van den Pmj Paul Hof

Adaptive repetitive control of a compact disc mechanism

Radial track following of a compact disc player servo mechanism is severely exposed to periodic disturbances, induced by the eccentric rotation of the disc. The period of this disturbance is not available for measurement and varies slowly in time. Periodic disturbances can be adequately attenuated using the concept of repetitive control, provided the period is known. To deal with time varying periodic disturbances, a repetitive controller is tuned based on a simple though inaccurate physical model of the time varying character of the period. The model is tuned based on an estimate of the period, obtained through recursive identification. Experimental results show that the proposed scheme enables a significant improvement of the tracking accuracy of the radial servo mechanism.

The Behavioral Approach to Linear Parameter-Varying Systems

Linear parameter-varying (LPV) systems are usually described in either state-space or input-output form. When analyzing system equivalence between different representations it appears that the time-shifted versions of the scheduling signal (dynamic dependence) need to be taken into account. Therefore, representations used previously to define and specify LPV systems are not equal in terms of dynamics. In order to construct a parametrization-free description of LPV systems that overcomes these difficulties, a behavioral approach is introduced that serves as a basis for specifying system theoretic properties. LPV systems are defined as the collection of trajectories of system variables (like inputs and outputs) and scheduling variables. LPV kernel, input-output, and state-space system representations are introduced with appropriate equivalence transformations.

MIMO closed-loop identification of an MSW incinerator

In this paper, the application of a specific system identification procedure to a municipal solid waste (MSW) incinerator is discussed. This procedure is a combination of, on the one hand, a particular closed-loop identification method called the two-stage method and, on the other hand, the approach of high-order multiple input multiple output (MIMO) ARX model estimation followed by model reduction. MIMO ARX model estimation is performed by means of a, so-called, multiple data set identification method, i.e. a method by means of which it is possible to estimate a model on the basis of several data sets instead of just one data set. Model reduction is applied to each transfer function of the resulting MIMO ARX model separately. It is shown that with the proposed identification procedure a model of the MSW incinerator is obtained which, according to system identification validation measures, is good. Using the estimated model, the influence of the disturbances on the identification and control of an MSW incinerator is discussed. Furthermore, the validation of a first-principles model of the MSW incineration process by means of the resulting low-order SISO models is discussed. The results show that the proposed way of validating a first-principles model is a powerful tool for determining its quality.

Order and structural dependence selection of LPV-ARX models using a nonnegative garrote approach

In order to accurately identify Linear Parameter-Varying (LPV) systems, order selection of LPV linear regression models has prime importance. Existing identification approaches in this context suffer from the drawback that a set of functional dependencies needs to be chosen a priori for the parametrization of the model coefficients. However in a black-box setting, it has not been possible so far to decide which functions from a given set are required for the parametrization and which are not. To provide a practical solution, a nonnegative garrote approach is applied. It is shown that using only a measured data record of the plant, both the order selection and the selection of structural coefficient dependence can be solved by the proposed method.

Control relevant identification of a compact disc pick-up mechanism

This paper discusses the control relevant parametric identification of a servo system present in a compact disc player. In this application an approximate closed loop identification problem is solved in order to come up with a linear multivariable discrete time model, suitable for control design. This identification problem is handled by a recently introduced two stage method. It yields an explicit and tunable expression for the bias distribution of the model being estimated, clearly showing the dynamics or the closed loop system in the (asymptotic) approximation criterion. This result is exploited to identify the model in a control relevant way by additional data filtering. The recently introduced method by Vries-Van den Hof (1993) for model uncertainty quantification is used to construct an upper bound for the corresponding model error.<<ETX>>

A Two-Level Strategy to Realize Life-Cycle Production Optimization in an Operational Setting

