Luise Senkel

Interval-Based Sliding Mode Control Design for Solid Oxide Fuel Cells With State and Actuator Constraints

The control design for many practical applications involves a need to specifically treat parameter uncertainty and disturbances. As shown in previous work of the authors, techniques from interval analysis can be used for this purpose in an efficient way. The two options that have been considered so far are the use of interval analysis in either a framework for model predictive control or in a framework for variable-structure sliding mode design. In the latter case, interval techniques can be used efficiently for a robust stabilization of continuous-time dynamic systems despite bounded uncertainty. To avoid unnecessarily conservative control strategies, it has to be shown in real time that the closed-loop control system is guaranteed to remain asymptotically stable despite bounded error variables. This online stability proof is performed on the basis of suitable candidates for Lyapunov functions, whereas functionalities for interval analysis are provided by C++ software libraries. Required partial derivatives, for transformations of state equations into suitable canonical forms and for the estimation of a finite number of time derivatives of the controlled variables, are efficiently computed by algorithmic differentiation. This paper presents an overview of interval-based variable-structure control approaches for the thermal behavior of solid oxide fuel cells. These approaches consist of trajectory tracking during nonstationary heating phases and disturbance compensation at high-temperature operating points. Finally, they rigorously account for state and actuator constraints.

Verified Stability Analysis for Interval-Based Sliding Mode and Predictive Control Procedures with Applications to High-Temperature Fuel Cell Systems

Abstract In previous work, control-oriented models have been derived for solid oxide high-temperature fuel cell systems. In these models, interval variables have been used to describe uncertainty due to a limited knowledge about system parameters and to handle effects of electric load variations on the temperature distribution in the fuel cell stack module as well as bounded measurement uncertainty. To deal with these types of uncertainty both in the design of robust controllers and during their online usage, interval techniques can be employed successfully. These control procedures make use of the basic principles of either sliding mode control or predictive control. The corresponding algorithms and the prerequisites for their real-time capable implementation using software libraries for interval arithmetic and algorithmic differentiation are described in this paper. Experimental results show the efficiency of these control laws for a fuel cell test rig that is available at the Chair of Mechatronics at the University of Rostock.

Sensitivity-Based State and Parameter Estimation for Fuel Cell Systems

Abstract The thermal behavior of high-temperature fuel cell systems is characterized by a large variety of parameters which are not directly accessible for measurements. To derive mathematical models for the dynamics of such systems, it is essential to identify the parameter values on the basis of knowledge about the current operating conditions. After an offline parameter identification with suitable experimental data, the values are further adjusted by online state and parameter estimation. In previous work, various approaches have been employed for the offline parameter identification of fuel cell systems. These approaches include the application of commercial local optimization procedures and novel interval arithmetic routines which aim at a global optimization within a bounded parameter range. Since it could be shown that interval procedures provide system parameterizations with an improved approximation quality, further alternative algorithms are investigated in this paper for the parameter identification of fuel cell systems. These algorithms make use of a sensitivity analysis of suitable performance criteria. These performance criteria can be employed both offline for parameter identification and online for state and disturbance estimation. Numerical results show the advantages of the sensitivity-based procedure in comparison with the above-mentioned estimation approaches.

Experimental validation of a sensitivity-based observer for solid oxide fuel cell systems

Fuel cells can be used to convert the chemical energy of fuel directly into electric energy. The thermodynamic and electrochemical processes involved in such systems are described by a large variety of parameters affecting the system states. These are the temperatures inside the fuel cell stack as well as partial pressures of gases and the electrical voltage. In general, it is not possible to measure all internal system states, disturbances, and parameters. However, knowledge about these quantities is necessary to implement efficient control strategies. Therefore, a novel state and parameter estimation procedure is described in this paper. The goals are the identification of parameters at non-stationary operating points as well as the reconstruction of the internal states of fuel cell systems during the heat-up phase. Using a procedure for sensitivity analysis with a suitable performance criterion, system states and disturbances can be estimated in real-time on a test rig available at the Chair of Mechatronics, University of Rostock. Experimental results show the practical applicability of the above-mentioned method which can be generalized to systems with a variable spatial resolution.

Sensitivity analysis for the design of robust nonlinear control strategies for energy-efficient pressure boosting systems in water supply

To characterize the dynamics of water supply systems in residential and non-residential buildings, it is necessary to develop mathematical models which can be evaluated in real time. For that purpose, generalized network models are applied to represent the dynamics of the water supply system as well as the pump-motor units and hydraulic capacitances, such as storage components, in terms of finite-dimensional models given by ordinary differential equations. The resulting representations are derived from a generalized network model for the water supply system in which both laminar and turbulent flow resistances, storage effects, as well as fluid inertia are modeled by lumped equivalent circuit elements. The corresponding dynamic model is the starting point for a systematic analysis of the overall water supply system with respect to parameter sensitivities. Moreover, this system model is the basis for the implementation of novel nonlinear control approaches which exploit the above-mentioned sensitivities to compensate disturbances in an optimal way.

