Robust stabilization of 2×22 \times 2 first-order hyperbolic PDEs with uncertain input delay

A backstepping-based compensator design is developed for a system of $2\times2$ first-order linear hyperbolic partial differential equations (PDE) in the presence of an uncertain long input delay at boundary. We introduce a transport PDE to represent the delayed input, which leads to three coupled first-order hyperbolic PDEs. A novel backstepping transformation, composed of two Volterra transformations and an affine Volterra transformation, is introduced for the predictive control design. The resulting kernel equations from the affine Volterra transformation are two coupled first-order PDEs and each with two boundary conditions, which brings challenges to the well-posedness analysis. We solve the challenge by using the method of characteristics and the successive approximation. To analyze the sensitivity of the closed-loop system to uncertain input delay, we introduce a neutral system which captures the control effect resulted from the delay uncertainty. It is proved that the proposed control is robust to small delay variations. Numerical examples illustrate the performance of the proposed compensator

Adaptive Control of Systems with Quantization and Time Delays

This thesis addresses problems relating to tracking control of nonlinear systems in the presence of quantization and time delays. Motivated by the importance in areas such as networked control systems (NCSs) and digital systems, where the use of a communication network in NCS introduces several constraints to the control system, such as the occurrence of quantization and time delays. Quantization and time delays are of both practical and theoretical importance, and the study of systems where these issues arises is thus of great importance. If the system also has parameters that vary or are uncertain, this will make the control problem more complicated. Adaptive control is one tool to handle such system uncertainty. In this thesis, adaptive backstepping control schemes are proposed to handle uncertainties in the system, and to reduce the effects of quantization. Different control problems are considered where quantization is introduced in the control loop, either at the input, the state or both the input and the state. The quantization introduces difficulties in the controller design and stability analysis due to the limited information and nonlinear characteristics, such as discontinuous phenomena. In the thesis, it is analytically shown how the choice of quantization level affects the tracking performance, and how the stability of the closed-loop system equilibrium can be achieved by choosing proper design parameters. In addition, a predictor feedback control scheme is proposed to compensate for a time delay in the system, where the inputs are quantized at the same time. Experiments on a 2-degrees of freedom (DOF) helicopter system demonstrate the different developed control schemes.publishedVersio

Underactuated Source Seeking by Surge Force Tuning: Theory and Boat Experiments

We extend source seeking algorithms, in the absence of position and velocity measurements, and with tuning of the surge input, from velocity-actuated (unicycle) kinematic models to force-actuated generic Euler-Lagrange dynamic underactuated models. In the design and analysis, we employ a symmetric product approximation, averaging, passivity, and partial-state stability theory. The proposed control law requires only real-time measurement of the source signal at the current position of the vehicle and ensures semi-global practical uniform asymptotic stability (SPUAS) with respect to the linear motion coordinates for the closed-loop system. The performance of our source seeker with surge force tuning is illustrated with both numerical simulations and experiments of an underactuated boat

Input shaping-based control schemes for a three dimensional gantry crane

The motion induced sway of oscillatory systems such as gantry cranes may decrease the efficiency of production lines. In this thesis, modelling and development of input shaping-based control schemes for a three dimensional (3D) lab-scaled gantry crane are proposed. Several input shaping schemes are investigated in open and closed-loop systems. The controller performances are investigated in terms of trolley position and sway responses of the 3D crane. Firstly, a new distributed Delay Zero Vibration (DZV) shaper is implemented and compared with Zero Vibration (ZV) shaper and Zero Vibration Derivative (ZVD) shaper. Simulation and experimental results show that all the shapers are able to reduce payload sway significantly while maintaining desired position response specifications. Robustness tests with ±20% error in natural frequency show that DZV shaper exhibits asymmetric robustness behaviour as compared to ZV and ZVD shapers. Secondly, as analytical technique could only provide good performance for linear systems, meta-heuristic based input shaper is proposed to reduce sway of a gantry crane which is a nonlinear system. The results show that designing meta-heuristic-based input shapers provides 30% to 50% improvement as compared to the analytical-based shapers. Subsequently, a particle swarm optimization based optimal performance control scheme is developed in closed-loop system. Simulation and experimental results demonstrate that the controller gives zero overshoot with 60% and 20% improvements in settling time and integrated absolute error value of position response respectively, as compared to a specific designed PID-PID anti swing controller for the lab-scaled gantry crane. It is found that crane control with changing cable length is still a problem to be solved. An adaptive input shaping control scheme that can adapt to variation of cable’s length is developed. Simulation with real crane dimensions and experimental results verify that the controller provides 50% reduction in payload sway for different operational commands with hoisting as compared to the average travel length approach