Adaptive Backstepping Controller Design for Stochastic Jump Systems

In this technical note, we improve the results in a paper by Shi et al., in which problems of stochastic stability and sliding mode control for a class of linear continuous-time systems with stochastic jumps were considered. However, the system considered is switching stochastically between different subsystems, the dynamics of the jump system can not stay on each sliding surface of subsystems forever, therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this technical note, the backstepping techniques are adopted to overcome the problem in a paper by Shi et al.. The resulting closed-loop system is bounded in probability. It has been shown that the adaptive control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. A numerical example is given to show the potential of the proposed techniques

Multivariable Super Twisting Based Robust Trajectory Tracking Control for Small Unmanned Helicopter

This paper presents a highly robust trajectory tracking controller for small unmanned helicopter with model uncertainties and external disturbances. First, a simplified dynamic model is developed, where the model uncertainties and external disturbances are treated as compounded disturbances. Then the system is divided into three interconnected subsystems: altitude subsystem, yaw subsystem, and horizontal subsystem. Second, a disturbance observer based controller (DOBC) is designed based upon backstepping and multivariable super twisting control algorithm to obtain robust trajectory tracking property. A sliding mode observer works as an estimator of the compounded disturbances. In order to lessen calculative burden, a first-order exact differentiator is employed to estimate the time derivative of the virtual control. Moreover, proof of the stability of the closed-loop system based on Lyapunov method is given. Finally, simulation results are presented to illustrate the effectiveness and robustness of the proposed flight control scheme

Dynamic modeling and control of a Quadrotor using linear and nonlinear approaches

With the huge advancements in miniature sensors, actuators and processors depending mainly on the Micro and Nano-Electro-Mechanical-Systems (MEMS/NEMS), many researches are now focusing on developing miniature flying vehicles to be used in both research and commercial applications. This thesis work presents a detailed mathematical model for a Vertical Takeo ff and Landing (VTOL) type Unmanned Aerial Vehicle(UAV) known as the quadrotor. The nonlinear dynamic model of the quadrotor is formulated using the Newton-Euler method, the formulated model is detailed including aerodynamic effects and rotor dynamics that are omitted in many literature. The motion of the quadrotor can be divided into two subsystems; a rotational subsystem (attitude and heading) and a translational subsystem (altitude and x and y motion). Although the quadrotor is a 6 DOF underactuated system, the derived rotational subsystem is fully actuated, while the translational subsystem is underactuated. The derivation of the mathematical model is followed by the development of four control approaches to control the altitude, attitude, heading and position of the quadrotor in space. The fi rst approach is based on the linear Proportional-Derivative-Integral (PID) controller. The second control approach is based on the nonlinear Sliding Mode Controller (SMC). The third developed controller is a nonlinear Backstepping controller while the fourth is a Gain Scheduling based PID controller. The parameters and gains of the forementioned controllers were tuned using Genetic Algorithm (GA) technique to improve the systems dynamic response. Simulation based experiments were conducted to evaluate and compare the performance of the four developed control techniques in terms of dynamic performance, stability and the effect of possible disturbances

Adaptive sliding-mode-backstepping trajectory tracking control of underactuated airships

The problem of trajectory tracking control for an underactuated stratospheric airship with model parameter uncertainties and wind disturbances is addressed in the paper. An adaptive backstepping sliding-mode controller is designed from the airship nonlinear dynamics model. The proposed controller has a two-level structure for trajectory guidance, tracking and stability, and the developed controller, based on nonlinear adaptive sliding-mode backstepping method, provides airship attitude and velocity control for the entire flight process. Furthermore, an active set based weighted least square algorithm is applied to find the optimal control surface inputs and the thruster commands under constraints of actuator saturation. The closed-loop system of trajectory tracking control plant is proved to be globally asymptotically stable by using Lyapunov theory. By comparing with traditional backstepping control and PID design, the results obtained demonstrate the capacity of the airship to execute a realistic trajectory tracking mission under two cases of lateral- and roll- underactuations, even in the presence of aerodynamic coefficient uncertainties, and wind disturbances

Output Feedback Controller Design for a Class of MIMO Nonlinear Systems Using High-Order Sliding-Mode Differentiators With Application to a Laboratory 3-D Crane

This paper addresses the problem of output feedback control design for a class of multi-input-multi-output (MIMO) nonlinear systems where the number of inputs is less than that of outputs. There are two difficulties in this design problem: 1) too few control inputs will not generally allow independent control over all outputs and 2) the state of the system is not available for measurements, and only the outputs are available through measurements. To address the first issue, a practical output feedback control problem is formulated, aiming to regulate only part of the outputs, and a controller structure with two design components in all or some chosen control inputs is proposed. To cope with the second difficulty, the recently developed high-order sliding mode differentiators (HOSMDs) are used to estimate the derivatives of the outputs needed in the controller design. With the derivatives estimated using HOSMDs, an output feedback controller is designed using the backstepping approach. Stability results are established for the designed controller under certain conditions. In order to test the applicability of the proposed output feedback controller in practical industrial problems, experiments are carried out though implementing the controller on a laboratory-scale 3-D crane. The experimental results are presented and reveal the advantage of the proposed controller structure, as well as the effect of controller gain and sampling periods

Robust Control Methods for Nonlinear Systems with Uncertain Dynamics and Unknown Control Direction