An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems

Abstract In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finite-dimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance, and parameter estimation techniques. Here, the modeling is based on the method of integrodifferential relations, which can be employed to determine accurate, finite-dimensional sets of state equations by using projection techniques. These lead to a finite element representation of the distributed parameter system. Where applicable, these finite element models are combined with finite volume representations to describe storage variables that are—with good accuracy—homogeneous over sufficiently large space domains. The advantage of this combination is keeping the computational complexity as low as possible. Under these prerequisites, real-time applicable control algorithms are derived and validated via simulation and experiment for a laboratory-scale heat transfer system at the Chair of Mechatronics at the University of Rostock. This benchmark system consists of a metallic rod that is equipped with a finite number of Peltier elements which are used either as distributed control inputs, allowing active cooling and heating, or as spatially distributed disturbance inputs.

Robust Sliding Mode Techniques for Control and State Estimation of Dynamic Systems with Bounded and Stochastic Uncertainty

Bounded and stochastic disturbances form a very important impact on system models in general. The consideration of these in control and observer strategies is a challenge for researchers. The problem is that common control procedures may depend on special properties of the system. Often, procedures for linear system models cannot be used for nonlinear ones. In this contribution, sliding mode techniques are further developed for control and estimation tasks such that the principle procedure is not limited to linear systems. To consider uncertain but bounded parameters and stochastic disturbances simultaneously, intervals are introduced in the resulting stochastic differential equations. Additionally, stability of the presented procedures can be guaranteed by involving the Itˆ o differential operator and linear matrix inequalities to obtain sliding mode strategies for robust control and estimation tasks in combination with interval arithmetic.

Design and experimental validation of control strategies for commercial gas preheating systems

Heating gases with a time-varying mass flow is a common task in many applications in process engineering. Despite the distributed parameter characteristics of gas preheaters, state-of-the-art controllers for such devices rely on the usage of a heuristically tuned PID control structure (proportional, integrating, differentiating) with built-in limitations of the actuator operating range. These actuator constraints are caused by the facts that an active cooling of gases is commonly not possible and that the maximum heating power is typically limited. The same may hold for underlying constraints on the admissible variation rates of the gas temperatures. However, the use of PID controllers may lead to an unsatisfactory control behavior if an application with rapid changes between different operating points is desired. In such cases, actuator constraints may become active if they are not explicitly accounted for by a suitable trajectory planning procedure. The activation of these constraints then leads to an integrator windup with its well-known performance degradation and risk of instability. For this reason, a modelbased anti-windup strategy is presented in this paper, which can be implemented by means of the internal model control principle. It can be used in combination with state feedback controllers in a cascaded architecture to significantly improve the systems capabilities for avoiding an integrator windup and for tracking predefined temperature trajectories which describe a smooth transition between different steady-state operating points.

Interval-based sliding mode observer design for nonlinear systems with bounded measurement and parameter uncertainty

The estimation of non-measurable state variables as well as the reliable identification of unknown system parameters are important prerequisites for the design and implementation of controllers for nonlinear dynamic systems. However, these tasks are often impeded by the nonlinearity of dynamic system models as soon as observer techniques are sought for, which can be used for large operating ranges. Moreover, parameters and measured data are typically only known within given tolerance bounds. Such uncertainty makes the proof of the asymptotic stability of the error dynamics of classical state observers quite difficult. Therefore, a novel interval-based sliding mode observer providing point-valued estimates is presented in this paper which is designed in such a way that asymptotic stability can be guaranteed by means of an online evaluation of a suitable Lyapunov function. Furthermore, an efficient strategy for the adaptation of the switching amplitude of the observers variable structure part is presented to reduce the amplification of measurement noise as far as possible if time-varying state variables and time-invariant system parameters are estimated simultaneously. An illustrative example, describing the longitudinal dynamics of a vehicle, is presented to highlight the practical applicability of the observer.

Optimal input design for online state and parameter estimation using interval sliding mode observers

A huge number of real-life models for dynamic systems in control engineering are characterized by nonlinear behavior. These systems often include both state variables that are not directly measurable and unknown or uncertain parameters. This uncertainty results from a lack of knowledge about specific system parameters, inaccurate measured data, and manufacturing tolerances. Considering these facts, the application of common sliding mode techniques may not be reliable if they are used for a simultaneous estimation of time-varying system states as well as for an online parameter identification. This is often caused by an observer design based on simplified system models that have to satisfy restrictive matching conditions even for exactly known parameters. Therefore, a novel interval sliding mode observer providing point-valued estimates is described in this paper. For an efficient operation, an optimal input design is exploited.