs for orienting the quadrotor and used for the roll, pitch and the yaw angles of the quadcopter respectively. Equation (11) can be decomposed into acceleration terms and may be written in terms of state variables as given in [1,4]:…”

“…Now the state vector for quadcopter system in general form and system state space representation based on (8) to (10) and (13) to (15) is given in (16) and (17) respectively [1,4,11]:…”

“…In order to have this, few assumptions are made so that quadcopter has stable hovering. As there are no any aero dynamical lifting surfaces therefore aerodynamic moments and forces are assumed to be negligible [1,4,11]. Mathematically, these assumptions are given as below and based on these assumptions the system in (11) may be reduced as given in (18 (18) This equation makes the designing of controller bit easy as well as robustness of the system may also be analyzed.…”

“…Different types of controllers including linear and nonlinear such as Linear Quadratic Regulator, Proportional Integral Derivative, Sliding Mode Controller have been incorporated and being implemented by using a variety of control algorithms to control different characteristics like altitude and attitude of quadcopter's nonlinear dynamical system. The altitude of flying robot was controlled by implementing the adaptive neuro PID controller with genetic algorithm by [3] and also same typed efforts were put by [4] by implementing the PID controller with genetic algorithm to have the nonlinear gain for controlling the altitude of the quadrotor and the mathematical designing and modeling of the dynamic system was also the main focus of this research. Similarly, [5] utilized a modified PID based controller to regulate the attitude factor of the quadrotor by controlling the roll, pitch and yaw angle in the presence of disturbances and also presenting the mathematical model of the nonlinear system.…”