Theory of Disturbance Observers: A New Perspective on Inverse Model-based Design

Abstract

The problem of compensating model uncertainty and external disturbance in control systems is one of long-standing and critical issues in academia and industry. Among several promising solutions to the problem, the disturbance observer approach has gained a particular attraction in the literature, due to its structural simplicity and powerful ability. This dissertation presents new theoretical results on the inverse-model based disturbance observers, in order to overcome the limitation of the existing disturbance observer approaches and to address several problems which modern control systems have encountered. Specific subjects dealt with in the dissertation are listed as follows: - The recovery of nominal performance is a key feature of the inverse model-based disturbance observers. It is remarkable that this property is generically an approximation, mainly because structural information of disturbance is not explicitly employed in the disturbance observer design. Motivated by the internal model principle, in the first part of this dissertation we propose a new disturbance observer into which a generating model of disturbance is embedded. Unlike those in the existing works, the proposed disturbance observer achieves asymptotic (rather than approximate) recovery of nominal performance in a sense of input-to-state stability. As a further research in this direction, we also find out that the asymptotic recovery of nominal performance is still possible even without exact knowledge on the frequencies of the sinusoidal disturbance, by realizing the internal model to be embedded in an adaptive fashion with a frequency identifier. - Modern control systems have often experienced not only persistent disturbances and model uncertainty, but also sudden faults of systems and actuators. Even though various fault-tolerant control schemes have been proposed to tackle the problem, guaranteeing satisfactory tracking performance under faults has been not fully studied yet. As another contribution of the dissertation, we propose a disturbance observer-based fault-tolerant controller that guarantees a fault-free tracking performance for the entire period (including the moment when an actuator fault occurs). By reminding that the disturbance observer approach is commonly applied to minimum phase systems, the underlying idea is to redefine a virtual input from the redundant control inputs such that the composite system from the virtual input to the output remains of minimum phase under any actuator faults. This work is in fact an extension of the disturbance observer for a larger class of systems that have more inputs than outputs, while the conventional disturbance observer scheme is mostly designed for square systems (that is, systems that have the same numbers of inputs and outputs). - While a physical plant is a continuous-time system, control schemes are usually implemented in discrete time. The mixture of continuous- and discrete-time components introduces some distinctive characteristics of the sampled-data systems, which possibly incurs unexpected situations when a discrete-time disturbance observer is employed for the sampled-data system. In the dissertation, a theoretical analysis of the discrete-time disturbance observer is newly provided in the sampled-data setting. In particular, by focusing on the limiting behavior of the overall system as the sampling period goes to zero, we obtain a necessary and sufficient condition for the robust stability under fast sampling. One important finding from our approach is that the discrete-time sampling zeros of the sampled-data model may hamper stability (even regardless of model uncertainty) when these zeros are not carefully taken into account in the disturbance observer design. Based on the stability analysis, we also present systematic design guidelines of the discrete-time disturbance observer to satisfy the stability constraint under arbitrarily large (but bounded) model uncertainty, and at the same time to embed a disturbance model (if available) into the discrete-time disturbance observer structure. - With increased interests in these days, the security of cyber-physical systems has been dealt with in the literature from a control-theoretical point of view. In the last part of this dissertation, we address the problem of constructing a robust stealthy attack that compromises uncertain cyber-physical systems having unstable zeros. It has been well known that the conventional zero-dynamics attack, a systematic stealthy attack to non-minimum phase systems, is easily detected as long as (even small) model uncertainty exists. Different from the conventional approach, our key idea is to isolate the real zero-dynamics from the plants input-output relation and to replace it with an auxiliary nominal zero-dynamics

as a result, this alternative attack does not require the exact model knowledge anymore. We show in this dissertation that all this can be realized by the disturbance observer, which now serves as an attack generator. This work explains the underlying principle of destabilizing phenomenon when the inverse model-based disturbance observer is applied to the non-minimum phase plants carelessly.