We present a two-level strategy to improve robustness against uncertainty and model errors in life-cycle flooding optimization. At the upper level, a physics-based large-scale reservoir model is used to determine optimal life-cycle injection and production profiles. At the lower level, these profiles are considered as set points (reference values) for a tracking control algorithm, also known as a model predictive controller (MPC), to optimize the production variables over a short moving horizon on the basis of a simple data-driven model. In the process industry such a two-level approach is a well-known strategy to correct for small local disturbances that may have a negative (cumulative) effect on the long-term production strategy. We used a conventional reservoir simulator with gradient-based optimization functionality to perform the life-cycle optimization. Next, we applied this long-term strategy to a reservoir model, representing the truth, with somewhat different geological characteristics and near-wellbore characteristics not captured in the reservoir model used for the longterm optimization. We compared the performance (oil recovery) of this truth model when applying the life-cycle strategy with and without the corrections provided by the data-driven algorithm and the tracking controller. In this theoretical study we observed that the use of the lower-level controller enabled successful tracking of the reference values provided by the upper-level optimizer. In our example, a performance drop of 6.4% in net present value (NPV), caused by differences between the reservoir model used for life-cycle optimization and the true reservoir, was successfully reduced to only 0.5% when applying the two-level strategy. Several studies have demonstrated that model-based life-cycle production optimization has a large scope to improve long-term economic performance of waterflooding projects. However, because of uncertainties in geology, economics, and operational decisions, such life-cycle strategies cannot simply be applied in reality. Our two-level approach offers a potential solution to realize life-cycle optimization in an operational setting.

Experiment design for parameter estimation in nonlinear systems based on multilevel excitation

An experiment design procedure for parameter estimation in nonlinear dynamical systems is presented in this paper. The input to the system is designed in such a way that the information content of the data, as measured by a scalar function of the information matrix, is maximized. By restricting the input to a finite number of possible levels, the experiment design problem is formulated as a convex optimization problem which can be solved efficiently. The method is applied to a Continuous Stirred Tank Reactor in a simulation study. The parameter estimation based on the input signal obtained in our procedure is shown to outperform the one based on random binary signals.

Discretization of Linear Fractional Representations of LPV systems

Commonly, controllers for linear parameter-varying (LPV) systems are designed in continuous time using a linear fractional representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a discrete-time model of the plant which is often derived from a continuous-time first-principle model. Existing discretization approaches for LFRs describing LPV systems suffer from disadvantages like the possibility of serious approximation errors, issues of complexity, etc. To explore the disadvantages, existing discretization methods are reviewed and novel approaches are derived to overcome them. The proposed and existing methods are compared and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling. Criteria to choose appropriate sampling times with respect to the investigated methods are also presented. The proposed discretization methods are tested and compared both on a simulation example and on the electronic throttle control problem of a race motorcycle.

Robust ensemble-based multi-objective optimization

We consider robust ensemble-based multi-objective optimization using a hierarchical switching algorithm for combined long-term and short term water flooding optimization. We apply a modified formulation of the ensemble gradient which results in improved performance compared to earlier formulations. We also apply multi-dimensional scaling to visualize projections of the high-dimensional search space, to aid in understanding the complex nature of the objective function surface and the performance of the optimization algorithm. This provides insights into the quality of the gradient, and confirms the presence of ridges in the objective function surface which can be exploited for multi-objective optimization. We used a 18553-gridblock reservoir model of a channelized reservoir with 4 producers and 8 injectors. The controls were the flow rates in the injectors, and the long-term and short-term objective functions were undiscounted net present value (NPV) and highly discounted (25%) NPV respectively. We achieved an increase of 15.2% in the secondary objective for a decrease of 0.5% in the primary objective, averaged over 100 geological realizations. The total number of reservoir simulations was around 20000, which indicates the potential to use the ensemble optimization method for robust multi-objective optimization of medium-sized reservoir models.

LPV system identification with globally fixed orthonormal basis functions

A global and a local identification approach are developed for approximation of linear parameter-varying (LPV) systems. The utilized model structure is a linear combination of globally fixed (scheduling-independent) orthonormal basis functions (OBFs) with scheduling-parameter dependent weights. Whether the weighting is applied on the input or on the output side of the OBFs, the resulting models have different modeling capabilities. The local identification approach of these structures is based on the interpolation of locally identified LTI models on the scheduling domain where the local models are composed from a fixed set of OBFs. The global approach utilizes a priori chosen functional dependence of the parameter-varying weighting of a fixed set of OBFs to deliver global model estimation from measured I/O data. Selection of the OBFs that guarantee the least worst-case modeling error for the local behaviors in an asymptotic sense, is accomplished through the fuzzy Kolmogorov c-max approach. The proposed methods are analyzed in terms of applicability and consistency of the estimates.