Nonlinear Internal Model Control Research Articles

Nonlinear Internal Model Control for Bearingless Induction Motor Based on Inverse System Theory

The bearingless induction motor is a nonlinear, multi-variable and strongly coupling system. In this paper, a new nonlinear internal model control (IMC) strategy based on inverse system theory is proposed to realize the decoupling control for the bearingless induction motor. The mathematical model of the motor is built and then the inverse system method is applied to decouple the original nonlinear system. Finally the internal model control method is introduced to ensure the robustness of the closed-loop system. The effectiveness of the proposed strategy are demonstrated by simulation.

Nonlinear Internal Model Control for Bearingless Induction Motor Based on Neural Network Inversion

Nonlinear Internal Model Control for Bearingless Induction Motor Based on Neural Network Inversion

Set membership inversion and robust control from data of nonlinear systems

SUMMARYA set membership method for right inversion of nonlinear systems from data is proposed in the paper. Both the cases where the system to invert is known or unknown and therefore identified from data are addressed. The method does not require the invertibility of the regression function describing the system and ensures tight bounds on the inversion error. In the case of unknown system, the method allows the derivation of a robust right‐inverse, guaranteeing the inversion error bound for all the systems belonging to the uncertainty set which can be defined from the available prior and experimental information. Based on such a set membership inversion, two methods for robust control of nonlinear systems from data are introduced: nonlinear feed‐forward control (NFFC) and nonlinear internal model control (NIMC). Both the design methods ensure robust stability and bounded tracking errors for all the systems belonging to the involved uncertainty set. Two applicative examples of robust control from data are presented: NFFC control of semi‐active suspension systems and NIMC control of vehicle lateral dynamics.Copyright © 2013 John Wiley & Sons, Ltd.

Multi-loop nonlinear internal model controller design based on a dynamic fuzzy partial least squares model

In this paper, a dynamic fuzzy partial least squares (DFPLS) modeling method is proposed. Under such framework, the multiple input multiple output (MIMO) nonlinear system can be automatically decomposed into several univariate subsystems in PLS latent space. Within each latent space, a dynamic fuzzy method is introduced to model the inherent dynamic and nonlinear feature of the physical system. The new modeling method combines the decoupling characteristic of PLS framework and the ability of dynamic nonlinear modeling in the fuzzy method. Based on the DFPLS model, a multi-loop nonlinear internal model control (IMC) strategy is proposed. A pH neutralization process and a methylcyclohexane (MCH) distillation column from Aspen Dynamic Module are presented to demonstrate the effectiveness of the proposed modeling method and control strategy.

Nonlinear Internal Model Control for Bearingless Induction Motor Based on Neural Network Inversion

The bearingless induction motor is a nonlinear, multi-variable and strong-coupled system. For this system, a novel internal model control strategy based on neural network αth-order inverse system theory is proposed to realize the decoupling control. By cascading the αth-order inverse model approximated by the dynamic neural network with the original system, the nonlinear bearingless induction motor system is decoupled into four independent pseudo-linear subsystems, that is, two radial displacement subsystems, a speed subsystem and a rotor flux subsystem. Then, the internal model control method is introduced to the four pseudo-linear subsystems to ensure the robustness and anti-jamming ability of the closed-loop system. The effectiveness and superiority of the proposed strategy are demonstrated by simulation and experiment.

Gaussian process internal model control

Nonlinear modelling approaches such as neural networks, fuzzy models and multiple model networks have been proposed for model based control, to improve the poor transient response of adaptive control techniques. The quality of control is known to be strongly related to the accuracy of the model which represents the process. A Bayesian Gaussian process (GP) approach provides an analytic prediction of the model uncertainty, which makes the GP model an ideal candidate for model based control strategies. This article extends the use of the GP model for nonlinear internal model control. The invertibility of the GP model is discussed and the use of predicted variance is illustrated on a simulated example.

