Practical Nonlinear Model Predictive Control with Hammerstein Model Applied to a Test Rig of Refrigeration Compressors

This paper discusses the implementation and presents the results of a suboptimal nonlinear model predictive controller used to control the suction and discharge pressures of compressors under test in a rig. The objective of this rig is to emulate operational conditions to which refrigeration compressors can be subjected when applied in a refrigeration system, such as household refrigerators and freezers, and allow quick measurements of some of the compressor characteristics under those conditions. There is a coupling between suction and discharge pressures and the behavior of such variables is nonlinear with respect to the valve openings, thus the plant to be controlled can be characterized as multivariable and nonlinear. Even though in industry it is common to use linear controllers to control nonlinear plants, the use of nonlinear controllers can bring advantages in terms of performance and robustness. The controller implemented in this paper is the practical nonlinear model predictive control algorithm, which is a general framework that can be used for the implementation of nonlinear model predictive controllers considering almost any class of nonlinear model. Even though model predictive control is harder to be implemented than classical controllers, such as PID, it poses the process control problem in the time domain, so the concepts involved are intuitive and at the same time the tuning is relatively easy, even for the multivariable case. In addition, model predictive control allows constraints, such as valve opening limitations and pressure limits, to be handled during the design phase. This paper considers a specific nonlinear model architecture, the nonlinear Hammerstein model, which is composed of a static nonlinear element in series with a linear dynamic part. Since this model is conceptually simple and presents good results in most of the practical situations, it is widely used in practice when a nonlinear model is desired. The dynamics of the real test rig were identified using this nonlinear model structure and the identification results are discussed. The practical nonlinear model predictive controller was implemented in the real test rig, being tested in a variety of operating conditions. The results of the controller are compared with the ones obtained with a classical PID controller. The modeling approach presented good results and the results obtained in this study show that it is possible to use nonlinear model predictive control algorithms in refrigeration test rigs, and that this use can contribute to increasing the productivity and operational efficiency of compressor tests

Structured Hammerstein-Wiener Model Learning for Model Predictive Control

This paper aims to improve the reliability of optimal control using models constructed by machine learning methods. Optimal control problems based on such models are generally non-convex and difficult to solve online. In this paper, we propose a model that combines the Hammerstein-Wiener model with input convex neural networks, which have recently been proposed in the field of machine learning. An important feature of the proposed model is that resulting optimal control problems are effectively solvable exploiting their convexity and partial linearity while retaining flexible modeling ability. The practical usefulness of the method is examined through its application to the modeling and control of an engine airpath system.Comment: 6 pages, 3 figure

A Simplified Wiener Based Model Predictive Control For Distillation Column

The distillation column process requires a large amount of energy, thus efficiently controlling the column can significantly minimize the operational costs. Nonlinear model predictive control (NMPC) is one of the best control strategies available to control such a column. In the NMPC implementation, the linearization technique is often used to guarantee the global optimum solution and to reduce the computational burden. One of the promising control schemes that uses the linearization technique is the Wiener based Linear Control (WLC) scheme which uses the inverse of the nonlinear block, and does not require the derivative of the model

ROBUST GENERIC MODEL CONTROL FOR PARAMETER INTERVAL SYSTEMS

A multivariable control technique is proposed for a type of nonlinear system with parameter intervals. The control is based upon the feedback linearization scheme called Generic Model Control, and alters the control calculation by utilizing parameter intervals, employing an adaptive step, averaging control predictions, and applying an interval problem solution. The proposed approach is applied in controlling both a linear and a nonlinear arc welding system as well in other simulations of scalar and multivariable systems

Networked Control System Design and Parameter Estimation

Networked control systems (NCSs) are a kind of distributed control systems in which the data between control components are exchanged via communication networks. Because of the attractive advantages of NCSs such as reduced system wiring, low weight, and ease of system diagnosis and maintenance, the research on NCSs has received much attention in recent years. The first part (Chapter 2 - Chapter 4) of the thesis is devoted to designing new controllers for NCSs by incorporating the network-induced delays. The thesis also conducts research on filtering of multirate systems and identification of Hammerstein systems in the second part (Chapter 5 - Chapter 6). Network-induced delays exist in both sensor-to-controller (S-C) and controller-to-actuator (C-A) links. A novel two-mode-dependent control scheme is proposed, in which the to-be-designed controller depends on both S-C and C-A delays. The resulting closed-loop system is a special jump linear system. Then, the conditions for stochastic stability are obtained in terms of a set of linear matrix inequalities (LMIs) with nonconvex constraints, which can be efficiently solved by a sequential LMI optimization algorithm. Further, the control synthesis problem for the NCSs is considered. The definitions of H₂ and H∞ norms for the special system are first proposed. Also, the plant uncertainties are considered in the design. Finally, the robust mixed H₂/H∞ control problem is solved under the framework of LMIs. To compensate for both S-C and C-A delays modeled by Markov chains, the generalized predictive control method is modified to choose certain predicted future control signal as the current control effort on the actuator node, whenever the control signal is delayed. Further, stability criteria in terms of LMIs are provided to check the system stability. The proposed method is also tested on an experimental hydraulic position control system. Multirate systems exist in many practical applications where different sampling rates co-exist in the same system. The l₂-l∞ filtering problem for multirate systems is considered in the thesis. By using the lifting technique, the system is first transformed to a linear time-invariant one, and then the filter design is formulated as an optimization problem which can be solved by using LMI techniques. Hammerstein model consists of a static nonlinear block followed in series by a linear dynamic system, which can find many applications in different areas. New switching sequences to handle the two-segment nonlinearities are proposed in this thesis. This leads to less parameters to be estimated and thus reduces the computational cost. Further, a stochastic gradient algorithm based on the idea of replacing the unmeasurable terms with their estimates is developed to identify the Hammerstein model with two-segment nonlinearities. Finally, several open problems are listed as the future research directions

