Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications.     

Generic distributed parameter model control of a biological nutrient removal (BNR) activated sludge process

This paper addresses nonlinear control of a class of distributed parameter systems by the generic distributed parameter model-based control (GDPMC) strategy. Case studies on a complex biological nutrient removal (BNR) activated sludge process for nitrogen and phosphorus removal show that the GDPMC strategy is applicable for controlling species of interest in specific bioreaction zones. The designs give much improved performances compared to well-tuned PI controllers in terms of the integral time absolute errors (ITAE). In a study on control of the entire BNR activated sludge plant, a multi-unit decentralised GDPMC strategy is shown to be robust to 25% plant-model mismatch in three sensitive and uncertain kinetic parameters. The advantages of the GDPMC strategy over lumped-model generic model control (GMC) are demonstrated in a comparative study on soluble phosphate control within the anaerobic zone of the plant.     

Robust controller design for a class of nonlinear uncertain chemical processes

This article considers the issue of designing robust controllers for single-input/single-output nonlinear chemical processes whose uncertainties satisfy the so-called generalized matching condition. The nominal system (mathematical model) is assumed to be input–output linearizable and the only assumption on uncertainties is that they are bounded. A design methodology of combining the techniques of the differential geometric feedback linearization, the sliding mode control strategy and the adaptive state feedback is presented. Based on the nominal system and the related bounds of uncertainties, a hybrid nonlinear controller, which is more practicable and easily implemented than many other existing ones in the literature, is proposed. A Lyapunov-based approach is utilized to guarantee the robust stability and behavior of the closed-loop system. For demonstrating the effectiveness and applicability of the proposed scheme, we applied it to the control of a continuously stirred tank reactor (CSTR) in the presence of uncertainties including unmodeled side reaction, measuring error, and/or extra unmeasured disturbances. The potential use of a sliding observer along with the proposed scheme is also investigated in this work. Extensive simulation results reveal that the proposed scheme appears to be a practical and promising approach to the robust control of nonlinear uncertain chemical processes.     

High performance controllers for unknown multivariable systems

Recent work on the design of robust proportional plus integral non-adaptive process controllers for unknown minimum-phase (but possibly unstable) multivariable systems is discussed and extended to predict permissible data inaccuracies and illustrated by application to an open-loop unstable batch process.     

多变量解耦控制的工业过程运行层次控制方法

基于多变量解耦控制技术,提出了一种工业过程运行的层次控制方法,用于实现表征过程整体运行性能的工艺指标.底层回路控制系统采用多回路PI/PID控制技术进行设计,用于将关键工艺参数控制在给定的工作点.针对中被控过程和底层回路控制系统构成的文义对象,采用扩展的单位反馈解耦方法设计上层回路设定控制器,该回路设定控制器能够克服系...     

Robust control design of power system stabilizers using multivariable frequency domain techniques

H_∞ and structured singular value optimization techniques are used to design robust power system stabilizers (PSS) for a single-machine and a two-machine system with varying operating conditions. Realistic uncertainty models to represent the possible operating conditions as perturbations from a nominal operating condition are developed. System experience is used to select weighting functions to provide adequate damping and shape the controller frequency response. Computer simulations show that the PSS designed using the proposed technique provides improved damping compared to a conventional PSS.     

Designing of non-fragile robust model predictive control for constrained uncertain systems and its application in process control

A non-fragile robust model predictive control (RMPC) is designed in the uncertain systems under bounded control signals. To this aim, a class of the nonlinear systems with additive uncertainty is considered in its general form. The RMPC synthesis could lead to the proper selection of the controller’s gains. Thus, the non-fragile RMPC design is translated into a minimization problem subjected to some constraints in terms of linear matrix inequality (LMI). Hence, the controller’s gains are computed by solving such a minimization problem. In some numerical examples, the suggested non-fragile RMPC is compared with the other methods. The simulation results demonstrate the effectiveness of the proposed RMPC in comparison with similar techniques.     

Robust sliding mode controllers design techniques for stabilization of multivariable time-delay systems with parameter perturbations and external disturbances

In this paper, robust delay-independent stabilization of multivariable single state-delayed systems with mismatching parameter uncertainties and matching/mismatching external disturbances are considered. To achieve this goal, two types of robust sliding mode controllers design techniques are advanced. The first is an integral sliding mode controller design modification to Shyu and Yan type controller design. The mismatching sliding conditions are parametrically obtained by using the Lyapunov-Razumikhin-Hale method and formulated in terms of some matrix norm inequalities. In the second contribution, a new combined sliding mode controller design technique for the stabilization of multivariable single state-delayed systems with mismatching parameter perturbations is advanced by using the Lyapunov-Krasovskii V-functional method. The sliding, global stability and delay-dependent β-stability conditions are parametrically obtained and formulated in terms of matrix inequalities. A sliding mode controller design example for AV-8A Harrier VTOL aircraft with lateral unstable dynamic model parameters is considered to illustrate the controller design method. Design procedures and simulation results show that our advanced method is useful, and unstable lateral dynamics is successfully stabilized by using the combined controller.     

Robust state feedback synthesis for control of non-square multivariable nonlinear systems

In this paper, a robust nonlinear controller is designed in the Input/Output (I/O) linearization framework, for non-square multivariable nonlinear systems that have more inputs than outputs and are subject to parametric uncertainty. A nonlinear state feedback is synthesized that approximately linearizes the system in an I/O sense by solving a convex optimization problem online. A robust controller is designed for the linear uncertain subsystem using a multi-model H₂/H_∞ synthesis approach to ensure robust stability and performance of non-square multivariable, nonlinear systems. This methodology is illustrated via simulation of a regulation problem in a continuous stirred tank reactor.