Robust nonlinear internal model control of stable Wiener systems

Many process systems can be modeled as a stable Wiener system, which is a stable linear system followed by a static nonlinearity. A nonlinear control design procedure is presented that provides robustness to uncertainties while being applicable to systems with unstable zero dynamics, unmeasured states, disturbances, and measurement noise. The design procedure combines nonlinear internal model control with linear matrix inequality feasibility or optimization problems, such that all robust stability and performance criteria are computable in polynomial-time using readily available software. Application to a pH neutralization case study demonstrates the importance of taking uncertainty into account during the design of controllers for Wiener systems. The approach is generalizable to Hammerstein and sandwich systems, whether well- or poorly conditioned, and to systems with actuator constraints.

Nonlinear Internal Model Control Using Echo State Network for Pneumatic Muscle System

Pneumatic muscle (PM) has many advantages such as light weight, high power to weight ratio and low price. However, it has strong time varying characteristic. The complex nonlinear dynamics of PM system poses some challenges for achieving accurate modeling and control. To solve these problems, we propose nonlinear internal model control (IMC) using echo state network (ESN) for PM system in this paper. The ESN based IMC is termed ESNBIMC, which fully embodies the virtues of ESN and IMC. In ESNBIMC, the dynamic model of PM system is identified by an ESN. The other ESN is trained to learn the inverse dynamics of the system, and then it can be used as a nonlinear controller. Recursive Least Square (RLS) algorithm can be applied to online training the ESN without affecting the previous weight structure, which is very suitable for real-time control problems. By using the identification ability of ESN and RLS, high accurate plant model of PM system without detailed model information can be built. In addition, strong robustness also can be attained by online self-tuning of controller and internal model. Experiment demonstrates the effectiveness of the proposed control algorithm. The results show that ESNBIMC achieves satisfactory tracking performance for PM system.

Multi-loop nonlinear internal model controller design under nonlinear dynamic PLS framework using ARX-neural network model

In this paper, a novel multi-loop nonlinear internal model control (IMC) strategy for multiple-input multiple-output (MIMO) systems is presented under the partial least squares (PLS) framework, which automatically decomposes the system into several univariate subsystems in the latent space. To formulate a nonlinear dynamic PLS framework, we propose an ARX-neural network (ARX-NN) cascaded structure, and incorporate it into PLS inner model. A gradient-based optimization approach is then provided to identify the parameter sets of the ARX-NN PLS model so that the plant-model mismatch is minimized. Furthermore, with perfect model, we show that the response of the closed loop system can be reduced to a simple linear IMC filter with the original system delay. The simulation results of a methylcyclohexane (MCH) distillation column from Aspen Dynamic Module, demonstrate the effectiveness of our approach in terms of disturbance rejection and tracking performance.

Interval type-2 fuzzy inverse controller design in nonlinear IMC structure

In the recent years it has been demonstrated that type-2 fuzzy logic systems are more effective in modeling and control of complex nonlinear systems compared to type-1 fuzzy logic systems. An inverse controller based on type-2 fuzzy model can be proposed since inverse model controllers provide an efficient way to control nonlinear processes. Even though various fuzzy inversion methods have been devised for type-1 fuzzy logic systems up to now, there does not exist any method for type-2 fuzzy logic systems. In this study, a systematic method has been proposed to form the inverse of the interval type-2 Takagi–Sugeno fuzzy model based on a pure analytical method. The calculation of inverse model is done based on simple manipulations of the antecedent and consequence parts of the fuzzy model. Moreover, the type-2 fuzzy model and its inverse as the primary controller are embedded into a nonlinear internal model control structure to provide an effective and robust control performance. Finally, the proposed control scheme has been implemented on an experimental pH neutralization process where the beneficial sides are shown clearly.

