Interaction bounds in multivariable control systems

Time-domain limitations due to right half-plane zeros and poles in linear multivariable control systems are studied. Lower bounds on the interaction are derived. They show not only how the location of zeros and poles are critical in multivariable systems, but also how the zero and pole directions influence the performance. The results are illustrated on the quadruple-tank process, which is a new multivariable laboratory process.     

Multivariable controller design in an adaptive control scheme

A multivariable control system design approach in the frequency domain is presented. The issue of control system redesign in an adaptive control scheme is discussed. Expert system techniques have been used for the automated design of controllers for multivariable systems. Design knowledge has been represented using rules, facts and objects. The design process consists of a sequence of operations obtained by heuristics and experience in the the design techniques. An automated design session of a multivariable plant using the expert system demonstrates that the expert system appears to work well in its prototype implementation.     

Multivariable adaptive control: A survey

Adaptive control is a control methodology capable of dealing with uncertain systems to ensure desired control performance. This paper provides an overview of some fundamental theoretical aspects and technical issues of multivariable adaptive control, and a thorough presentation of various adaptive control schemes for multi-input–multi-output systems, literature reviews on adaptive control foundations and multivariable adaptive control methods, and related technical problems. It covers some basic concepts and issues such as certainty equivalence, stability, tracking, robustness, and parameter convergence. It discusses some of the most important topics of adaptive control: plant uncertainty parametrization, stable controller adaptation, and design conditions for different adaptive control schemes. The paper also presents a detailed study of well-developed multivariable model reference adaptive control theory and design techniques. It provides an introduction to multivariable adaptive pole placement and adaptive nonlinear control, and it concludes by identifying some open research problems.     

THE EFFECT OF OPERATING VARIABLES ON THE DYNAMICS OF CATALYTIC CRACKING PROCESSES

The dynamic Characteristics of a Fluidized Catalytic Cracking Process are examined over a wide range of operating conditions. A novel Order of Magnitude Approach is introduced to successfully provide physical insight into the cause and effect relationship between operating conditions and dynamic characteristics. It is shown that the original five-dimensional dynamic model is characterized by three fast time constants and two slow ones that dominate the dynamic responses. The two most important time constants are expressed as explicit functions of the operating conditions. These formulas correctly indicate in which parameter regions the open loop response is oscillatory (underdamped) or nonoscillatory (overdamped). Extensive process variables, that are either flow or capacity, related are defined in order to provide an approximate physical meaning for the dynamic modes of the system. It is shown that the two slow modes of the process are related to the enthalpy content of the regenerator and the sensible heat content of the catalyst phase in both the reactor and regenerator.     

Multi-loop design of multi-scale controllers for multivariable processes

Based on the recently proposed (SISO) multi-scale control scheme, a new approach is introduced to design multi-loop controllers for multivariable processes. The basic feature of the multi-scale control scheme is to decompose a given plant into a sum of basic modes. To achieve good nominal control performance and performance robustness, a set of sub-controllers are designed based on the plant modes in such a way that they are mutually enhanced with each other so as to optimize the overall control objective. It is shown that the designed multi-scale controller is equivalent to a conventional PID controller augmented with a filter. The multi-scale control scheme offers a systematic approach to designing multi-loop PID controllers augmented with filters. Numerical studies show that the proposed multi-loop multi-scale controllers provide improved nominal performance and performance robustness over some well-established multi-loop PID controller schemes.     

A new calculation method of feedback controller gain for bilinear paper-making process with disturbance

This paper presents a new method to calculate the feedback control gain for a class of multivariable bilinear system, and also applied this method on the control of two sections of paper-making process with disturbance. The robust H∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H∞ performance of the resulting closed-loop system are ensured. The controller turns out to be robust with respect to the disturbance in the plant. Utilizing the Schur complement and some variable transformations, the stability conditions of the multivariable bilinear systems are formulated in terms of Lyapunov function via the form of linear matrix inequality (LMI). The gain of controller will be calculated via LMI. Finally, the application examples of a headbox section and a dryer section of paper-making process are used to illustrate the applicability of the proposed method.     

An analytical tuning approach to multivariable model predictive controllers

Multivariable model predictive control is a widely used advanced process control methodology, where handling delays and constraints are its key features. However, successful implementation of model predictive control requires an appropriate tuning of the controller parameters. This paper proposes an analytical tuning approach to multivariable model predictive controllers. The considered multivariable plants are square and consist of first-order plus dead time transfer functions. Most of the existing model predictive control tuning methods are based on trial and error or numerical approaches. In the case of no active constraints, closed loop transfer function matrices are derived and decoupling conditions are addressed. For control horizon of one, analytical tuning equations and achievable performances are obtained. Finally, simulation results are used to verify the effectiveness of the proposed tuning strategy.     

Estimating performance enhancement with alternate control strategies for multiloop control systems

A filter based methodology, studied earlier for SISO systems, is extended to MIMO systems. The presented approach facilitates the calculation of best achievable performance for proportional-integral (PI) controller and the optimal multiloop (ML) PI settings for stochastic disturbance rejection in ML control systems. The filter based approach is further extended to answer some of the key questions for ML control systems such as: (a) performance enhancement possible with the alternate pairing scheme, (b) benefits that will accrue through the employment of decouplers and (c) the performance achievable with the use of multivariable controller (as opposed to an ML controller). Further, the trade-off curve between output variance and control effort is generated for the various control configurations within PI controller domain.     

Non-diagonal H∞ weighting function design: Exploiting spatio-temporal deformations in precision motion control

Model-based control design requires a careful specification of performance and robustness requirements. In typical norm-based control designs, performance and robustness requirements are specified in a scalar optimization criterion, even for complex multivariable systems. This paper aims to develop a novel approach for the formulation of this optimization criterion for multivariable motion systems that exhibit spatio-temporal deformations. To achieve this, characteristics of the underlying system are exploited to design multivariable weighting functions. In contrast to pre-existing approaches, which typically lead to diagonal weighting functions, the proposed approach enables the design of non-diagonal weighting functions. Extensive experimental results confirm that the proposed procedure can significantly improve the performance of an industrial motion system compared to earlier approaches.     

Predictive control of an activated sludge process: An application to the Viikinmäki wastewater treatment plant

In this work, we discuss the application of multivariable predictive control for the activated sludge process in a full-scale municipal wastewater treatment plant. Emphasis is given to the selection of a control configuration that contributes to minimising the economic costs while improving the removal efficiency of the nitrogen compounds. For this task, a simple dynamic matrix control algorithm is favoured for controlling the nitrogen concentrations at the end of the biological process. The behaviour of the activated sludge process is reproduced in a commercial simulator that acts as a real-time testing platform and that is also used for identifying the multivariable input–output models for the predictive controller. For demonstrating the effectiveness of the proposed approach, different control configurations are considered and compared against the aeration control strategies currently used at the plant. Based on the simulation results, this work shows the potentiality of the dynamic matrix control which is able to decrease the energy consumption costs and, at the same time, reduce the ammonia peaks and nitrate concentration in the effluent.