Asymptotic Stability of Active Disturbance Rejection Control for Linear SISO Plants with Low Observer Gains

This paper theoretically investigates the closed-loop performance of active disturbance rejection control (ADRC) on a third-order linear plant with relative degree 3, subject to a class of exogenous disturbances. While PID control cannot be guaranteed to be capable of stabilizing such plants, ADRC offers a model-free alternative. However, many existing works on ADRC consider the observer gains to be taken arbitrarily large, in order to guarantee desired performance, such as works which consider parameterizing ADRC by bandwidth. This work finds that, for constant exogenous disturbances, arbitrary eigenvalue assignment is possible for the closed-loop system under linear ADRC, thus guaranteeing the existence of an ADRC controller for desired performance without taking any gains arbitrarily large. We also find that stabilization is possible when the exogenous disturbance is stable, and show how ADRC can recover the performance of model-based observers. We demonstrate aspects of the resulting closed-loop systems under ADRC in simulations

Optimized active disturbance rejection control for DC-DC buck converters with uncertainties using a reduced-order GPI observer

The output voltage regulation problem of a PWM- based DC-DC buck converter under various sources of uncertainties and disturbances is investigated in this paper via an optimized active disturbance rejection control (ADRC) approach. Aiming to practical implementation, a new reduced-order generalized proportional integral (GPI) observer is first designed to estimate the lumped (possibly time-varying) disturbances within the DC- DC circuit. By integrating the disturbance estimation information raised by the reduced-order GPI observer (GPIO) into the output prediction, an optimized ADRC method is developed to achieve optimized tracking performance even in the presence of distur- bances and uncertainties. It is shown that the proposed controller will guarantee the rigorous stability of closed-loop system, for any bounded uncertainties of the circuit, by appropriately choosing the observer gains and the bandwidthfactor. Experimental results illustrate that the proposed control solution is characterised by improved robustness performance against various disturbances and uncertainties compared to traditional ADRC and integral MPC approaches

On Vibration Suppression and Trajectory Tracking in Largely Uncertain Torsional System: An Error-based ADRC Approach

In this work, a practically relevant control problem of compensating harmonic uncertainties is tackled. The problem is formulated and solved here using an active disturbance rejection control (ADRC) methodology. A novel, custom ADRC structure is proposed that utilizes an innovative resonant extended state observer (RESO), dedicated to systems subjected to harmonic interferences. In order to make the introduced solution more industry-friendly, the entire observer-centered control topology is additionally restructured into one degree-of-freedom, compact, feedback error-based form (similar to ubiquitous in practice PID controller). Such reorganization enables a straightforward implementation and commission of the proposed technique in wide range of industrial control platforms, thus potentially increasing its outreach. In order to verify the efficiency of the introduced method, a multi-criteria experimental case study using a torsional plant is conducted in a trajectory tracking task, showing satisfactory performance in vibration suppression, without the often problem of noise amplification due to high observer/controller gains. Finally, a frequency analysis and a rigorous stability proof of the proposed control structure are given

Disturbance rejection for nonlinear uncertain systems with output measurement errors: Application to a helicopter model

As a virtual sensor, disturbance observer provides an alternative approach to reconstruct lumped disturbances (including external disturbances and system uncertainties) based upon system states/outputs measured by physical sensors. Not surprisingly, measurement errors bring adverse effects on the control performance and even the stability of the closed-loop system. Toward this end, this paper investigates the problem of disturbance observer based control for a class of disturbed uncertain nonlinear systems in the presence of unknown output measurement errors. Instead of inheriting from the estimation-error-driven structure of Luenberger type observer, the proposed disturbance observer only explicitly uses the control input. It has been proved that the proposed method endows the closed-loop system with strong robustness against output measurement errors and system uncertainties. With rigorous analysis under the semiglobal stability criterion, the guideline of gain choice based upon the proposed structure is provided. To better demonstrate feature and validity of the proposed method, numerical simulation and comparative experiments of a helicopter model are implemented

Practical Solutions to the Non-Minimum Phase and Vibration Problems Under the Disturbance Rejection Paradigm

This dissertation tackles two kinds of control problems under the disturbance rejection paradigm (DRP): 1) the general problem of non-minimum phase (NMP) systems, such as systems with right half plane (RHP) zeros and those with time delay 2) the specific problem of vibration, a prevailing problem facing practicing engineers in the real world of industrial control. It is shown that the DRP brings to the table a refreshingly novel way of thinking in tackling the persistently challenging problems in control. In particular, the problem of NMP has confounded researchers for decades in trying to find a satisfactory solution that is both rigorous and practical. The active disturbance rejection control (ADRC), originated from DRP, provides a potential solution. Even more intriguingly, the DRP provides a new framework to tackle the ubiquitous problem of vibration, whether it is found in the resonant modes in industrial motion control with compliant load, which is almost always the case, or in the microphonics of superconducting radio frequency (SRF) cavities in high energy particle accelerators. That is, whether the vibration is caused by the environment or by the characteristics of process dynamics, DRP provides a single framework under which the problem is better understood and resolved. New solutions are tested and validated in both simulations and experiments, demonstrating the superiority of the new design over the previous ones. For systems with time delay, the stability characteristic of the proposed solution is analyze