# Process control

## Fuzzy activity time-based model predictive control of open station assembly lines

The sequencing and line balancing of manual mixed-model assembly lines are challenging tasks due to the complexity and uncertainty of operator activities. The control of cycle time and the sequencing of production can mitigate the losses due to non-optimal line balancing in the case of open-station production where the operators can work ahead of schedule and try to reduce their backlog. The objective of this paper is to provide a cycle time control algorithm that can improve the e ciency of assembly lines in such situations based on a specially mixed sequencing strategy. To handle the uncertainty of activity times, a fuzzy model-based solution has been developed. As the production process is modular, the fuzzy sets represent the uncertainty of the elementary activity times related to the processing of the modules. The optimistic and pessimistic estimates of the completion of activity times extracted from the fuzzy model are incorporated into a model predictive control algorithm to ensure the constrained optimization of the cycle time. The applicability of the proposed method is demonstrated based on a wire-harness manufacturing process with a paced conveyor, but the proposed algorithm can handle continuous conveyors as well. The results confirm that the application of the proposed algorithm is widely applicable in cases where a production line of a supply chain is not well balanced and the activity times are uncertain.

## Fuzzy model based control

For the effective application of Takagi-Sugeno fuzzy models in model based control a control-related framework have been worked out. This framework is based on the following generating elements: Identification, Adaptation, Inversion, and Linearization. By means of these building blocks, inverse model based and model predictive (MPC) controllers were generated. Because of the learning capacity of the fuzzy model, the adaptive version of these solutions has been also worked out.

J. Abonyi, Fuzzy Model Identification for Control, Birkhäuser Basel, 165-241, 2003

## Fuzzy modeling with multivariate membership functions: Gray-box identification and control design

A novel framework for fuzzy modeling and model-based control design is described. The fuzzy model is of the Takagi-Sugeno (TS) type with constant consequents. It uses multivariate antecedent membership functions obtained by Delaunay triangulation of their characteristic points. The number and position of these points are determined by an iterative insertion algorithm. Constrained optimization is used to estimate the consequent parameters, where the constraints are based on control-relevant a priori knowledge about the modeled process. Finally, methods for control design through linearization and inversion of this model are developed. The proposed techniques are demonstrated by means of two benchmark examples: identification of the well-known Box-Jenkins gas furnace and inverse model-based control of a pH process. The obtained results are compared with results from the literature.

## Fuzzy model-based predictive control by instantaneous linearization

A linearization technique for product-sum crisp-type fuzzy model and a multistep predictive control strategy for the construction of a model-based predictive fuzzy controller is presented in this paper. A model-based predictive controller is based on a local linear model generated by using the proposed linearization technique that linearizes the product-sum crisp-type fuzzy process model around the current operating point. The control of pH in a continuous stirred tank reactor is chosen as a realistic nonlinear case study for the demonstration of the proposed control algorithm. The controller is shown to be capable of controlling the nonlinear processes that operate over a wide range, and of providing better overall system performance than the optimal PI controller.

## Identification and Control of Nonlinear Systems Using Fuzzy Hammerstein Models

This paper addresses the identification and control of nonlinear systems by means of Fuzzy Hammerstein (FH) models, which consist of a static fuzzy model connected in series with a linear dynamic model. For the identification of nonlinear dynamic systems with the proposed FH models, two methods are proposed. The first one is an alternating optimization algorithm that iteratively refines the estimate of the linear dynamics and the parameters of the static fuzzy model. The second method estimates the parameters of the nonlinear static model and of the linear dynamic model simultaneously by using a constrained recursive least-squares algorithm. The obtained FH model is incorporated in a model-based predictive control scheme and a new constraint-handling method is presented. A simulated water-heater process is used as an illustrative example. A comparison with an affine neural network and a linear model is given. Simulation results show that the proposed FH modeling approach is useful for modular parsimonious modeling and model-based control of nonlinear systems.

