Predictive Control of 3 DOF Helicopter Using a Kalman and Neural Network Estimator

Abstract

This paper presents the design and simulation of two predictive controllers with different estimators on a 3 DOF helicopter. The work begins with the modeling of the helicopter, obtaining the equations using LaGrange method with a matrix form representation, including viscous friction and assuming a drive-motor with stationary behavior. With the dynamic equations defined, the next step was to obtain the identification of real parameters for the dynamic system. This was carried out using a grey box method applied in a real 3DOF Helicopter prototype built at the university. After verifying the model with the best fit-test, the controller design step begins. To have a comparison point of the advanced controller's performance, a classical PID was tuned. To use the Kalman estimator, a linearization process was achieved and verified with the respective simulation. To get the neural network estimator a NARX type of neural network was used with a layer size of 14 and with 2 delays per input and output. In the design of the MPC controller's the same weights and limitations were assumed, considering the real limitations of the prototype and keeping the reference input near to the linearization point. To get proper evaluation criteria the setting time, overshoot, noise rejection, computational time and ITAE index were the values used to determine the performance for each controller. Simulations were performed on the dynamic system, with step and random steps and tracking-trajectory. According to the obtained data in the step test, the three strategies were able to control the vehicle obtaining negligible differences. In the random step and trajectory tracking test was observed than MPC controller with a neural network estimator gets a better response without noise but, some noise levels were added and the Kalman filter gets a better rejection level. Analyzing the computation time, it was observed that the neural network estimator has the longest simulation times in comparison to the Kalman filter and the classical PID.