Nonlinear System Identification of Laboratory Heat Exchanger Using Artificial Neural Network Model

This paper addresses the nonlinear identification of liquid saturated steam heat exchanger (LSSHE) using artificial neural network model. Heat exchanger is a highly nonlinear and non-minimum phase process and often its working conditions are variable. Experimental data obtained from fluid outlet temperature measurement in laboratory environment is used as the output variable and the rate of change of fluid flow into the system as input too. The results of identification using neural network and conventional nonlinear models are compared together. The simulation results show that neural network model is more accurate and faster in comparison with conventional nonlinear models for a time series data because of the independence of the model assignment.DOI:http://dx.doi.org/10.11591/ijece.v3i1.195

Development of U-model enhansed nonlinear systems

Nonlinear control system design has been widely recognised as a challenging issue where the key objective is to develop a general model prototype with conciseness, flexibility and manipulability, so that the designed control system can best match the required performance or specifications. As a generic systematic approach, U-model concept appeared in Prof. Quanmin Zhu’s Doctoral thesis, and U-model approach was firstly published in the journal paper titled with ‘U-model based pole placement for nonlinear plants’ in 2002.The U-model polynomial prototype precisely describes a wide range of smooth nonlinear polynomial models, defined as a controller output u(t-1) based time-varying polynomial models converted from the original nonlinear model. Within this equivalent U-model expression, the first study of U-model based pole placement controller design for nonlinear plants is a simple mapping exercise from ordinary linear and nonlinear difference equations to time-varying polynomials in terms of the plant input u(t-1). The U-model framework realised the concise and applicable design for nonlinear control system by using such linear polynomial control system design approaches.Since the first publication, the U-model methodology has progressed and evolved over the course of a decade. By using the U-model technique, researchers have proposed many different linear algorithms for the design of control systems for the nonlinear polynomial model including; adaptive control, internal control, sliding mode control, predictive control and neural network control. However, limited research has been concerned with the design and analysis of robust stability and performance of U-model based control systems.This project firstly proposes a suitable method to analyse the robust stability of the developed U-model based pole placement control systems against uncertainty. The parameter variation is bounded, thus the robust stability margin of the closed loop system can be determined by using LMI (Linear Matrix Inequality) based robust stability analysis procedure. U-block model is defined as an input output linear closed loop model with pole assignor converted from the U-model based control system. With the bridge of U-model approach, it connects the linear state space design approach with the nonlinear polynomial model. Therefore, LMI based linear robust controller design approaches are able to design enhanced robust control system within the U-block model structure.With such development, the first stage U-model methodology provides concise and flexible solutions for complex problems, where linear controller design methodologies are directly applied to nonlinear polynomial plant-based control system design. The next milestone work expands the U-model technique into state space control systems to establish the new framework, defined as the U-state space model, providing a generic prototype for the simplification of nonlinear state space design approaches.The U-state space model is first described as a controller output u(t-1) based time-varying state equations, which is equivalent to the original linear/nonlinear state space models after conversion. Then, a basic idea of corresponding U-state feedback control system design method is proposed based on the U-model principle. The linear state space feedback control design approach is employed to nonlinear plants described in state space realisation under U-state space structure. The desired state vectors defined as xd(t), are determined by closed loop performance (such as pole placement) or designer specifications (such as LQR). Then the desired state vectors substitute the desired state vectors into original state space equations (regarded as next time state variable xd(t) = x(t) ). Therefore, the controller output u(t-1) can be obtained from one of the roots of a root-solving iterative algorithm.A quad-rotor rotorcraft dynamic model and inverted pendulum system are introduced to verify the U-state space control system design approach for MIMO/SIMO system. The linear design approach is used to determine the closed loop state equation, then the controller output can be obtained from root solver. Numerical examples and case studies are employed in this study to demonstrate the effectiveness of the proposed methods