Parameter Identification and Model Predictive Control for Hammerstein Systems


Student thesis: Doctoral Thesis

View graph of relations



Awarding Institution
Award date3 Aug 2018


Hammerstein system is a typical blocked-oriented nonlinear system, which consists of a nonlinear static function followed by a linear dynamic subsystem.It has been widely used to describe practical processes in chemical, mechanical, biological, electrical and other industries.Modeling and control for Hammerstein systems are of great significance for achieving high industrial process performance.

Parameter identification is the key step of modeling and thus it is important to building accurate Hammerstein models. Parameter identification for Hammerstein systems is still under development. Some existing methods are not complete, which lack necessary derivation procedures and theoretical analysis. The frequently used input test signals with arbitrarily randomly amplitudes are not applicable to the practical systems with strict safety requirements. The required noise-free condition and the stochastic noise assumption generally cannot be satisfied in some practical systems. To better model industrial processes, it is necessary to develop more practical Hammerstein system identification methods.

Once accurate Hammerstein models are identified, control algorithms are needed for achieving good control performance. Model predictive control (MPC) algorithms are considered in this study due to its ability to deal with constraints, multivariable coupling and time-delay. The existing MPC algorithms for Hammerstein systems are restricted by high computational burden, the difficulty to train certain types of nonlinear approximators, the limited applicable range for just single-input single-output processes and so on. To overcome these restrictions, it is important to improve the existing MPC algorithms for Hammerstein systems.

This thesis aims to improve modeling and control performance of practical industrial processes by using Hammerstein systems.
Four main studies are thus carried out.

Firstly, a multiple-amplitude step response based Hammerstein system identification method is developed. The input step signals with small amplitudes are recommended to act as the test signals for parameter identification. To ensure the identification accuracy and the robustness against system noise, the exiting time integral approach is improved to identify the linear sub-model parameters. Then, the nonlinear parameters are identified by solving the least squares problem formed by the step amplitudes of intermediate variable estimated by the improved time integral approach. Two numerical examples are initially used to illustrate the effectiveness of the proposed identification method. Then, for good flow field control performance, the identification method is applied into the practical 2.4m large-scale intermittent transonic wind tunnel to model the static pressure drift caused by varying angles of attack.

Secondly, a recursive Hammerstein system identification algorithm is proposed. Based on the system parametric model, the algorithm is derived by minimizing the feasible parameter membership set. The sufficient conditions guaranteeing the uniform convergence are analyzed theoretically. The adaptive weighting factor and the adaptive covariance matrix are introduced to improve the convergence. The validity of this algorithm is demonstrated by three numerical examples, including a simulated DC motor case.

Thirdly, a nonlinear MPC algorithm based on piecewise linear (PWL) Hammerstein models is developed. The canonical PWL function is used as the static nonlinear part of the Hammerstein model. To reduce computational burden, at each sampling period, the predicted output trajectory is firstly linearized at an assumed input trajectory, and then the optimal control actions are simply calculated by solving a quadratic programming problem. In particular, due to the character that a PWL function becomes a linear function at a specific input sub-region, the derivatives used in the linearization process are obtained in a computationally efficient look-up table style. Inversion of input nonlinearity is not required. This algorithm can directly integrate input constraints without any transformation. Two benchmark systems, a continuous stirred tank reactor and a pH neutralization reactor, are simulated to show the advantages of this control algorithm.

Fourthly, a multilinear control scheme is developed for multi-input multi-output (MIMO) Hammerstein-like systems. A normal vector included angle division method is initially proposed to decompose the system operating space and determine the minimum linear model bank. Then, a novel multilinear MPC algorithm is developed with the trajectory scheduling technique for local controller combination. A benchmark MIMO continuous stirred tank reactor system is studied to illustrate the effectiveness of the proposed division method and the developed control algorithm.

The main contribution of this thesis is the complete scheme for enhancing industrial process performance, which includes the two identification methods and the two nonlinear MPC algorithms for Hammerstein systems. The step response based identification method can be used offline and can cope with the strict safety requirement. The recursive identification method can be implemented online under the practical bounded noise assumption. They provide process models for understanding, analysis and developing corresponding control algorithms. The nonlinear MPC algorithm based on PWL Hammerstein models can incorporate accurate system static nonlinearity and is computationally efficient. The proposed multilinear control scheme is easy to understand and to implement, and has the advantage of low computational burden. Both of the two nonlinear MPC algorithms are able to contribute high process control performance.

    Research areas

  • Parameter Identification, Model Predictive Control, Hammerstein Systems