A family of asymptotically stable control laws for flexible robots based on a passivity approach

A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility

A passivity based control methodology for flexible joint robots with application to a simplified shuttle RMS arm

The main goal is to develop a general theory for the control of flexible robots, including flexible joint robots, flexible link robots, rigid bodies with flexible appendages, etc. As part of the validation, the theory is applied to the control law development for a test example which consists of a three-link arm modeled after the shoulder yaw joint of the space shuttle remote manipulator system (RMS). The performance of the closed loop control system is then compared with the performance of the existing RMS controller to demonstrate the effectiveness of the proposed approach. The theoretical foundation of this new approach to the control of flexible robots is presented and its efficacy is demonstrated through simulation results on the three-link test arm

Guidance of Nonlinear Nonminimum-Phase Dynamic Systems

The first two years research work has advanced the inversion-based guidance theory for: (1) systems with non-hyperbolic internal dynamics; (2) systems with parameter jumps; (3) systems where a redesign of the output trajectory is desired; and (4) the generation of recovery guidance maneuvers

Resource-aware motion control:feedforward, learning, and feedback

Controllers with new sampling schemes improve motion systems’ performanc

Nonlinear system guidance in the presence of transmission zero dynamics

An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples

Feedforward control approach to precision trajectory design and tracking : Theory and application to nano-mechanical property mapping using Scanning Probe Microscope

The output tracking problem has been extensively studied. The linear system case has been addressed by B. A. Francis. (1976) by converting the tracking problem to a regulator problem. Such an approach was later extended to nonlinear systems by A. Isidori. et al. (1990). On the feedforward control side, the stable inversion theory solved the challenging output tracking problem and achieved exact tracking of a given desired output trajectory for nonminimum phase systems (linear and nonlinear). The obtained solution is noncausal and requires the entire desired trajectory to be known a priori. This noncausality constraint has been alleviated through the development of the preview-based inversion approach, which showed the precision tracking can be achieved with a finite preview of the future desired trajectory, and the effect of the limited future trajectory information on output tracking can be quantified. Moreover, optimal scan trajectory design and control method provided a systematic approach to the optimal output-trajectory-design problem, where the output trajectory is repetitive and composed of pre-specified trajectory and unspecified trajectory for transition that returns from ending point to starting point in a given time duration. This dissertation focuses on the development of novel inversion-based feedforward control technique, with applications to output tracking problem with tracking and transition switchings, possibly non-repetitive. The motivate application examples come from atomic force microscope (AFM) imaging and material property measurements. The raster scanning process of AFM and optimal scan trajectory design and control method inspired the repetitive output trajectory tracking problem and attempt to solve in frequency domain. For the output tracking problem, especially for the AFM, there are several issues that have to be addressed. At first, the shape of the desired trajectory must be designed and optimized. Optimal output-trajectory-design problem provided a systematic approach to design the desired trajectory by minimizing the total input energy. However, the drawback is that the desired trajectory becomes very oscillatory when the system dynamics such as the dynamics of the piezoelectric actuator in AFM is lightly damped. Output oscillations need to be small in scanning operations of the AFM. In this dissertation, this problem is addressed through the pre-filter design in the optimal scan trajectory design and tracking framework, so that the trade off between the input energy and the output energy in the optimization is achieved. Secondly, the dissertation addressed the adverse effect of modeling error on the performance of feedforward control. For example, modeling errors can be caused in process of curve fitting. The contribution of this dissertation is the development of novel inversion based feedforward control techniques. Based on the inversion-based iterative learning control (S. Tien. et al. (2005)) technique, the dissertation developed enhanced inversion-based iterative control and the model-less inversion-based iterative control. The convergence of the iterative control law is discussed, and the frequency range of the convergence as well as the effect of the disturbance/noise to signal ratio is quantified. The proposed approach is illustrated by implementing them to high-speed force-distance curve measurements by using atomic force microscope (AFM). Then the control approach is extended to high-speed force-volume mapping. In high-speed force-volume mapping, the proposed approach utilizes the concept of signal decoupling-superimposition and the recently-developed model-less inversion-based iterative control (MIIC) technique. Experiment of force volume mapping on a Polydimethylsiloxane (PDMS) sample is presented to illustrate the proposed approach. The experimental results show that the mapping speed can be increased by over 20 times

Fault tolerant control for nonlinear aircraft based on feedback linearization

The thesis concerns the fault tolerant flight control (FTFC) problem for nonlinear aircraft by making use of analytical redundancy. Considering initially fault-free flight, the feedback linearization theory plays an important role to provide a baseline control approach for de-coupling and stabilizing a non-linear statically unstable aircraft system. Then several reconfigurable control strategies are studied to provide further robust control performance:- A neural network (NN)-based adaption mechanism is used to develop reconfigurable FTFC performance through the combination of a concurrent updated learninglaw. - The combined feedback linearization and NN adaptor FTFC system is further improved through the use of a sliding mode control (SMC) strategy to enhance the convergence of the NN learning adaptor. - An approach to simultaneous estimation of both state and fault signals is incorporated within an active FTFC system.The faults acting independently on the three primary actuators of the nonlinear aircraft are compensated in the control system.The theoretical ideas developed in the thesis have been applied to the nonlinear Machan Unmanned Aerial Vehicle (UAV) system. The simulation results obtained from a tracking control system demonstrate the improved fault tolerant performance for all the presented control schemes, validated under various faults and disturbance scenarios.A Boeing 747 nonlinear benchmark model, developed within the framework of the GARTEUR FM-AG 16 project “fault tolerant flight control systems”,is used for the purpose of further simulation study and testing of the FTFC scheme developed by making the combined use of concurrent learning NN and SMC theory. The simulation results under the given fault scenario show a promising reconfiguration performance