Kalman filter based state/model parameter estimation and robust controller design for two degree of freedom helicopter

This thesis presents the implementation of a discrete-time model reference sliding mode controller (MR-SMC) robust to nonlinearity, model uncertainties and disturbances for twin rotor multiple-input multiple-output system (TRMS) with a similar aerodynamic structure to a helicopter in real time experiments. The TRMS system has significant challenges for control applications due to its nonlinearity, multi-input multi-output structure, model uncertainties, significant coupling effect, and the fact that not all states are measured. The dynamic equations of the TRMS system are obtained using the Lagrangian method. The unmeasured states of TRMS are estimated by Kalman-based methods and the performances of Kalman-based methods are compared. In addition, the joint estimation performances of the Kalman-based methods, where state and parameter estimations are made simultaneously, are compared. Finally, the performance of MR-SMC is analysed by simulation and real time studies on the TRMS system. TRMS is a two-degree-of-freedom mechatronic system that can move in horizontal and vertical planes. The system consists of a free beam, a tower, and a balance beam perpendicular to the free beam. The balance beam is placed to stabilize the system, and the behaviour of the system can be changed by changing the position of the weight on it. The free beam is positioned on the tower so that it can move on the horizontal and vertical axis. There are two motors, two propellers, and two protectors at each end of the free beam, perpendicular to each other. The terminal inputs of the motors are the inputs of the system, and the angles between the free beam and the horizontal/vertical axes are the outputs of the system. TRMS has a striking resemblance to a helicopter, although it has fewer degrees of freedom. The thrust generated by the helicopter's propellers is adjusted by changing the angles of the propeller blades. In the TRMS, the propellers have a fixed propeller angle, and the thrust is adjusted by the rotational speed of the propellers. The change in propeller speeds causes the total angular moment of the TRMS system to change and has a more coupling effect than the helicopter due to the conservation of angular momentum. Therefore, TRMS can be considered a complex aircraft. The purpose of control in the TRMS is to move the angles of the free beam with both the horizontal and vertical axis to the desired positions as quickly and accurately as possible. The new control approaches implemented in the TRMS can be extended to helicopters and other related aerodynamic systems. Mathematical models are defined as a set of equations that represent the dynamics of a system as accurately or as possible. A system can be modeled using many different modeling methods and therefore can have many mathematical models depending on the method used. The success of the modeling expressing the dynamics of the system in control system designs significantly affects the success of the control system to be designed. In the modeling, the TRMS system is separated into electrical and mechanical systems and the dynamic equations of the mechanical system are obtained using the Lagrangian approach. System identification is an integral part of system modeling because it increases the accuracy of the mathematical model of a system by using the input and output of a system. Models can be obtained by using only the input and output without knowing the physical model of the system. In this method, called the black box approach, the model structure of the system is lost. When the system is expressed with differential equations obtained using physical laws, the model may contain parameters that cannot be measured or calculated. In such a model, unknown parameters can be estimated by using the input and output quantities of the system and the accuracy of the model can be increased. In this method, called the grey box modeling approach, both the dynamic information of the system is not lost, and the model accuracy of the system is increased with optimization methods. The optimization problem that occurs in system identification has many difficulties such as nonlinearity, multidimensionality, discontinuity and heuristic algorithms provide effective results in solving this optimization problem. In the TRMS model, unknown parameters such as air friction and moment of inertia are estimated offline by minimizing the error between the real system output and the model output using heuristic optimization methods. The parameter estimation performances of particle swarm optimization (PSO) and artificial bee colony (ABC) methods are compared. Since not all states of the TRMS system are measured, a state observer design is required to apply control methods such as sliding mode control, model predictive control and linear quadratic regulator to the TRMS system. In order to estimate the states of the TRMS system, complex-step extended Kalman filter (CS-EKF), finite difference extended Kalman filter (FD-EKF), unscented Kalman filter (UKF) and cubature Kalman filter (CKF) are implemented and compared in terms of computational load and ease of application. Due to the complexity of the TRMS model and the difficulty of obtaining the Jacobian matrix partially, it is difficult to apply the extended Kalman filter (EKF) to the TRMS system. In CS-EKF, the Jacobian matrix is calculated by the complex-step derivative method, which is a numerical differentiation method, and it facilitates the application of EKF to the TRMS. The results show that CS-EKF and UKF have high estimation accuracy, but CS-EKF offers significant advantages in terms of implementation compared to UKF and CKF. Moreover, CS-EKF requires almost one third less computational time than UKF and CKF. The results show that CS-EKF outperforms FD-EKF at small values of step h. In addition, the parameters in the TRMS, which vary according to the operating point, are estimated online with Kalman-based algorithms using the joint estimation method and Kalman based algorithms are compared in terms of speed and accuracy in estimating parameters. In the comparisons made in the simulation where there is no model uncertainty and disturbance effects, it is seen that CS-EKF and FD-EKF estimated the parameters faster and more accurately than UKF and CKF. It was seen that in UKF and CKF algorithms, when Q and R matrices were not selected carefully, they went into instability and diverged from the real states. Despite the model uncertainty and disturbance effects in real-time applications, although CS-EKF, FD-EKF and CKF showed good performance in state and parameter estimation, UKF algorithm also diverged in estimating the outputs and states. Sliding mode controllers (SMC) are widely used in the control of TRMS system because SMC can eliminate the model uncertainties, excessive nonlinearity, coupling effects etc. found in TRMS system. In the controller design, TRMS coupling effects are accepted as disturbing and divided into two as TRMS horizontal axis system and TRMS vertical axis system. MR-SMC controller designs are designed for both systems. Controller design is realized as direct discrete time based. Steady state error occurring in SMC was eliminated by the integrator added to the error dynamics. The integrator added to the error dynamics contribute to the elimination of disturbing and coupling effects. In the simulation and real-time experiments conducted in TRMS 1 DOF horizontal axis, TRMS 1 DOF vertical axis and TRMS 2 DOF systems, despite the uncertainties, external disturbances and nonlinearities in the system, the MR-SMC controller proves its reference signal tracking performance. The steady-state error occurring in the standard SMC is eliminated by the integrator added to the error dynamics. Although the TRMS system is an extremely nonlinear system, the controller response to the step reference signal in different regions as if it is a linear system. Despite the model uncertainty in the vertical axis system, the controller ensured that the vertical axis system followed the reference at the specified performance. The apparent coupling effect in the TRMS 2 DOF system was eliminated by the controllers, and it could be applied to the real-time system without the need for a decoupler design.