Robust adaptive control of uncertain nonlinear systems

Ph.DDOCTOR OF PHILOSOPH

Model-Free Control of an Unmanned Aircraft Quadcopter Type System

A model-free control algorithm based on the sliding mode control method for unmanned aircraft systems is proposed. The mathematical model of the dynamic system is not required to derive the sliding mode control law for this proposed method. The knowledge of the system’s order, state measurements and control input gain matrix shape and bounds are assumed to derive the control law to track the required trajectories. Lyapunov’s Stability criteria is used to ensure closed-loop asymptotic stability and the error estimate between previous control inputs is used to stabilize the system. A smoothing boundary layer is introduced into the system to eliminate the high frequency chattering of the control input and the higher order states. The [B] matrix used in the model-free algorithm based on the sliding mode control is derived for a quadcopter system. A simulation of a quadcopter is built in Simulink and the model-free control algorithm based on sliding mode control is implemented and a PID control law is used to compare the performance of the model-free control algorithm based off of the RMS (Root-Mean-Square) of the difference between the actual state and the desired state as well as average power usage. The model-free algorithm outperformed the PID controller in all simulations with the quadcopter’s original parameters, double the mass, double the moments of inertia, and double both the mass and the moments of inertia while keep both controllers exactly the same for each simulation

Discrete-time sliding mode control based on disturbance observer applied to current control of permanent magnet synchronous motor

This paper proposes a robust current control technique based on a discrete-time sliding mode controller and a disturbance observer for high-performance permanent magnet synchronous motor (PMSM) drives. This scheme is applied in the PMSM current control loops to enable the decoupling between the dq current axes, rejection of disturbances caused by mechanical load changes and robustness under parametric uncertainties. In order to ensure the discrete-time sliding mode properties, which make the system cross the sliding surface at each sampling period, the PMSM model is extended, including the digital implementation delay resulting from the discrete-time algorithm execution. The development of this method allows direct implementation in microcontrollers and digital signal processors. Stability and convergence analysis are developed in the discrete-time domain. Simulation and experimental results demonstrate the effectiveness and good performance of the proposed current control approach

Modelling, identification, and control of a quadrotor helicopter

In this dissertation, we focused on the study of an autonomous flight control of quadrotor helicopter. Robust nonlinear control design strategies using observer-based control are developed, which are capable of achieving reliable and accurate tracking control for quadrotor UAV containing dynamic uncertainties, external disturbances. In order to ease readability of this dissertation, detailed explanations of the mathematical model of quadrotor UAV is provided, including the Newton-Euler formalism, Lyapunov-based stability analysis methods, sliding mode control (SMC) and backstepping fundamentals, and observer-based nonlinear control tools. The tracking control problem of a quadrotor in the presence of model uncertainties and external disturbances is investigated. Particularly, this dissertation presents the design and experimental implementation of nonlinear controller of quadrotor with observer to estimate the uncertainties and external disturbances to meet the desired control objectives. Based on a nonlinear model which considers basic aerodynamic forces and external disturbances, the quadrotor UAV model is simulated to perform a variety of maneuvering such as take-off, landing, smooth translation and horizontal and circular trajectory motions. Backstepping and sliding mode techniques combined with observers are studied, tested and compared. Simulation and a real platform were developed to prove the ability of the observer-based controller to successfully perform certain missions in the presence of unknown external disturbances and can obtain good and satisfactory estimation

A High Order Sliding Mode Control with PID Sliding Surface: Simulation on a Torpedo

Position and speed control of the torpedo present a real problem for the actuators because of the high level of the system non linearity and because of the external disturbances. The non linear systems control is based on several different approaches, among it the sliding mode control. The sliding mode control has proved its effectiveness through the different studies. The advantage that makes such an important approach is its robustness versus the disturbances and the model uncertainties. However, this approach implies a disadvantage which is the chattering phenomenon caused by the discontinuous part of this control and which can have a harmful effect on the actuators. This paper deals with the basic concepts, mathematics, and design aspects of a control for nonlinear systems that make the chattering effect lower. As solution to this problem we will adopt as a starting point the high order sliding mode approaches then the PID sliding surface. Simulation results show that this control strategy can attain excellent control performance with no chattering problem.Comment: 13 pages, 17 figure

Time-Delay Systems

Time delay is very often encountered in various technical systems, such as electric, pneumatic and hydraulic networks, chemical processes, long transmission lines, robotics, etc. The existence of pure time lag, regardless if it is present in the control or/and the state, may cause undesirable system transient response, or even instability. Consequently, the problem of controllability, observability, robustness, optimization, adaptive control, pole placement and particularly stability and robustness stabilization for this class of systems, has been one of the main interests for many scientists and researchers during the last five decades