Type-2 Fuzzy Model Inverse Controller Design Based on BB-BC Optimization Method

AbstractThe use of inverse system model as a controller might be an efficient way in controlling nonlinear systems. It is also a known fact that type-2 fuzzy models can represent nonlinear systems better than type-1 fuzzy models. Therefore, an inverse type-2 fuzzy model can be used as a controller for controlling processes with nonlinearities and/or uncertainties. In the case of uncertainties and/or disturbances, an inverse type-2 fuzzy model based nonlinear internal model control structure is proposed to compensate these errors.

Linearization of radio frequency amplifiers using nonlinear Internal Model Control method

In the present paper, the nonlinear Internal Model Control (IMC) method is introduced and applied to linearize high frequency power amplifiers (PAs). The IMC is based on the description of a process model and of a controller. It is shown that baseband frequency descriptions are suitable for the model and the controller. Their description parameters are derived from input and output modulation signals processed in Cartesian form. Simulation results are given to illustrate the design procedure and to demonstrate the performances of the IMC linearizer.

Adaptive peak seeking control of a proton exchange membrane fuel cell

The primary aim of operating any fuel cell (PEMFC) system is to produce the power/electricity at maximum efficiency. The cell voltage/current manipulation appear to be the most suitable choice for controlling the power density. However, the power density exhibits a highly nonlinear and complex dynamic relationship with respect to the cell voltage. Since the process output variable (i.e. power density) itself is the objective function for the optimization, there exists a singularity at the optimum operating condition. In addition, the location of the optimum operating point changes with time due to the occurrence of variety of disturbances and/or changes in the operating conditions. Thus, the need to operate the PEMFC at its peak power density and track the shifting optimum turns out to be a challenging control problem. The task of on-line optimizing control of PEMFC poses difficulties in real time control due to its fast dynamics and it is impractical to employ a mechanistic model for locating the changing optimum on-line. In this context the adaptive optimizing control scheme developed by Bamberger and Isermann (1978) [1] appears interesting. Their scheme is based on on-line adaptation of a nonlinear black box time series models and facilitates analytical computation of changing optimum. Recently, Bedi et al. (2007) [2] have developed a closed form multi-step predictive control law under nonlinear internal model control framework using a black-box nonlinear model and employed it for peak power control in PEMFC. From the viewpoint of PEMFC operation, this nonlinear IMC controller meets the demand on the fast computations as a closed form solution is obtained for the nonlinear control problem at each time step. In this work, we propose to develop an adaptive optimizing control scheme, which combines the attractive features of the on-line optimization approach proposed by Bamberger and Isermann (1978) [1] and closed form control law developed by Bedi et al. (2007) [2]. We demonstrate the effectiveness of the proposed adaptive optimizing scheme by conducting simulation studies on the distributed an along-the-channel model of PEMFC. Analysis of the simulation results indicate that the proposed adaptive optimizing control scheme satisfactorily tracks the shifting optimum operating point in the face of changing unmeasured disturbances

Adaptive Neural-based Fault Tolerant Control for Nonlinear Systems

A neural network based fault tolerant control for unknown nonlinear systems is proposed. The faultless system is controlled by a nonlinear Internal Model Controller (IMC), where both the direct and inverse models of the plant are carried out by neural networks. Using the residual signal generated from the fault detection path, an extra neural-network fault compensation loop is introduced. This neural network is a two layer perceptron and the weights and bias are updated on-line by the modified-gradient approach, which tries to minimize the control error induced by the fault. In this context, a fault tolerant control scheme is obtained. This scheme is tested in simulation in a pH plant with good results.

Fuzzy Feedback Linearizing Controller and Its Equivalence With the Fuzzy Nonlinear Internal Model Control Structure

Fuzzy Feedback Linearizing Controller and Its Equivalence With the Fuzzy Nonlinear Internal Model Control StructureThis paper examines the inverse control problem of nonlinear systems with stable dynamics using a fuzzy modeling approach. Indeed, based on the ability of fuzzy systems to approximate any nonlinear mapping, the nonlinear system is represented by a Takagi-Sugeno (TS) fuzzy system, which is then inverted for designing a fuzzy controller. As an application of the proposed inverse control methodology, two popular control structures, namely, feedback linearization and Nonlinear Internal Model Control (NIMC) are investigated. Moreover, the paper points out that, under some conditions, both of the control structures are equivalent and naturally implement a Smith predictor in the presence of time delays.