## Hybrid fuzzy convolution model and its application in model predictive control

In this paper a new method for synthesising nonlinear, control-oriented process models is presented. The proposed hybrid fuzzy convolution model (HFCM) consists of a steady-state fuzzy model and a gain-independent impulse response model. The proposed HFCM is applied in model based predictive control of a laboratory-scale electrical water-heater. Simulation and real-time studies confirm that the method is capable of controlling this delayed and distributed parameter system with a strong nonlinear feature.

## Hybrid Convolution Model and its Application in Predictive pH Control

This paper presents a new method for synthesising chemical process models that combines prior knowledge and fuzzy models. The hybrid convolution model consists of a fuzzy model based steady-state, and an impulse response model based dynamic part. Prior knowledge enters to the dynamic part as a resident time distribution model of the process. The proposed approach is applied in the modelling and model based control of a highly nonlinear pH process.

## Predictor Corrector Controller using Wiener Fuzzy Convolution Model

This paper investigates the application of hybrid fuzzy models in modelling and model based predictive control of a delayed and distributed parameter system with a nonlinear feature.

The presented hybrid fuzzy convolution model consists of a nonlinear fuzzy steady-state model and an impulse response model based dynamic part. The proposed non-linear block-oriented dynamic model is applied to form a predictor corrector controller.

The control of a laboratory-sized heating system is chosen as a realistic nonlinear case study for the demonstration of the control algorithm. The proposed model based controller is shown to be capable of controlling the nonlinear process that operates over wide range.

## Tendency model-based improvement of the slave loop in cascade temperature control of batch process units

In the fine chemical industry, the batch or fed-batch reactor functions as the heart of the transformation process. Due to the complexity of chemical synthesis, the control of these reactors remains a problem of temperature control commonly performed indirectly via the jacket of the reactor. This results in a cascade control scheme based on the control a secondary, more responsive process that influences the main process. This control loop is often referred to as the slave loop of the process. This paper highlights that the slave process of batch process units, i.e. the jacket of the reactor, can have more complex dynamics than the master loop has; and very often this could be the reason for the non-satisfying control performance. Since the slave process is determined by the mechanical construction of the unit, the above mentioned problem can be effectively handled by a model-based controller designed using an appropriate nonlinear tendency model. The presented analysis shows that the complex dynamics of the slave process can be decomposed into static nonlinear and dynamic linear parts. This decomposition is beneficial since it allows the effective incorporation of the resulted tendency model into nonlinear model-based control algorithms. Real-time control results show that the proposed methodology gives superior control performance over the widely applied cascade PID-PID control scheme.

## Direct and indirect adaptive control

## (Controller Output Error Method)

This research studies inverse fuzzy-model-based controllers to compensate non-linear terms that affect the system dynamics. The controller is based on an inverse semi-linguistic fuzzy process model, identified and adapted via input-matching technique. This entails generating two control signals; the first control signal is applied to the plant and the second is inferred from the plant’s response to the first control signal. The controller output error is the difference between these two control signals and is used by the algorithm to adapt the controller.

For the adaptation of the fuzzy model a general learning rule has been developed employing gradient-descent algorithm. The on-line learning ability of the fuzzy model allows the controller to be used in applications, where the knowledge to control the process does not exist or the process is subject to changes in its dynamic characteristics.

## Adaptive fuzzy inference system and its application in modelling and model based control

This study presents an adaptation method for Sugeno fuzzy inference systems that maintain the readability and interpretability of the fuzzy model during and after the learning process. This approach can be used for modelling of dynamical systems and for building adaptive model-based control algorithms for chemical processes.

The gradient-descent based learning algorithm can be used on-line to form an adaptive fuzzy controller—this ability allows these controllers to be used in applications where the knowledge to control the process does not exist or the process is subject to changes in its dynamic characteristics. The proposed approach was applied in an internal model (IMC) fuzzy control structure based on the inversion of the fuzzy model. The adaptive fuzzy controller was applied in the control of a non-linear plant and is shown to be capable of providing good overall system performance.

