Multivariable PID control by decoupling

This paper presents a new methodology to design multivariable proportional-integral-derivative (PID) controllers based on decoupling control. The method is presented for general n × n processes. In the design procedure, an ideal decoupling control with integral action is designed to minimise interactions. It depends on the desired open-loop processes that are specified according to realisability conditions and desired closed-loop performance specifications. These realisability conditions are stated and three common cases to define the open-loop processes are studied and proposed. Then, controller elements are approximated to PID structure. From a practical point of view, the wind-up problem is also considered and a new anti-wind-up scheme for multivariable PID controller is proposed. Comparisons with other works demonstrate the effectiveness of the methodology through the use of several simulation examples and an experimental lab process.     

Decentralized robust PI controller design for an industrial boiler

This paper presents a new scheme to design decentralized robust PI controllers for uncertain LTI multivariable systems. Sufficient conditions for closed-loop stability and closed-loop diagonal dominance (almost decoupling) of a multivariable system are obtained. Satisfying these conditions and robust performance of the overall system are modeled as local robust performance problems. Then, by appropriately selecting the time constants of the closed-loop isolated subsystems in the IMC (Internal Model Control) strategy, the defined local robust performance problems are solved. To design a decentralized robust PI controller for a real industrial utility boiler, a control oriented nonlinear model for the boiler is identified. The nonlinearity of the system is modeled as uncertainty for a nominal LTI multivariable system. Using the new proposed method, a decentralized PI controller for the uncertain LTI model is designed. The designed controller is applied to the real system. The simulation results show the effectiveness of the proposed methodology.     

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.     

Design of multivariable feedback systems with simple unstable plant

This paper proposes a design methodology for distributed linear multivariable feedback systems with simple unstable plants (a simple unstable plant has either first- or second-order unstable poles). The methodology developed provides a global characterization of all realizable compensators which stabilize a given simple unstable plant. A design example is given to show that this methodology can be used to generate, in an appropriate computer-aided design environment, controllers which are optimal with respect to designer-specified criteria. Additionally, it is shown that the nature of the design methodology gives geometric insight into the dynamics of the process whereby an unstable plant is stabilized.     

Robust digital control of a high-performance engine

The design of a robust digital multivariable feedback control system for the F-100 turbofan jet engine is considered. The control system design problem is posed, and conditions for satisfying performance specifications and stability robustness are stated. The discrete LQG/LTR methodology is used to design a compensator that meets the stated specifications. New results for multi-input LQR loop shaping are derived. To get a reasonably low-order compensator, frequency-weighted reduced-order models are exploited, with the reduction error treated as an uncertainty.     

STATE‐SPACE DIGITAL PID CONTROLLER DESIGN FOR MULTIVARIABLE ANALOG SYSTEMS WITH MULTIPLE TIME DELAYS

This paper presents a discrete‐time state‐space methodology for optimal design of digital PID controllers for multivariable analog systems with multiple time delays. The multiple time‐delayed multivariable analog systems are formulated in a state‐space generic form so that the exact discrete‐time state‐space model can be constructed. Then, the optimal digital PID controller is designed via a state‐feedback and state‐feedforward LQR approach. The developed PID controller can be applied to a general time‐delayed multivariable analog system represented by a semi‐proper or strictly proper transfer function matrix. Illustrative examples are given to compare the performance of the proposed approach with alternative techniques.     

Optimal design of robust quantitative feedback controllers using random optimization techniques

Quantitative design of robust control systems proposes a transparent and practical controller design methodology for uncertain single-input single-output and multivariable plants. There are several steps involved in the design of such controllers. The main steps involved in the design are template generation, loop shaping and pre-filter design. In the case of multivariable uncertain plants, manipulation of tolerance bounds within the available freedom, for both sequential and non-sequential designs, consideration of template size of next step in sequential design, and the appropriate selection of the nominal transfer function matrices in the equivalent disturbance attenuation design are also crucial steps. In all the quantitative designs, a time-consuming trial-and-error procedure is adapted and a successful compromise between various design requirements is very much dependent on the designer experience and expertise. In this paper, these steps are reformulated in terms of different cost functions, and it is shown that the optimization of these cost functions leads to an optimal design of quantitative controllers, for both single input single output and multivariable plants. This proposes a nonlinear constrained optimization problem that can be easily solved using any of the random optimization techniques. Simulation results are used to show the effectiveness of the proposed method.     

Coprime-factorized Model Predictive Control for Unstable Processes with Delay

This paper presents coprime-factorized model predictive control. The main idea of the proposed approach is in process-output prediction based on a coprime-factorized process model. The proposed approach provides a framework to design the control for a wide range of processes such as: higher order, phase non-minimal, unstable and also multivariable. In the paper the coprime-factorized predictive design methodology was studied and implemented on unstable processes with a time-delay which are very difficult to control. The proposed methodology leads to a simple analytical control law, which results in much better performance than previously known control methods.     

An observer-based decentralized tracker for sampled-data systems: an evolutionary programming approach

Decentralized control is a practical control methodology for large-scale multivariable systems. This paper presents a LQR design methodology to design a state-feedback decentralized high-gain analog controller, which gives the desired decentralized performance of the controlled analog system. Then, a prediction-based decentralized low-gain digital controller is developed from the decentralized high-gain analog controller for the hybrid controlled system. As a result, the complexity and cost of hardware implementation of the controller can be significantly reduced. In order to improve the performance of the decentralized hybrid system, the evolutionary programming (EP) is employed to tune the observer-based decentralized tracker. Some examples are presented to illustrate the developed design methodology.     