NONLINEAR INTERNAL MODEL CONTROL OF PEM FUEL CELL

Proton exchange membrane fuel cells (PEMFCs) are known to exhibit strongly nonlinear dynamics and input multiplicities. This paper presents an approach for identifying GOBF-Wiener models towards representing the nonlinear dynamics. The identified model is used to synthesis a MIMO nonlinear internal model controller (NIMC). The average power density and solid temperature of the PEMFC are controlled using (a)cell voltage and inlet coolant temperatures (b) inlet molar flow rates of hydrogen and coolant. The proposed NIMC scheme is able to operate the PEMFC at the optimum power density point where the steady state gain reduces to zero and changes its sign.

Adaptive IMC Controller Design for Nonlinear Process Control

In this paper, a new adaptive internal model control (IMC) controller is proposed based on just-in-time learning (JITL) technique for nonlinear process control. The parameters of the proposed IMC controller are updated not only based on the information provided by the JITL, but also its filter parameter is adjusted online by an adaptive learning algorithm. Compared with the previous nonlinear IMC controller design methods, it is straightforward for the proposed method to obtain the model inversion based on the JITL modelling technique. Simulation results are presented to demonstrate the advantage of the proposed adaptive IMC controller design over its conventional counterpart.

Nonlinear model based control of two-product reactive distillation column

Nonlinear feedback control scheme for reactive distillation column has been proposed. The proposed control scheme is derived in the framework of Nonlinear Internal Model Control. The product compositions and liquid and vapor flow rates in sections of the reactive distillation column are estimated from selected tray temperature measurements by an observer. The control scheme is applied to an example reactive distillation column in which two products are produced in a single column and the reversible reaction A+B=C+D occurs. The relative volatilities are favorable for reactive distillation so that the reactants are intermediate boilers between the light product C and the heavy product D. Ideal physical properties, kinetics, and vapor-liquid equilibrium are also assumed. It is shown that the proposed control scheme keeps tight product composition control.

A nonlinear internal model control using backstepping method for attitude control of a helicopter model

The backstepping method is to design nonlinear control systems to follow a given reference signal by iterative recursive procedure. Although it is an effective approach to design stable closed loop systems for nonlinear controlled systems, it has drawbacks to become extremely complex when the relative order of the controlled system is large. In order to make the design procedure more tractable, we need to approximate the controlled system to a low order system. However, the approximated error between the model and the real process due to model reduction might bring significant performance degradation. Hence, this paper proposes a nonlinear internal model control (IMC) incoporated with the inverse of a low order system designed from the backstepping method. In the proposed method, the backstepping design procedure becomes simple because it can be done for a low order system. Furthermore, the peformance degradation due to model reduction can be compensated from an IMC structure. The proposed control method is applied to the attitude control for a helicopter model, and we compare the proposed method with the usual backstepping method through simulation experiments. From the comparative study, it follows that the proposed one is especially effective for improving the characteristic of input signals.

Nonlinear internal model control using neural networks: an application for machining processes

This paper presents a novel approach to the control of the cutting force on the basis of the internal model control (IMC) principle. The main goal is to control a single output variable, the cutting force, by changing a single input variable, the feedrate. A neural model is used as an internal model to determine the control inputs (feedrate) necessary to keep the cutting force constant. Three approaches, the fuzzy logic controller (FLC), the direct inverse controller (DIC) and the IMC, based on artificial neural networks (IMC-NN), are simulated and their performances are assessed in terms of several performance measurements. The results demonstrate that IMC-NN strategy provides a better disturbance rejection than FLC for the cases analysed.