**Controller Design and Implementation for Twin Rotor MIMO System [TRMS] using Classical Control Techniques**

This article is focused on design and implementation of a controller, based on mathematical model of Twin Rotor Multi Input Multi Output System (TRMS) using classical control techniques. In developing a classical control system to control a plant, the designer needs to construct a mathematical model of the system. This model contains all the dynamics of the plant that affects controlling it. This type of control is called the Mathematicians approach since the designer must mathematically model the plant to be controlled. The mathematical modelling is done using MATLAB/Simulink. The techniques which we applied include Proportional Integral and Derivative (PID) and Linear Quadratic Regulator (LQR). The TRMS is considered as a prototype model of Helicopter. The aim of studying the TRMS model and designing the controller for TRMS is that it provides a platform for controlling the flight of Helicopter. In this work, the nonlinear model of Twin Rotor MIMO system has been linearized and expressed in state space form. One degree of freedom (1 DOF) as well as Two degree of freedom (2 DOF) dynamic model involving Pitch and Yaw motion has been considered for controller design. The PID tuning is done by trial and error method. The trial and error tuning method is based on guess-and check. The tuning parameters of LQR that is ‘Q’ and ‘R’ are varied randomly to get the desired response. The real time implementation of PID controller has been done and the system was balanced successfully. The result of LQR shows better response as compared to PID controller.

# INTRODUCTION

The twin rotor MIMO system (TRMS) has similarity with helicopter. The Helicopter term is derived from the French word “helicopter” which has link with Greek terms *helix*(spiral) and *pteron *(wing). The TRMS contains a beam with two rotors- the main rotor and tail rotor at ends of the beam. Both the rotors are derived by DC motors. There is a counterbalance at the hinge of the TRMS. TRMS can be defined by two positions (horizontal and vertical) and two angular speeds (horizontal and vertical). The TRMS resembles to a Helicopter in some respects. But there is a key difference between Helicopter and TRMS. Helicopter and TRMS has dissimilarity in their control action. Helicopter flight is controlled by changing both rotor’s angles i.e., angle of attack- which is the angle between chord of airfoil and direction of wind. But, in TRMS controlling is done by varying the speed of both rotors. Lots of work has been done on the modeling, linearizing, and controlling of TRMS.

TRMS controller can be designed by optimal control technique.** **Linear Parameter Varying (LPV) modeling, PID control technique**,** Fuzzy logic control technique** **and several other techniques have been applied on the model and on the controlling of the TRMS dynamics. Considering the nonlinear model of TRMS**,** it is linearized, and state space model has been derived so that we can apply the LQR. The state space representation is done by Jacobian method. PID consists of three tuning parameters- Proportional Kp, Integral Ki and differential Kd to acquire the desired results. PID helps to track the input signal and provides the desired outcome. PID parameters modification is done by trial and error technique. PID controls the horizontal and vertical angles individually as well as both angles simultaneously i.e., 2 DOF control. Linear Quadratic Regulator (LQR) is an optimal controller.** **Ricati equation is used to implement this controller.

# TRMS MODEL

The mathematical equations of TRMS are derived from TRMS physical model shown in Figure, which is extremely nonlinear. It means that there are nonlinear functions in TRMS mathematical equations. The TRMS mathematical model is linearized so that linear control technique can be applied.