Development and Implementation of Some Controllers for Performance Enhancement and Effective Utilization of Induction Motor Drive

The technological development in the field of power electronics and DSP technology is rapidly changing the aspect of drive technology. Implementations of advanced control strategies like field oriented control, linearization control, etc. to AC drives with variable voltage, and variable frequency source is possible because of the advent of high modulating frequency PWM inverters. The modeling complexity in the drive system and the subsequent requirement for modern control algorithms are being easily taken care by high computational power, low-cost DSP controllers. The present work is directed to study, design, development, and implementation of various controllers and their comparative evaluations to identify the proper controller for high-performance induction motor (IM) drives. The dynamic modeling for decoupling control of IM is developed by making the flux and torque decoupled. The simulation is carried out in the stationary reference frame with linearized control based on state-space linearization technique. Further, comprehensive and systematic design procedures are derived to tune the PI controllers for both electrical and mechanical subsystems. However, the PI-controller performance is not satisfactory under various disturbances and system uncertainties. Also, precise mathematical model, gain values, and continuous tuning are required for the controller design to obtain high performance. Thus, to overcome these drawbacks, an adapted control strategy based on Adaptive Neuro-Fuzzy Inference System (ANFIS) based controller is developed and implemented in real-time to validate different control strategies. The superiority of the proposed controller is analyzed and is contrasted with the conventional PI controller-based linearized IM drive. The simplified neuro-fuzzy control (NFC) integrates the concept of fuzzy logic and neural network structure like conventional NFC, but it has the advantages of simplicity and improved computational efficiency over conventional NFC as the single input introduced here is an error instead of two inputs error and change in error as in conventional NFC. This structure makes the proposed NFC robust and simple as compared to conventional NFC and thus, can be easily applied to real-time industrial applications. The proposed system incorporated with different control methods is also validated with extensive experimental results using DSP2812. The effectiveness of the proposed method using feedback linearization of IM drive is investigated in simulation as well as in experiment with different working modes. It is evident from the comparative results that the system performance is not deteriorated using proposed simplified NFC as compared to the conventional NFC, rather it shows superior performance over PI-controller-based drive. A hybrid fuel cell (FC) supply system to deliver the power demanded by the feedback linearization (FBL) based IM drive is designed and implemented. The modified simple hybrid neuro-fuzzy sliding-mode control (NFSMC) incorporated with the intuitive FBL substantially reduces torque chattering and improves speed response, giving optimal drive performance under system uncertainties and disturbances. This novel technique also has the benefit of reduced computational burden over conventional NFSMC and thus, suitable for real-time industrial applications. The parameters of the modified NFC is tuned by an adaptive mechanism based on sliding-mode control (SMC). A FC stack with a dc/dc boost converter is considered here as a separate external source during interruption of main supply for maintaining the supply to the motor drive control through the inverter, thereby reducing the burden and average rating of the inverter. A rechargeable battery used as an energy storage supplements the FC during different operating conditions of the drive system. The effectiveness of the proposed method using FC-based linearized IM drive is investigated in simulation, and the efficacy of the proposed controller is validated in real-time. It is evident from the results that the system provides optimal dynamic performance in terms of ripples, overshoot, and settling time responses and is robust in terms of parameters variation and external load

Advanced Computational-Effective Control and Observation Schemes for Constrained Nonlinear Systems

Constraints are one of the most common challenges that must be faced in control systems design. The sources of constraints in engineering applications are several, ranging from actuator saturations to safety restrictions, from imposed operating conditions to trajectory limitations. Their presence cannot be avoided, and their importance grows even more in high performance or hazardous applications. As a consequence, a common strategy to mitigate their negative effect is to oversize the components. This conservative choice could be largely avoided if the controller was designed taking all limitations into account. Similarly, neglecting the constraints in system estimation often leads to suboptimal solutions, which in turn may negatively affect the control effectiveness. Therefore, with the idea of taking a step further towards reliable and sustainable engineering solutions, based on more conscious use of the plants' dynamics, we decide to address in this thesis two fundamental challenges related to constrained control and observation. In the first part of this work, we consider the control of uncertain nonlinear systems with input and state constraints, for which a general approach remains elusive. In this context, we propose a novel closed-form solution based on Explicit Reference Governors and Barrier Lyapunov Functions. Notably, it is shown that adaptive strategies can be embedded in the constrained controller design, thus handling parametric uncertainties that often hinder the resulting performance of constraint-aware techniques. The second part of the thesis deals with the global observation of dynamical systems subject to topological constraints, such as those evolving on Lie groups or homogeneous spaces. Here, general observability analysis tools are overviewed, and the problem of sensorless control of permanent magnets electrical machines is presented as a case of study. Through simulation and experimental results, we demonstrate that the proposed formalism leads to high control performance and simple implementation in embedded digital controllers

