Christian A. Larsson

On optimal input design for nonlinear FIR-type systems

We consider optimal input design for system identification of nonlinear FIR-type systems in the prediction error (PEM) framework. The input sequences are designed in terms of their statistical properties and not directly in time domain. The starting point is the asymptotic properties of PEM estimates. The fact that the inverse covariance matrix of the estimated parameters is linear in the input probability density function is exploited to formulate convex optimization problems. The main issues considered are the parameterization of the input pdf, reduction of the number of free variables in the optimization and to some extent signal generation. Two special model classes where tractable problems are obtainable are studied in detail. Convex formulations of the input design problem are presented for the static nonlinear and nonlinear FIR cases. Numerical examples of the discussed ideas are also presented.

On optimal input design in system identification for model predictive control

This paper considers a method for optimal input design in system identification for model predictive control. The objective is to provide the user with a model that guarantees, with high probability, that a specified control performance is achieved. We see that, even though the system is nonlinear, using linear theory in the input design can reduce the experimental effort. The method is illustrated in a minimum power input signal design in identification of a water tank system.

MPC oriented experiment design

In this contribution we outline an experiment procedure tailored for Model Predictive Control (MPC). The design criterion takes the MPC criterion into account explicitly. The Scenario Approach is u ...

Application set approximation in optimal input design for model predictive control

This contribution considers one central aspect of experiment design in system identification, namely application set approximation. When a control design is based on an estimated model, the achievable performance is related to the quality of the estimate. The degradation in control performance due to plant-modeling missmatch is quantified by an application cost function. A convex approximation of the set of models that satisfy the control specification is typically required in optimal input design. The standard approach is to use a quadratic approximation of the application cost function, where the main computational effort is to find the corresponding Hessian matrix. Our main contribution is an alternative approach for this problem, which uses the structure of the underlying optimal control problem to considerably reduce the computations needed to find the application set. This technique allows the use of applications oriented input design for MPC on much more complex plants. The approach is numerically evaluated on a distillation control problem.

Application-Oriented Input Design in System Identification: Optimal Input Design for Control [Applications of Control]

Model-based control design plays a key role in todays industrial practice, and industry demands cuttingedge methods for identifying the necessary models. However, additional tools are needed to handle the increasingly stringent conditions on cost and performance related to identifying the models.

Generation of excitation signals with prescribed autocorrelation for input and output constrained systems

This paper considers the problem of realizing an input signal with a desired autocorrelation sequence satisfying both input and output constraints for the system it is to be applied to. This is a important problem in system identification. Firstly, the properties of the identified model are highly dependent on the used excitation signal during the experiment and secondly, on real processes, due to actuator saturation and safety considerations, it is important to constrain the inputs and outputs of the process. The proposed method is formulated as a nonlinear model predictive control problem. In general this corresponds to solving a non-convex optimization problem. Here we show how this can be solved in one particular case. For this special case convergence is established for generation of pseudo-white noise. The performance of the algorithm is successfully verified by simulations for a few different auto-correlation sequences, with and without input and output constraints.

On the way to autonomous model predictive control : A distillation column simulation study

Model Predictive Control (MPC) is a powerful tool in the control of large scale chemical processes and has become the standard method for constrained multivariable control problems. Hence, the number of MPC applications is increasing steadily and it is being used in application domains other than petrochemical industries. A common observation by the industrial practitioners is that success of any MPC application requires not only efficient initial deployment but also maintenance of initial effectiveness. To this end, we propose a novel high level automated support strategy for MPC systems. Such a strategy consists of components such as performance monitoring, performance diagnosis, least costly closed loop experiment design, re-identification and autotuning. This work presents the novel technological developments in each component and demonstrates them on a distillation column case study. We show that automated support strategy restores nominal performance after a performance drop is detected and takes the right course of action depending on its cause.

An application-oriented approach to dual control with excitation for closed-loop identification

Identification of systems operating in closed loop is an important problem in industrial applications, where model-based control is used to an increasing extent. For model-based controllers, plant changes over time eventually result in a mismatch between the dynamics of any initial model in the controller and the actual plant dynamics. When the mismatch becomes too large, control performance suffers and it becomes necessary to re-identify the plant to restore performance. Often the available data are not informative enough when the identification is performed in closed loop and extra excitation needs to be injected. This paper considers the problem of generating such excitation with the least possible disruption to the normal operations of the plant. The methods explicitly take time domain constraints into account. The formulation leads to optimal control problems which are in general very difficult optimization problems. Computationally tractable solutions based on Markov decision processes and model predictive control are presented. The performance of the suggested algorithms is illustrated in two simulation examples comparing the novel methods and algorithms available in the literature.

Robust Input Design for Resonant Systems Under Limited A Priori Information

Abstract Optimal input design typically depends on the unknown system parameters that need to be identified. In this paper we consider robust input design for resonant systems that may span over a large frequency band. The concept is to use classical D-optimal design combined with a robust excitation signal which guarantees the same estimate variance regardless of resonance frequency. Simulations show that the proposed signal has the desired properties.

Input Signal Generation for Constrained Multiple-Input Multple-Output Systems

In this paper we extend a recent method for generating an input signal with a desired auto-correlation function while satisfying both input and output constraints for the system it is to be applied ...