Stefan Koch

Sampled describing function analysis of second order sliding modes

The describing function method is applied to characterize the steady state behavior of the linear sampled data systems stabilized by a second-order sliding mode algorithm. A describing function of the nonlinearity including a sample and hold element is derived. The proposed method allows to predict the amplitude, frequency and phase of occurring limit cycles caused by the discrete time implementation of discontinuous control algorithms. It is shown that the derived describing function is closely related to its classical continuous time counterpart. The proposed approach is demonstrated using a numerical simulation example as well as a real world experiment.

A novel saturated super-twisting algorithm

Abstract In this paper, a feedback control law adopting the super-twisting algorithm is designed such that a continuous and saturated control signal is generated to regulate a first-order system affected by disturbances. For the unperturbed as well as perturbed systems under the proposed control law, global finite-time stability properties are established. In order to indicate the feasibility and effectiveness of the approach, numerical simulations are employed.

Indirect Adaptive Sliding-Mode Control Using the Certainty-Equivalence Principle

A fundamental asset of sliding-mode control is their robustness against unstructured uncertainties. For a successful controller design very little information about the nature of the uncertainty is required. However, in practical control problems often some information about the uncertainty is available. In this case, indirect adaptive control methods may exploit the available information about the uncertainty structure, resulting in powerful adaptation schemes. In this contribution we present a design method that combines these two control concepts. The link is given by the certainty-equivalence approach that relies on the availability of a Lyapunov function for the stabilizing control law. We analyze how various choices of Lyapunov functions impact on our proposed design method. To this end, we briefly review classes of uncertainties that may be handled by various sliding-mode design algorithms. An example serves to illustrate that the violation of these assumptions may yield an unstable closed loop system. We provide an experimental case study that demonstrates the efficiency of the proposed control concept when compared with the conventional super-twisting algorithm.

Model Predictive Temperature Control of a Distribution System for Chemicals

In semiconductor manufacturing tight temperature control of chemicals is crucial for meeting clean application requirements. The use of multiple chemistries as well as various configuration options makes precise temperature control a challenging task. In this paper a generic solution for the temperature control in a single wafer manufacturing machinery for wet-chemical processing based on a model predictive control technique is presented. The developed control strategy is implemented and evaluated on a real world unit with realistic wafer cleaning recipes.

Observer-based saturated output feedback control using twisting algorithm

In this paper, second-order systems in the presence of both uncertainties and disturbances are considered. It is revealed that super-twisting controllers based on high-order sliding mode observers cannot be implemented when uncertainties are taken into account. An output feedback control law adopting the twisting algorithm is designed such that a Lipschitz continuous as well as saturated control signal is introduced to the system. In order to illustrate the feasibility and effectiveness of the proposed approach, numerical simulations are employed.

Discrete implementation of sliding mode controllers satisfying accuracy level specifications

Exploiting a particular system setting, this paper discusses approaches for the design of sliding mode control laws based on a sampling time dependent specified accuracy. It is well-known that this accuracy is ensured by the implementation of a control law of appropriate sliding order. However, it turns out, that in a discrete time framework this also may be achieved by a sliding mode controller of lower order enhanced by a disturbance estimation scheme. In this context the combination of a 2nd-order sliding mode control with a first-order disturbance estimator is analyzed in particular. The achieved performance is evaluated in a numerical example as well as in a practical experiment.