H ∞ control of a Wiener-type system

A Wiener system is a system which can be modelled as a linear dynamic followed by a static gain. The goal of this paper is to develop a robust H _∞ compensator for controlling an SISO Wiener system. The controller also takes the form of a Wiener model. The design approach consists of the approximation of the non-linear gain using a piecewise linear (PWL) function and in using a linear controller for each sector obtained from this approximation. Therefore, the general controller structure can be stated as a linear dynamic compensator in series with a PWL static gain.

As an illustrative case, a neutralization pH reaction between a strong acid and a strong base in the presence of a buffer agent is dealt with. Computer simulations are developed for showing the performance of the proposed controller.     

A two‐degree‐of‐freedom ℋ︁∞ control design method for robust model matching

We propose an ??_∞ controller design method which achieves a closed‐loop transfer function equal or otherwise sensibly close to a desired transfer function, viz. a model reference design. The proposed controller design method inherits the model reference feature of the internal model control design method and incorporates the weighting scheme of the ??_∞ loop‐shaping. It utilizes Youla–Kucera parameterization in a two‐degree‐of‐freedom scheme to achieve robust model reference and high performance design while ensuring a sensible robust stability margin, and can be readily applied to the generic class of LTI systems (SISO, MIMO, stable, unstable). Copyright © 2006 John Wiley & Sons, Ltd.     

Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T–S fuzzy approach

By utilising Takagi–Sugeno (T–S) fuzzy set approach, this paper addresses the robust H_∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics’ enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T–S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H_∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T–S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.     

Adaptive controller design and disturbance attenuation for SISO linear systems with noisy output measurements and partly measured disturbances

In this article, we present robust adaptive controller design for SISO linear systems with noisy output measurements and partly measured disturbances. Using the worst-case analysis approach, we formulate the robust adaptive control problem as a non-linear H ^∞-optimal control problem under imperfect state measurements and solve it using game theory. The design paradigm is the same as (Pan, Z. and Ba?ar, T., 1998, Adaptive Controller Design for Tracking and Disturbance Attenuation for SISO Linear Systems with Noisy Output Measurements, CSL report, Urbana, IL: University of Illinois at Urbana-Champaign) with the only difference being the treatment of the measured disturbances. The same result as (Pan and Ba?ar l998) is achieved. In addition, when the relative degrees from the measured disturbances to the output are no less than that from the control input, the controller designed achieves the zero disturbance attenuation level with respect to the measured disturbance inputs. The asymptotic tracking objective is achieved even if the measured disturbance is only uniformly bounded, without requiring it to be of finite energy. This strong robustness property is then illustrated by numerical examples.     

Identification and idle speed control of internal combustion engines

This paper presents an integrated approach for the identification and control of internal combustion engines in idle-speed conditions. The inputs of the nonlinear identification model are the position of the idle speed air actuation system and the spark advance, while its outputs are the pressure inside the air intake manifold and the crank shaft speed. The estimated model is then used to synthesize an idle speed controller with the linear quadratic technique. The design procedure outlined here is currently being used by Magneti Marelli for the synthesis of commercial idle-speed regulators. Some identification and control results obtained by applying this method to a 1400 cm³ commercial engine are reported to witness the effectiveness of the proposed approach.     

Controller design for nonlinear systems using the Contoured Robust Controller Bode plot

In this paper, we develop the Contoured Robust Controller Bode (CRCBode) plot and demonstrate its use in the design of robust controllers for nonlinear single‐input single‐output (SISO) systems. The CRCBode plot shows contours (level sets) of a robust performance quantity on the Bode magnitude and phase plots of the controller. An iterative frequency domain loop‐shaping design approach is employed to eliminate all intersections of the controller frequency response with certain ‘forbidden regions,’ indicating that a standard SISO robust stability and performance criterion is satisfied. Nonlinearities are accounted for by avoiding the maximum forbidden regions over a structured uncertainty set consisting of linearizations of the system dynamics about several operating points. We demonstrate this technique by designing and experimentally verifying a flow‐rate controller for a butterfly‐valve based liquid cooling system, which is robust to valve nonlinearities and flow disturbances. Finally, we compare this compensator with one generated using an automated H _∞ synthesis algorithm and discuss the advantages of the CRCBode approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Plasma multivariable robust control system design and simulation for a thermonuclear tokamak-reactor