## Inverse fuzzy-process-model based direct adaptive control

This paper proposes a direct adaptive fuzzy-model-based control algorithm. The controller is based on an inverse semi-linguistic fuzzy process model, identified and adapted via input-matching technique. For the adaptation of the fuzzy model a general learning rule has been developed employing gradient-descent algorithm. The on-line learning ability of the fuzzy model allows the controller to be used in applications, where the knowledge to control the process does not exist or the process is subject to changes in its dynamic characteristics. To demonstrate the applicability of the method, a realistic simulation experiments were performed for a non-linear liquid level process. The proposed direct adaptive fuzzy logic controller is shown to be capable of handling non-linear and time-varying systems dynamics, providing good overall system performance.

## Model predictive control of a continuous vacuum crystalliser in an industrial environment: A feasibility study

Crystallisers are essentially multivariable systems with high interaction amongst the process variables. Model Predictive Controllers (MPC) can handle such highly interacting multivariable systems efficiently due to their coordinated approach.

In the absence of a real continuous crystalliser, a detailed momentum-model was applied using the process simulator in Simulink.

This process has been controlled by a model predictive controller widely used in industry. A new framework has been worked out for the incorporation of the Honeywell Profit. Suite controller to the simulator of the crystalliser. The engineering model and the controller were connected via OPC (OLE-Object Linking and Embedding for Process Control standard). Models were developed in Profit. Suite using the new fully-automated identification method. The feasibility study illustrated that the applied identification tool gave an accurate and robust model, and that the non-linear crystalliser may be controlled and optimised very well with the Honeywell Profit. Suite package. The developed system is proven to be useful in research and development.

## Fuzzy supervisory control

In industrial applications of adaptive controllers, standard algorithms have to be combined with heuristically derived safety nets. These safety nets are often realised in expert systems. The aim of this research is to develop an intelligent supervision system, where the heuristic knowledge is represented by fuzzy rules. The aim of the application of fuzzy techniques on the supervisory level is to design an easily interpretable and transparent algorithm that allows the incorporation of control specifications and a priori knowledge of the operators by using linguistic terms.

## Effective optimization for fuzzy model predictive control

This work addresses the optimization in fuzzy model predictive control. When the prediction model is a nonlinear fuzzy model, nonconvex, time-consuming optimization is necessary, with no guarantee of finding an optimal solution. A possible way around this problem is to linearize the fuzzy model at the current operating point and use linear predictive control (i.e., quadratic programming). For long-range predictive control, however, the influence of the linearization error may significantly deteriorate the performance. In our approach, this is remedied by linearizing the fuzzy model along the predicted input and output trajectories. One can further improve the model prediction by iteratively applying the optimized control sequence to the fuzzy model and linearizing along the so obtained simulated trajectories. Four different methods for the construction of the optimization problem are proposed, making difference between the cases when a single linear model or a set of linear models are used. By choosing an appropriate method, the user can achieve a desired tradeoff between the control performance and the computational load. The proposed techniques have been tested and evaluated using two simulated industrial benchmarks: pH control in a continuous stirred tank reactor and a high-purity distillation column.

## Feedback linearizing control using hybrid neural networks identified by sensitivity approach

Globally linearizing control (GLC) is a control algorithm capable of using nonlinear process model directly. In GLC, mostly, first-principle models derived from dynamic mass, energy and momentum balances are used. When the process is not perfectly known, the unknown parts of the first principles model should be represented by black-box models, e.g. by neural networks. This paper is devoted to the identification and application of such hybrid models for GLC. It is shown that the first principles part of the model determines the dominant structure of the controller, while the black-box elements of the hybrid model are used as state and/or disturbance estimators. For the identification of the neural network elements of the hybrid model a sensitivity approach based algorithm has been developed. The underlying framework is illustrated by the temperature control of a continuous stirred tank reactor where a neural network is used to model the heat released by an exothermic chemical reaction.