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In this paper, in order to control a nonlinear dynamic system via multi-model controller, we propose a systematic approach to determine the nominal local linear models. These models are selected from the local models bank and results in a reduced nominal models set that provides enough information to design a multi-model controller. To determine the initial local models bank, gap metric is used so that the distance between two successive local models is smaller than a threshold value. Then, a systematic approach that aims to get a reduced nominal models bank is developed. Based on this approach, first, a binary gap matrix is defined by combining gap metric and stability information. Then, several rows of this matrix are selected such that the sum of them becomes a non-zero vector. The proposed approach along with a designed robust controller is validated on a pH neutralization regarding to its highly nonlinear behavior.

This paper presents a cooperative fuzzy model predictive control (CFMPC) for heating and cooling of buildings. Because of different supply zones, the large time constants and the non-linear building dynamics with respect to the different seasons, a CFMPC concept is proposed. The overall non-linear building is split into different zones, which are consisting of input-coupled Takagi-Sugeno (TS)-fuzzy models. Each such TS-fuzzy model is constituted by a local linear model network (LLMN). The LLMN consists of local linear models (LLM), which are representing the different seasons: winter, transition season (fall and spring), and summer. The control of each LLM is realized by model predictive control (MPC). For each building zone the associated MPCs are output-blended by the fuzzy membership functions, which leads to fuzzy model predictive control (FMPC). In addition to the FMPCs a global MPC is controlling the thermally activated building systems, which affect all other zones. To coordinate the different controllers a cooperative iteration-loop is assumed, which leads to cooperative fuzzy model predictive control (CFMPC). The concept is developed for a specific demonstration building and can be easily adapted for other complex buildings. A simulation example demonstrates that the proposed CFMPC achieves a performance increase with less energy consumption, as compared to FMPC controllers and historical measured data of the demonstration building.

In this paper, a new PID controller design scheme is proposed for non-linear systems. According to this scheme, the system model is first generated by using local linear models. Then, it is described a design of internal model controllers(IMC) based on the local linear models. The internal model control has a simple structure and has a high robustness for system uncertainties. However, there are few studies of IMC schemes for non-linear systems. On the other hand, lots of controlled systems have non-linearities. Finally the effectiveness of the newly proposed control scheme is experiment examples in comparison with the conventional control methods for non-linear systems.

© 2017 IEEE. This paper presents a comparative study of two widely accepted model predictive control schemes based on mixed logical dynamical (MLD) and nonlinear modeling approaches with application to a continuous stirred tank reactor (CSTR) system. Specifically, we approximate the nonlinear behavior of a CSTR system with multiple local linear models in a MLD framework. The main benefit of such a scheme is the significant improvement in model accuracy when compared with a single linearized model. The benefits and trade-offs associated with predictive control laws synthesized using MLD and nonlinear modeling approaches are also compared.

A new and systematic method to design digital controllers for uncertain chaotic systems with structured uncertainties is presented in this paper. Takagi–Sugeno (TS) fuzzy model is used to model the chaotic dynamic system, while the uncertainties are decomposed such that the uncertain chaotic system can be rewritten as a set of local linear models with an additional disturbed input. Conventional control techniques are utilized to develop the continuous-time controllers first. Then, the digital controllers are obtained as the digital redesign of the continuous-time controllers using the state-matching approach. The performance of the proposed controller design is illustrated through numerical examples.

Takagi-Sugeno (TS) modeling formalism has been widely used to build up multi-model representations for nonlinear systems. In this paper, TS approach is applied to get a multi-model description of Ozone generation process in a specific geographical zone. This is done in two steps: firstly, an adequate structure of the desired multi-model is designed. This structure involves a set of local linear models (each one is valid for a certain range of operating conditions) and an interpolative mechanism that combines the outputs of the local models into a continuous global output. The second step consists in identifying the parameters of the local models using the parametric identification approach. The identification scheme developed is applied to model ozone generation in the Basse-Normandie region (France). The model thus obtained turned out to be satisfactory and currently used to build-up a predictor for this region.