The paper reports results on the design and analysis of the multivariable feedback H_infin; robust system for plasma current, position and shape control in the fusion energy advanced tokamak (FEAT) developed in the International Thermonuclear Experimental Reactor (ITER) project. The system contains the fast loop with the SISO plasma vertical speed robust controller and the slow loop with the MIMO plasma current and shape robust controller. The goal is to study the resources of the system robustness to achieve a higher degree of the FEAT operation reliability. Two H_infin; block diagonal controllers {K _SISO, K _MIMO} were designed by a mixed sensitivity approach in the framework of the disturbance rejection configuration. These controllers were compared with block diagonal decoupling, PI and LQG controllers at the set of FEAT key scenario points according to the multiple-criterion: nominal performance at minor disruptions, robust stability and robust performance. The H_infin; controllers showed larger multivariable stability margin and better nominal performance.     

Robust control of multivariable critical systems

Based on the method of inequalities and H _∞-optimization method, this paper develops an approach to robust control design of multivariable critical systems with external and internal uncertainties. In this approach the formulation of the robust control design of these systems is expressed by a set of inequalities which includes output performance criteria in the time domain and a robust performance criterion in the frequency domain of the system. Some relationships between an input space, a modelling error space, a controller, output performance and robust performance are established by inequalities for SISO and MIMO critical systems so that the robust control design problem of these systems is largely simplified.     

Constructing NARMAX models using ARMAX models

This paper outlines how it is possible to decompose a complex non-linear modelling problem into a set of simpler linear modelling problems. Local ARMAX models valid within certain operating regimes are interpolated to construct a global NARMAX (non-linear NARMAX) model. Knowledge of the system behaviour in terms of operating regimes is the primary basis for building such models, hence it should not be considered as a pure black-box approach, but as an approach that utilizes a limited amount of a priori system knowledge. It is shown that a large class of non-linear systems can be modelled in this way, and indicated how to decompose the systems range of operation into operating regimes. Standard system identification algorithms can be used to identify the NARMAX model, and several aspects of the system identification problem are discussed and illustrated by a simulation example.     

Robust control of distillation columns: μ- vs H∞-synthesis

High-purity distillation columns are known to be difficult to control due to their ill-conditioned and non-linear behaviour. Two approaches for the design of robust controllers yielding high performance are presented. For the first approach, first principles are used to develop an uncertainty model describing the nonlinear dynamics within the entire operating range of an industrial distillation column. This structured uncertainty model is used for μ-synthesis. In a second approach which is based on loop shaping ideas, an H_∞-controller is designed. This controller performs as well as the μ-controller. The H_∞-approach offers the advantage that the burden for uncertainty modelling and computation is greatly reduced. However, the GS/T augmentation scheme, which is developed in this paper, must be used for the design of the H_∞-controller to avoid the inversion of the plant in the controller. The paper concludes with a comparison of the H_∞- and μ-synthesis methods.     

Integrated identification and robust control

A framework for integrated identification and control is presented. As part of this framework, frequency domain uncertainty bounds are derived for robust stability tests, a robust stability test for elliptical bounds is developed for SISO systems, a methodology for estimating controller performance is derived, and an optimal experiment design methodology for control-relevant identification is outlined. An example is presented to illustrate how the tools of the framework fit together.     

Adaptive control with optimal robust tracking

The problem of optimal robust tracking in two-parameter adaptive control systems under non-linear time-varying unmodelled dynamics is examined. A new robust stability criterion is derived for analysing the robustness of adaptive control systems with non-linear time-varying model errors. Based on the concept of excess robustness and the theory of the minimum H^∞norm, a simple and feasible design algorithm is presented to synthesize a two-parameter adaptive controller which ensures that adaptive control systems can achieve the object of optimal robust tracking in the presence of non-linear time-varying unmodelled dynamics. Simulation results that demonstrate features of the two-parameter adaptive controller with optimal robust tracking in the light of the design algorithm are included.     