An expert autotuner for multiloop SISO controllers

In this paper, an on-line expert autotuner for a class of 2-input-2-output multivariable process control applications is proposed. The autotuning controller, which uses a pattern-recognition technique is designed with a view to its practical implementation in multivariable processes. The main idea of the autotuning methodology is to use the observed multiloop responses with reference to the single-loop responses such that proper detuning of the SISO controllers is achieved. Customized identification techniques in SISO and MIMO environments based on closed-loop responses are developed for this application. Simulation results for a range of 2-input-2-output multivariable processes characterized by the Relative Gain (RG) and the relative dynamics are used to evaluate the performance of the autotuning controller under different conditions. The time response of the autotuning controller is compared to that of Biggest Log Modulus Tuning (BLT) method with a few distillation column models proposed in the literature.     

A linear-interpolation-based controller design for trajectory tracking of mobile robots

This work presents a novel linear interpolation based methodology to design control algorithms for the trajectory tracking of mobile robotic systems. Particularly, a typical nonlinear multivariable system—a mobile robot—is analysed. The methodology is simple and can be applied to the design of a large class of control systems. Simulation and experimental results are presented and discussed, demonstrating the good performance of the proposed methodology.     

Control of the ALSTOM gasifier benchmark problem using H2 methodology

This paper considers the analysis and controller design for the ALSTOM gasifier system. The inherent properties of this highly coupled and numerically ill conditioned multivariable system are studied. A simple reduction is used to determine a minimal realization of the system after using the Osborne transformation to improve the numerical condition of the system. The relative gain array (RGA) is used to achieve suitable input–output (I/O) pairings for the gasifer system, and Edmunds scaling is used to improve the diagonal dominance of the system and numerical conditioning. Model order reduction methods are applied to simplify the subsequent design. A controller is designed using the H₂ methodology at the 100% load condition. The robustness of this controller at other load conditions is assessed and gives satisfactory results.     

Smith predictor with inverted decoupling for square multivariable time delay systems

This paper presents a new methodology to design multivariable Smith predictor for n×n processes with multiple time delays based on the centralised inverted decoupling structure. The controller elements are calculated in order to achieve good reference tracking and decoupling response. Independent of the system size, very simple general expressions for the controller elements are obtained. The realisability conditions are provided and the particular case of processes with all of its elements as first-order plus time delay systems is discussed in more detail. A diagonal filter is added to the proposed control structure in order to improve the disturbance rejection without modifying the nominal set-point response and to obtain a stable output prediction in unstable plants. The effectiveness of the method is illustrated through different simulation examples in comparison with other works.     

Design of a sliding mode control system for chemical processes

This paper considers the non-linear regulation control of chemical processes. A novel and systematic sliding mode control system design methodology is proposed, which integrates an identified second-order plus dead-time (SOPDT) model, an optimal sliding surface and a delay-ahead predictor. The convergence property of the closed-loop system is guaranteed theoretically by means of satisfying a sliding condition and the control system performance is examined with some typical chemical processes. Besides, with the concept of delay equivalent, the proposed sliding mode control scheme can be utilized directly to the regulation control of a non-minimum phase process. As a special case the proposed scheme is further extended to the control of chemical processes whose dynamics are simply described by a first-order plus dead-time (FOPDT) model. In addition, the decentralized sliding mode control scheme for multivariable processes is also explored in this paper. Extensive simulation results reveal that the proposed sliding mode control system design methodology is applicable and promising for the non-linear regulation of time-delay chemical processes.     

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.     

基于INA设计方法的多变量PID控制器设计方法

在查阅总结大量相关文献的基础上,本文提出了一种基于逆Nyquist阵列（INA）设计方法的多变量控制器设计方法。在简要介绍了设计方法的理论基础和相关概念（极限点以及极限增益和极限频率）的基础上,以TITO多变量控制系统为例,简述设计思路,并给出其推导过程及其设计步骤;并借助仿真实验,与文献[8]所提出的设计方法进行了一系列的对比仿真实验,并给出了相关的分析和结论。     

Modern Wiener-Hopf design of optimal controllers--Part II: The multivariable case

In many modern-day control problems encountered in the fluid, petroleum, power, gas and paper industries, cross coupling (interaction) between controlled and manipulated variables can be so severe that any attempt to employ single-loop controllers results in unacceptable performance. In all these situations, any workable control strategy most take into account the true multivariable nature of the plant and address itself directly to the design of a compatible multivariable controller. Any practical design technique most be able to cope with load disturbance, plant saturation, measurement noise, process lag, sensitivity and also incorporate suitable criteria delimiting transient behavior and steady-state performance. These difficulties, when compounded by the fact that many plants (such as chemical reactors) are inherently open-loop unstable have hindered the development of an inclusive frequency-domain analytic design methodology. However, a solution based on a least-square Wiener-Hopf minimization of an appropriately chosen cost functional is now available. The optimal controller obtained by this method guarantees an asymptotically stable and dynamical closed-loop configuration irrespective of whether or not the plant is proper, stable, or minimum-phase and also permits the stability margin of the optimal design to be ascertained in advance. The main purpose of this paper is to lay bare the physical assumptions underlying the choice of model and to present an explicit formula for the optimal controller.     

Dynamic inversion for multivariable non-affine-in-control systems via time-scale separation

This paper presents a tracking design methodology applicable to multivariable non-affine-in-control systems. The main focus is on solving the tracking problem for non-linear systems whose dynamics depend non-linearly on the control input. The latter is designed to be faster than the main system dynamics. Using singular perturbation theory along with the Lyapunov stability theorems, it is shown that the proposed controller approximates an unknown dynamic inversion based solution with bounded errors, provides closed-loop stability, and solves the tracking problem with bounded errors. Simulations illustrate the theoretical results.     

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.