Relating H2 and H∞ bounds for finite-dimensional systems

For a linear time invariant system, the infinity-norm of the transfer function can be used as a measure of the gain of the system. This notion of system gain is ideally suited to the frequency domain design techniques such as H_∞ optimal control. Another measure of the gain of a system is the H₂ norm, which is often associated with the LQG optimal control problem. The only known connection between these two norms is that, for discrete time transfer functions, the H₂ norm is bounded by the H_∞ norm. It is shown in this paper that, given precise or certain partial knowledge of the poles of the transfer function, it is possible to obtain an upper bound of the H_∞ norm as a function of the H₂ norm, both in the continuous and discrete time cases. It is also shown that, in continuous time, the H₂ norm can be bounded by a function of the H_∞ norm and the bandwidth of the system.     

An integrated plant/control design method and application in hard disk drives

One approach in servo control to achieve a high track density in hard disk drives is to minimise the H₂ norm from disturbances to position error signal. The H₂ performance optimisation is then deemed as a matter of great significance. This paper presents an integrated design method involving plant modification and controller design sequentially to achieve the H₂ performance requirement. A linear matrix inequality-based approach is developed for the plant damping ratio modification using the plant output. The proposed model modification method is then applied to the voice coil motor plant in hard disk drives, followed by the optimal H₂ controller design using the Riccati equation method with the modified plant. It turns out that the modified plant leads to better H₂ performance, stability margins than the original plant.     

Robust control design for best mean performance over an uncertain-parameters box

This paper deals with robust, polytopic, probabilistic H_∞ analysis and state-feedback synthesis of linear systems and focuses on the performance distribution over the uncertainty region (rather than on the performance bound). The proposed approach allows different disturbance attenuation levels (DALs) at the vertices of the uncertainty polytope. It is shown that the mean disturbance attenuation level (DAL) over an uncertain parameters-box is the average of the DALs at the vertices, if each parameter has an independent, symmetrical, centered probability density function. In such a (most common) case, the mean DAL over the uncertain parameters-box can be optimized by minimizing the sum of the DALs at the vertices. The standard deviation of the DAL over the uncertain parameters-box is also addressed, and a method to minimize this standard deviation is shown. A new robust H_∞ state-feedback synthesis theorem is given; it is based on a recent, most efficient analysis method and applies the proposed multiple-vertex-DALs approach. A state-feedback design example utilizing the latter theorem shows that a control design which minimizes the sum of the vertex-DALs leads to a better actual closed-loop performance than a similar design which minimizes only the bound of the DAL over the uncertainty polytope. The comparison is based on the statistics of a population of closed-loop ‘point-wise’ H_∞-norms created by a Monte-Carlo mechanism.     

On the gap between H2 and entropy performance measures in H∞ control design

Recent papers have considered the problem of minimizing an entropy functional subject to an H_∞ performance constraint. Since the entropy is an upper bound for the H₂ cost, there remains a gap between entropy minimization and H₂ minimization. In this paper we consider a generalized cost functional involving both H₂ and entropy aspects. This approach thus provides a means for optimizing H₂ performance within H_∞ control design.     

Nonlinear robust H∞ control via dynamic output feedback

The problem on robust H_∞ control for a class of nonlinear systems with parameter uncertainty is studied. Sufficient conditions for the existence of the dynamic output feedback controller are obtained. Under these conditions, the closed-loop systems have robust H_∞-performance. A numerical example is given to illustrate the design of a robust controller using the proposed approach.     

Analytical decoupling control strategy using a unity feedback control structure for MIMO processes with time delays

An analytical decoupling control method is proposed for multiple-input–multiple-output (MIMO) processes with multiple time delays. The desired diagonal system transfer matrix is proposed first in terms of the H₂ optimal performance specification, resulting in the ideal desired decoupling controller matrix derived within the framework of a unity feedback control structure. It is demonstrated that dead-time compensators must be enclosed in the decoupling controller matrix to realize absolute decoupling for MIMO processes with multiple time delays. To alleviate the difficulties associated with the implementation, the ideal desired decoupling controller matrix is transformed into a practical form using an analytical approximation approach. Correspondingly, the stability of the resultant control system is assessed, together with its robust stability in the presence of process uncertainties. An on-line tuning rule for the single adjustable parameter of each column controllers in the decoupling controller matrix is given to cope with the process unmodeled dynamics. Finally, illustrative examples are given to show the superiority of the proposed method over the recently improved decoupling control methods.     

An improved approach to H-two control with regional stability constraints

This paper presents an improved method for H-two control with regional stability constraints for the closedloop system. The controller is given by the convex combination of a set of fixed gains. Both continuous and discrete-time systems in a known polytopic domain are investigated. New LMI-based sufficient conditions for the existence of parameterdependent Lyapunov functions are proposed. Numerical examples are given to show the proposed conditions provide useful and less conservative results for the problems of H-two control with regional stability constraints.     

主动悬架H2/ 广义H2输出反馈控制

本文提出了一种主动悬架控制的H₂ /广义H₂ 输出反馈控制方法. 依照国际标准ISO2631.3选择垂直和俯仰加速度的频率加权. 根据路面干扰谱特征, 选用H₂ 范数作为乘坐舒适性的指标, 广义H₂ 范数描述轮胎接地性等时域约束要求. 在多目标控制框架下, 将输出反馈控制器的设计转化为求解LMI优化问题. 基于半车模型, 给出了输出反馈主动悬架系统的频域分析和时域仿真.     