Nonlinear control and synchronization of multiple Lagrangian systems with application to tethered formation flight spacecraft

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 217-228).This dissertation focuses on the synchronization of multiple dynamical systems using contraction theory, with applications to cooperative control of multi-agent systems and synchronization of interconnected dynamics such as tethered formation flight. Inspired by stable combinations of biological systems, contraction nonlinear stability theory provides a systematic method to reduce arbitrarily complex systems into simpler elements. One application of oscillation synchronization is a fully decentralized nonlinear control law, which eliminates the need for any inter-satellite communications. We use contraction theory to prove that a nonlinear control law stabilizing a single-tethered spacecraft can also stabilize arbitrarily large circular arrays of tethered spacecraft, as well as a three-spacecraft inline configuration. The convergence result is global and exponential due to the nature of contraction analysis. The proposed decentralized control strategy is further extended to robust adaptive control in order to account for model uncertainties. Numerical simulations and experimental results validate the exponential stability of the tethered formation arrays by implementing a tracking control law derived from the reduced dynamics.(cont.) This thesis also presents a new synchronization framework that can be directly applied to cooperative control of autonomous aerospace vehicles and oscillation synchronization in robotic manipulation and locomotion. We construct a dynamical network of multiple Lagrangian systems by adding diffusive couplings to otherwise freely moving or flying vehicles. The proposed tracking control law synchronizes an arbitrary number of robots into a common trajectory with global exponential convergence. The proposed control law is much simpler than earlier work in terms of both the computational load and the required signals. Furthermore, in contrast with earlier work which used simple double integrator models, the proposed method permits highly nonlinear systems and is further extended to adaptive synchronization, partial-joint coupling, and concurrent synchronization. Another contribution of the dissertation is a novel nonlinear control approach for underactuated tethered formation flight spacecraft. This is motivated by a controllability analysis that indicates that both array resizing and spin-up are fully controllable by the reaction wheels and the tether motor. This work reports the first propellant-free underactuated control results for tethered formation flight.(cont.) We also fulfill the potential of the proposed strategy by providing a new momentum dumping method. This dissertation work has evolved based on the research philosophy of balancing theoretical work with practicality, aiming at physically intuitive algorithms that can be directly implemented in real systems. In order to validate the effectiveness of the decentralized control and estimation framework, a new suite of hardware has been designed and added to the SPHERES (Synchronize Position Hold Engage and Reorient Experimental Satellite) testbed. Such recent improvements described in this dissertation include a new tether reel mechanism, a force-torque sensor and an air-bearing carriage with a reaction wheel. This thesis also introduces a novel relative attitude estimator, in which a series of Kalman filters incorporate the gyro, force-torque sensor and ultrasound ranging measurements. The closed-loop control experiments can be viewed at ...by Soon-Jo Chung.Sc.D

A Model-Free Control Algorithm Based on the Sliding Mode Control Method with Applications to Unmanned Aircraft Systems

Control methods require the use of a system model for the design and tuning of the controllers in meeting and/or exceeding the control system performance objectives. However, system models contain errors and uncertainties that also may be complex to develop and to generalize for a large class of systems such as those for unmanned aircraft systems. In particular, the sliding control method is a superior robust nonlinear control approach due to the direct handling of nonlinearities and uncertainties that can be used in tracking problems for unmanned aircraft system. However, the derivation of the sliding mode control law is tedious since a unique and distinct control law needs to be derived for every individual system and cannot be applied to general systems that may encompass all classifications of unmanned aircraft systems. In this work, a model-free control algorithm based on the sliding mode control method is developed and generalized for all classes of unmanned aircraft systems used in robust tracking control applications. The model-free control algorithm is derived with knowledge of the system’s order, state measurements, and control input gain matrix shape and bounds and is not dependent on a mathematical system model. The derived control law is tested using a high-fidelity simulation of a quadrotor-type unmanned aircraft system and the results are compared to a traditional linear controller for tracking performance and power consumption. Realistic type hardware inputs from joysticks and inertial measurement units were simulated for the analysis. Finally, the model-free control algorithm was implemented on a quadrotor-type unmanned aircraft system testbed used in real flight experimental testing. The experimental tracking performance and power consumption was analyzed and compared to a traditional linear-type controller. Results showed that the model-free approach is superior in tracking performance and power consumption compared to traditional linear-type control strategies