Christoph Hametner

Battery Emulation for Power-HIL Using Local Model Networks and Robust Impedance Control

Battery emulation with a controllable high-power dc supply enables repeatable hardware-in-the-loop testing of powertrains for hybrid and electric vehicles. For this purpose, not only the power flow but also the nonlinear characteristic and dynamic impedance of batteries need to be emulated. In this paper, nonlinear local model networks are used to obtain dynamic battery models with high fidelity that can be computed in real time. This approach also allows the extraction of local linear impedance models for high-bandwidth impedance emulation, leading to a tighter coupling between the test bed and simulation model with predictable closed-loop dynamics. A model predictive controller that achieves optimal control with adherence to system constraints is extended to impedance control and robustness against constant power loads. This results not only in superior dynamic performance but also in stable dc-bus voltage control even for testing of tightly controlled electric motor inverters with negative differential input resistance. Since the controller design is based on a model of the test bed setup including the virtual battery model, emulator hardware, and input characteristics of the powertrain under test, it is possible to systematically analyze stability.

Identification of Neurofuzzy Models Using GTLS Parameter Estimation

In this paper, nonlinear system identification utilizing generalized total least squares (GTLS) methodologies in neurofuzzy systems is addressed. The problem involved with the estimation of the local model parameters of neurofuzzy networks is the presence of noise in measured data. When some or all input channels are subject to noise, the GTLS algorithm yields consistent parameter estimates. In addition to the estimation of the parameters, the main challenge in the design of these local model networks is the determination of the region of validity for the local models. The method presented in this paper is based on an expectation-maximization algorithm that uses a residual from the GTLS parameter estimation for proper partitioning. The performance of the resulting nonlinear model with local parameters estimated by weighted GTLS is a product both of the parameter estimation itself and the associated residual used for the partitioning process. The applicability and benefits of the proposed algorithm are demonstrated by means of illustrative examples and an automotive application.

Neuro-Fuzzy Modelling Using a Logistic Discriminant Tree

An algorithm for nonlinear static and dynamic identification using Takagi-Sugeno fuzzy models is presented. For practical applications the incorporation of prior knowledge and the interpretability of the local models is of great interest. Using a tree structured algorithm in combination with the distinction between the input arguments for the consequents and for the premises the nonlinear optimisation is performed in an efficient way. The axis oblique decomposition of the partition space is based on an expectation-maximisation (EM) algorithm. Simulation results demonstrate the capabilities of the proposed concept.

Optimal experiment design based on local model networks and multilayer perceptron networks

This paper addresses the topic of model based design of experiments for the identification of nonlinear dynamic systems. Data driven modeling decisively depends on informative input and output data obtained from experiments. Design of experiments is targeted to generate informative data and to reduce the experimentation effort as much as possible. Furthermore, design of experiments has to comply with constraints on the system inputs and the system output, in order to prevent damage to the real system and to provide stable operational conditions during the experiment. For that purpose a model based approach is chosen for the optimization of excitation signals in this paper. Two different modeling architectures, namely multilayer perceptron networks and local model networks are chosen and the experiment design is based on the optimization of the Fisher information matrix of the associated model architecture. The paper presents and discusses feasible problem formulations and solution approaches for the constrained dynamic design of experiments. In this context the effects of the Fisher information matrix in the static and the dynamic configurations are discussed. The effectiveness of the proposed method is demonstrated on a complex nonlinear dynamic engine simulation model and an analysis as well as a comparison of the presented model architectures for model based experiment design is given.

Total least squares in fuzzy system identification: An application to an industrial engine

Takagi-Sugeno fuzzy models have proved to be a powerful tool for the identification of nonlinear dynamic systems. Their generic nonlinear model representation is particularly useful if information about the structure of the nonlinearity is available. In view of a practical applicability in industrial applications two important issues are addressed. First, the problem of unbiased estimation of local model parameters in the presence of input and output noise is considered. For that purpose the concept of total least squares for parameter estimation is reviewed and a related partitioning algorithm based on statistical criteria is presented. Second, the steady-state accuracy of dynamic models is addressed. A concept of constrained TLS parameter optimisation is introduced which enforces the adherence of the model to selected steady-state operating points and thus significantly improves the model accuracy during steady-state phases. Results from a simulation model and from an industrial gas engine power plant demonstrate the capabilities of the proposed concepts.