Evaluation of fuzzy neural network run-to-run controller using numerical simulation analysis for SISO process

During the past decade, a variety of run-to-run (R2R) control techniques have been proposed and extensively used to control various semiconductor manufacturing processes. The R2R control methodology combines response surface modeling, engineering process control, and statistical process control, with the main objective of fine-tuning the recipe so that the process output of each run can be maintained as close to the nominal target as possible. In this paper, the single-input single-output (SISO) model is addressed. To overcome the shortcomings in the traditional R2R EWMA controller, a fuzzy neural network (FNN) control strategy is proposed. When a process has large autoregressive parameters, traditional EWMA control methods cannot establish stable SISO process control. To solve this problem, an SISO process control model based on an FNN was used to build an SISO process control procedure. The analysis results from a numerical simulation indicated that when the coefficient of autocorrelation  > 0.6, the MSE ratio when using the FNN controller was 97.11% lower than when using the EWMA controller and 61.12% lower than when using an adaptive EWMA controller. This showed that the FNN control method established better SISO process control than the EWMA and adaptive EWMA control methods.     

基于U模型的Buck变换器控制器设计

为了提高Buck变换器控制系统的设计精度和效率,对Buck变换器非线性建模及控制器的设计进行了研究。结合U模型不损失NARMAX模型非线性特性且易于设计控制器的特点,提出了一个基于输入输出数据的NARMAX建模方法,根据模型的残差,进行了相关性检验以验证模型的有效性。通过将NARMAX模型转化为U模型并基于U模型设计了Buck变换器的极点配置控制器。仿真结果显示,基于U模型的Buck变换器极点配置控制器在调节时间和超调量控制上优于传统的PID控制器。     

A design procedure for the exact H∞ siso-robust performance problem

Presented in this paper is a loop-shaping solution to the H^∞ robust performance problem for a class of SISO systems. The key feature of this work is the explicit incorporation of phase information into the controller synthesis to facilitate loop-shaping over all frequencies. Consequently, a significant reduction in the required controller gain/bandwidth is achieved. It is also shown that the optimal solution, in the sense of controller gain/bandwidth minimization, to the robust performance problem is that which makes μ = 1 over all frequencies. This is different from the usual definition of optimality in the H^∞/μ literature. An example is included for completeness.     

Robust control of a distillation column by the method of inequalities

The method of inequalities is applied to design a robust PI controller for the control of distillate composition using the reflux flow as the manipulated variable. The controller design method takes into account wide variations in k,τ and τ_D of the first order plus the delay transfer function of the process. The performance of the controlled system is evaluated for different levels and changes in direction of set point changes on the linear and also on the original non-linear model equations. The performance of the proposed controller is compared with that of a controller with Zieglar-Nichols (Z-N) settings based on a nominal operating point. The closed loop system becomes unstable at other operating points for the Z-N method whereas the present controller gives good response for wide operating points.     

Delay-dependent guaranteed cost control for state-delayed system with disturbance and its application to engine idle speed control

This paper proposes a delay-dependent guaranteed cost control scheme for engine idle speed control （ISC） with induction-to-torque delay and external load disturbance. An augmented linearization model of engine at idle speed operating mode was developed based on physical principle and experiment data. To provide a compromise between disturbance rejection and other performance requirements of ISC, a multi-objective cost function upper bound was given, which can help us to take into account the fuel economy and disturbance rejection performance together in ISC. Poles constraint was added to the closed-loop system to guarantee convergence rates of state. The whole optimization solution to ISC can be solved under the framework of LMI. A commercial engine model was utilized to assess the performance of the controller. Simulation results on this model show us that designed controller can achieve desired performance.     

Direct passivity of a class of MIMO non-linear systems using adaptive feedback

In this paper, an adaptive controller with adaptive laws specially designed is proposed to solve the problem of making a multi-input multi-output (MIMO) non-linear system, with explicit linear parametric uncertainty, equivalent to a passive system. These results are an extension of those obtained by the authors for the SISO case. Some stability issues associated to the resultant closed-loop passive system are also discussed. The results obtained are applied to models of dynamical MIMO systems, to illustrate the controller design methodology.