Robust nonlinear control design strategies using sliding mode control (SMC) and integral SMC (ISMC) are developed, which are capable of achieving reliable and accurate tracking control for systems containing dynamic uncertainty, unmodeled disturbances, and actuator anomalies that result in an unknown and time-varying control direction. In order to ease readability of this dissertation, detailed explanations of the relevant mathematical tools is provided, including stability denitions, Lyapunov-based stability analysis methods, SMC and ISMC fundamentals, and other basic nonlinear control tools. The contributions of the dissertation are three novel control algorithms for three different classes of nonlinear systems: single-input multipleoutput (SIMO) systems, systems with model uncertainty and bounded disturbances, and systems with unknown control direction. Control design for SIMO systems is challenging due to the fact that such systems have fewer actuators than degrees of freedom to control (i.e., they are underactuated systems). While traditional nonlinear control methods can be utilized to design controllers for certain classes of cascaded underactuated systems, more advanced methods are required to develop controllers for parallel systems, which are not in a cascade structure. A novel control technique is proposed in this dissertation, which is shown to achieve asymptotic tracking for dual parallel systems, where a single scalar control input directly affects two subsystems. The result is achieved through an innovative sequential control design algorithm, whereby one of the subsystems is indirectly stabilized via the desired state trajectory that is commanded to the other subsystem. The SIMO system under consideration does not contain uncertainty or disturbances. In dealing with systems containing uncertainty in the dynamic model, a particularly challenging situation occurs when uncertainty exists in the input-multiplicative gain matrix. Moreover, special consideration is required in control design for systems that also include unknown bounded disturbances. To cope with these challenges, a robust continuous controller is developed using an ISMC technique, which achieves asymptotic trajectory tracking for systems with unknown bounded disturbances, while simultaneously compensating for parametric uncertainty in the input gain matrix. The ISMC design is rigorously proven to achieve asymptotic trajectory tracking for a quadrotor system and a synthetic jet actuator (SJA)-based aircraft system. In the ISMC designs, it is assumed that the signs in the uncertain input-multiplicative gain matrix (i.e., the actuator control directions) are known. A much more challenging scenario is encountered in designing controllers for classes of systems, where the uncertainty in the input gain matrix is extreme enough to result in an a priori-unknown control direction. Such a scenario can result when dealing with highly inaccurate dynamic models, unmodeled parameter variations, actuator anomalies, unknown external or internal disturbances, and/or other adversarial operating conditions. To address this challenge, a SMCbased self-recongurable control algorithm is presented, which automatically adjusts for unknown control direction via periodic switching between sliding manifolds that ultimately forces the state to a converging manifold. Rigorous mathematical analyses are presented to prove the theoretical results, and simulation results are provided to demonstrate the effectiveness of the three proposed control algorithms

Quadcopter: Design, modelling, control and trajectory tracking

A quadcopter is a type of unmanned aerial vehicles (UAV). The industry of this type of UAVs is growing exponentially in terms of new technology development and the increase of potential applications that may cover construction inspections, search and rescue, surveillance, aerial photography, monitoring, mapping, etc. A quadcopter is a nonlinear and under-actuated system that introduces complex aerodynamics properties and create challenges which demands the development of new, reliable and effective control techniques to enhance the stability of flight control, plan and track a desired trajectory while minimizing the effect induced by the operational environment and its own sensors. Hence, many control techniques have been developed and researched. Some of such developments work well with the provision of having an accurate mathematical model of the system while other work is associated with a mathematical model that can accommodate certain level of wind disturbances and uncertainties related to measurement noise. Moreover, various linear, nonlinear and intelligent control techniques were developed and recognized in the literature. Each one of such control techniques has some aspect that excels in under certain conditions. The focus of this thesis is to develop different control techniques that can improve flight control stability, trajectory tracking of a quadcopter and evaluate their performance to select the best suitable control technique that can realize the stated technical flight control requirements. Accordingly, three main techniques have been developed: Standard PID, Fuzzy based control technique that tune PID parameters in real time (FPID) and a Hybrid control strategy that consists of three control techniques: (a) FPID with state coordinates transformation (b) State feedback (c) Sliding mode The configuration of the hybrid control strategy consists of two control loops. The inner control loop aims to control the quadcopter\u27s attitude and altitude while the outer control loop aims to control the quadcopter\u27s position. Two configurations were used to configure the developed control techniques of the control loops. These configurations are: (a) A sliding mode control is used for the outer loop while for the inner loop two control techniques are used to realize it: a Fuzzy gain scheduled PID with state coordinates transformation and a state feedback control. (b) Fuzzy gain scheduled PID control is used for the outer loop while for the inner loop two control techniques are used to realize it using the same formation as in (a) above. Furthermore, in order to ensure a feasible desired trajectory before tracking it, a trajectory planning algorithm has been developed and tested successfully. Subsequently, a simulation testing environment with friendly graphical User Interface (GUI) has been developed to simulate the quadcopter mathematical model and then to use it as a test bed to validate the developed control techniques with and without the effect of wind disturbance and measurement noise. The quadcopter with each control technique has been tested using the simulation environment under different operational conditions. The results in terms of tracking a desired trajectory shows the robustness of the first configuration of control techniques within the hybrid control strategy under the presence of wind disturbance and measurement noise compared to all the other techniques developed. Then, the second configuration of the control techniques came second in terms of results quality. The third and fourth results in the sequence shown by the fuzzy scheduled PID and the standard PID respectively. Finally, Validating the simulation results on a real system, a quadcopter has been successfully designed, implemented and tested. The developed control techniques were tested using the implemented quadcopter and the results were demonstrated and compared with the simulation results