Local model network identification for online engine modelling

In this paper an evolving local model network (LMN) which is especially suited for engine modelling is presented and discussed. The incremental construction of the model tree allows to gradually increase the model complexity while a proper initialisation of new model parameters is easily possible when the LMN is extended. Especially in dynamic system identification the computational speed is an important requirement for online training. Therefore, a new evolving optimisation algorithm for the online training of the LMN is proposed which allows for a recursive computation of the model parameters. while the local interpretability of the consequent parameters is conserved. The decision when to grow the tree is based on an effective statistical criterion. The proposed concepts are validated by means of an illustrative example and by real dynamic measurement data from a state-of-the-art 4-cylinder EURO5 diesel engine.

New Concepts for the Identification of Dynamic Takagi-Sugeno Fuzzy Models

Takagi-Sugeno fuzzy models have proved to be a powerful tool for the identification of nonlinear dynamic systems. Recent publications have addressed the problems of local versus global accuracy and the identifiability and interpretability of local models as true linearisations. The latter issue particularly concerns off-equilibrium models. Well-established solution approaches involve techniques like regularisation and multi-objective optimisation. In view of a practical application of these models by inexperienced users this paper addresses the following issues: 1) unbiased estimation of local model parameters in the presence of input- and output noise. At the same time the dominance of the trend term in off-equilibrium models is balanced. 2) The concept of stationary constraints is introduced. They help to significantly improve the accuracy of equilibrium models during steady-state phases. A simulation model demonstrates the capabilities of the proposed concepts

PID controller design for nonlinear systems represented by discrete-time local model networks

This paper deals with proportional–integral–derivative (PID) controller design for nonlinear systems represented by local model networks. The proposed method is based on the concept of parallel distributed compensators where the scheduling of the local model network is adopted for the PID parameters. The proposed design method for nonlinear PID controllers considers closed-loop stability by means of a Lyapunov stability criterion as well as closed-loop performance. All PID parameters are determined by a multi-objective genetic algorithm (multiGA), which handles the trade-off between stability and performance. A simulation example demonstrates the effectiveness of the proposed method.

Combustion engine modelling using an evolving local model network

In this paper a new evolving parameter estimation algorithm for a local model network under special consideration of combustion engine modelling is presented. For practical applications computational speed, incorporation of prior knowledge and the interpretability of the local models is of great interest. Accordingly, a robust and efficient online training algorithm with a particular focus on computational requirements involved in dynamic system identification of complex nonlinear processes is presented. The incremental construction of the model tree allows to gradually increase the model complexity while a proper initialisation of new model parameters is easily possible. The proposed evolving local model network is validated using real measurement data from a state-of-the-art 4-cylinder EURO5 diesel engine.

Piecewise Quadratic stability analysis for local model networks

This paper deals with the problem of stability analysis of dynamic local model networks. Established methods in this context are mainly based on Lyapunov stability theory and are targeted to be as little conservative as possible. In previous works the so called Piecewise Quadratic Lyapunov approach was developed. For discrete time systems the state space is partitioned into local subspaces, which are defined by the validity functions of the local models. Because of the overlapping validity functions, so-called uncertainty terms exist which describe the influence of the dynamics of other local models. In this respect, it is necessary to pay attention to the determination of these uncertainty terms. This paper presents and discusses a method to determine the upper bounds for the uncertainty terms of the local models. The method is based on quadratic optimization to achieve a stability criterion where the conservatism is not additionally increased. The effectiveness of the proposed method is shown by a simulation example in connection with the Piecewise Quadratic Lyapunov approach as a stability criterion.