The multi-objective identification of nonlinear dynamic models consisting of local linear models is considered. The tradeoff between global model accuracy and local model interpretability is explicitly considered by introducing weights on the criteria for local model accuracy. A strategy is proposed to tune the local weights in order to achieve similar tradeoff for each local model. In this way, better generalization is achieved. The multi-objective identification algorithm has been applied to predict the engine load of an off-road vehicle operating under varying working load conditions. The analysis tools have proven useful for the construction of an accurate and robust engine load prediction model. The resulting model can directly be used in model-based control algorithms in automatic tuning systems that explicitly deal with constraints on the working region.

A simple gain-scheduling approach to the position control of electrostatically levitated materials is presented. An electrostatic levitator is currently being constructed at the German Aerospace Center (DLR). It can be used for containerless processing of metals and nonconducting materials. Time-varying sample charges and the fact that the plant is open-loop unstable make this a difficult and challenging control problem. The nonlinear parameter-dependent system is approximated by two local linear models. Based on these models, two local linear controllers are designed. LMI-based pole region assignment is used to reduce the design procedure to the tuning of three parameters with intuitive meaning. The sample charge is estimated with a discrete-time extended Kalman filter and used as scheduling parameter. Experimental results demonstrate that gain-scheduled control achieves a significantly better performance than fixed-gain, observer-based state feedback control.

A method for combining multiple local models to describe a nonlinear system. The local model weights are based on the linear interpolation of the current operating point from the closest local model operating points defined as the filtered value of the current process input. This local modeling method can be used to describe systems with changing system gains and dynamics, as well as input multiplicity. A case study for a benchmark CSTR reactor is presented. Local linear models are used to synthesize IMC based PID controllers.

International audience; This paper presents a new air traffic complexity metric based on dynamical systems. Based on a set of radar observations (position and speed) a vector field interpolating these data is constructed. Once the field has been obtained, the Lyapunov spectrum of the associated dynamical system is computed on points evenly spaced on a spatial grid. The results of the computations are summarized on complexity maps, with high values indicating areas to avoid or to carefully monitor. A first approach based on linear dynamical system enable to compute an aggregate complexity metric. In order to produce complexity maps, two extensions of the previous approach have been developed (one in space and another in space and time). Finally, an approximation is proposed in order to localize the computation of the vector field by the mean of Local Linear Models.

This paper presents a case study of model predictive control (MPC) applied to a continuous stirred tank reactor (CSTR). It is proposed to approximate nonlinear behavior of a plant by several local linear models, enabling a piecewise affine (PWA) description of the model used to predict and optimize future evolution of the reactor behavior. Main advantage of the PWA model over traditional approaches based on single linearization is a significant increase of model accuracy which leads to a better control quality. It is also illustrated that, by adopting the PWA modeling framework, MPC strategy can be implemented using significantly less computational power compared to nonlinear MPC setups.

This paper presents a new method for control of complex MIMO plants based on a quantised state description. The control algorithm solves a minimisation problem for a set of user defined convex control objective functions with the plant dynamics as a constraint. The solution makes use of local linear models that are effectively calculated by propagating the state on-line using a quantised state description. The method is demonstrated on a model of an autonomous underwater vehicle.

Four new filters for nonlinear estimation have been introduced based on a local linear modelling approach. Simulations on a highly nonlinear target tracking application suggest the performance of the four fuzzy Kalman filters (FKF) to be comparable to the extended Kalman filter, and FKF3 to be consistently better, especially when system noise is added. This highlights the effect of composite modelling, which in general leads to greater modelling accuracy and hence to more accurate tracking. A major advantage of the local modelling based approach is that further linearisation of the model is not required for application of Kalman filtering (except in FKF4). Also, as the approach is model based it lends itself to systems for which analytical equations may not be available.

Almost real-world plants are represented by non-linear systems. Therefore, it is important to consider PID control schemes to cope with such systems. In this paper, a PID control method for non-linear systems is newly proposed. Some local linear models on typical equilibrium points are first designed, followed by linear PID controllers corresponding to these models. The distances between the query and these local models are calculated, and the weights are computed in proportion to the distances. These weights are put for local PID controllers, and the PID controller corresponding to the query can be designed. According to the proposed scheme, the good PID control performance can be easily obtained. The effectiveness of the PID control scheme is illustrated by some simulation examples and experiment.