Static synchronous compensator (STATCOM) is a non-linear system so that the conventional linear output feedback controller with synthesised feedback control cannot guarantee uniform tracking performance, although it improves the stability margin in an inductive operating range. Recently, the input-output linearisation via feedback has been applied to STATCOM and it shows uniform transient performance but owing to lightly damped internal dynamics it results in current ripples in DC-side capacitors. To reduce the ripples, a damping term, time derivative of active current multiplied by a constant gain, was added to the input-output linearisation. This damping controller brings improved internal stability by moving the poles of internal dynamics from the imaginary axis. However, there exists one important limitation that it cannot guarantee stability of internal dynamics at every operating point for some system parameters. A modified non-linear damping controller is proposed to improve the limitation. The proposed method has the damping term with a variable gain, thus provides improved transient performance over the whole operating range. Stability of the closed-loop system is verified by the parameter-dependent Lyapunov function. Owing to the damping term, the exact input-output linearisation is not performed; thus the output is not decoupled from internal dynamics and oscillatory transient response appears. Using the parameter-dependent Lyapunov function, it is also shown that the oscillatory output response is bounded. Improved transient performance in time-domain is validated by simulations with the topological model.

Modified non-linear damping of internal dynamics via feedback linearisation for static synchronous compensator

The past few decades have witnessed a significant research effort in the area of motion control for autonomous robotic vehicles. This paper presents a brief survey related to two topics in this area: i) the design of control systems to drive a vehicle to track a time-parameterized trajectory (trajectory tracking), or to follow a geometric path (path-following); and ii) the problem of making a group of autonomous robotic vehicles follow desired geometric paths while keeping a specified formation pattern (cooperative path-following). From a theoretical standpoint, special attention is given to a number of challenging problems that include the complex and nonlinear vehicle dynamics, uncertainty, disturbances, and when in cooperation, the problem of communication constraints. Illustrative examples using Lyapunov based techniques for motion control design will be presented for wheeled mobile robots, autonomous underwater vehicles, and unmanned aerial vehicles.

Single and multiple motion control of autonomous robotic vehicles

Summary. Among Alberto Isidori’s many seminal contributions, his solution of the nonlinear tracking problem and the underlying concept of zero dynamics have had the widest and strongest impact. Here we use these results to investigate and quantify the limit to tracking performance posed by unstable zero dynamics. While some aspects of this limit are nonlinear analogs of Bode’s T-integral formula, the dependence on the exosystem dynamics is an added complexity of nonlinear tracking.

Jo˜ao P. Hespanha

Papers

Zero Dynamics and Tracking Performance Limits in Nonlinear Feedback Systems