Enhanced H2S sensing characteristics of SnO2 nanowires functionalized with CuO

The CuO-functionalized SnO₂ nanowire (NW) sensors were fabricated by depositing a slurry containing SnO₂ NWs on a polydimethylsiloxane (PDMS)-guided substrate and subsequently dropping Cu nitrate aqueous solution. The CuO coating increased the gas responses to 20 ppm H₂S up to 74-fold. The R_a/R_g value of the CuO-doped SnO₂ NWs to 20 ppm H₂S was as high as 809 at 300 °C, while the cross-gas responses to 5 ppm NO₂, 100 ppm CO, 200 ppm C₂H₅OH, and 100 ppm C₃H₈ were negligibly low (1.5–4.0). Moreover, the 90% response times to H₂S were as short as 1–2 s at 300–400 °C. The selective detection of H₂S and enhancement of the gas response were attributed to the uniform distribution of the sensitizer (CuO) on the surface of the less agglomerated network of the SnO₂ NWs.     

Mixed H2/H∞ multi-channel linear parameter-varying control in discrete time

This paper develops a new method for the synthesis of linear parameter-varying (LPV) controllers in discrete time. LPV plants under consideration have a linear fractional transformation (LFT) representation. In contrast to earlier results which are restricted to single-objective LPV problems, the proposed method can handle a set of H₂/H_∞ specifications that can be defined channel-wise. This practically attractive extension is derived by using specific transformations of both the Lyapunov and scaling/multiplier variables in tandem with appropriate linearizing transformations of the controller data and of the controller scheduling function. It is shown that the controller gain-scheduling function can be constructed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameter, hence is easily implemented on line. Finally, these manipulations give rise to a tractable and practical LMI formulation of the multi-objective LPV control problem.     

A mixed H2/H∞ adaptive tracking control for constrained non-holonomic systems

In this study, a PID type controller incorporating an adaptive control scheme for the mixed H₂/H_∞ tracking performance is developed for constrained non-holonomic mechanical systems under unknown or uncertain plant parameters and external disturbances. By virtue of the skew-symmetric property of the non-holonomic mechanical systems and an adequate choice of a state variable transformation, sufficient conditions are developed for the adaptive mixed H₂/H_∞ tracking control problems in terms of a pair of coupled algebraic equations instead of a pair of coupled non-linear differential equations. The coupled algebraic equations can be solved analytically.     

An algebraic approach to H∞ output feedback control problems

We derive an output feedback controller which stabilizes a system and satisfies a prescribed H_∞ norm bound of the closed loop transfer function. The proposed design method is available for any system, i.e. there are no restrictions on D₁₂ and D₂₁. This approach utilizes only algebraic operations, thus proofs are simple and clear.     

H∞ control design in bilinear systems: a tensor formal series approach

In this paper, the H_∞ disturbance attenuation problem of bilinear system is discussed. Dynamic game theory is used to solve this bilinear minimax problem. The solvability of H_∞ disturbance attenuation in bilinear system is also discussed. The techniques of tensor products and formal power series are employed to solve the nonlinear Bellman-Isaac differential equation. Furthermore, the convergence for the tensor formal series approach of this H_∞ control problem is discussed, and the radius of convergence for this H_∞ control to be well defined is also obtained.     

A new equation of state and Fortran 77 program to calculate vapor–liquid phase equilibria of CH4–H2O system at low temperatures

A new equation of state (EOS) and the corresponding computer program package VLEWM are developed to calculate vapor–liquid phase equilibria and volumetric properties of CH₄–H₂O system at low temperatures. The EOS can predict vapor–liquid equilibria and volumetric properties of CH₄–H₂O system accurately at temperatures 273–383 K, and at pressures 0–1000 bar. The program package VLEWM is written in FORTRAN 77. It provides two main functions: (1) to calculate the composition in vapor phase and liquid phase of CH₄–H₂O system at equilibrium and (2) to judge the phase and to calculate molar volume of CH₄–H₂O mixture.     

Robust stabilisation control for discrete-time networked control systems

We consider the analysis and synthesis of discrete-time networked control systems (NCSs), where the plant has additive uncertainty and the controller is updated with the sensor information at stochastic time intervals. It is shown that the problem is linked to H_∞-control of linear discrete-time stochastic systems and a new small gain theorem is established. Based on this result, sufficient conditions are given for ensuring mean square stability of the NCS, and the genetic algorithm is utilised to design the controller of the NCS based on a linear matrix inequality technique. An illustrative example is given to demonstrate the effectiveness of our proposed method.     

A convex optimization approach to the mode acceleration problem

The purpose of this note is to introduce an alternative procedure to the mode acceleration method when the underlying structure model includes damping. We will show that the problem can be cast as a convex optimization problem that can be solved via linear matrix inequalities.     

Mixed output feedback of the finite frequency H∞ control for singularly perturbed system

This paper considers the H_∞ control problem for a class of linear singularly perturbed systems in the finite frequency range. A mixed output feedback controller comprising of a static output feedback controller and a dynamic output feedback controller is developed for the system stabilisation. Based on the generalised Kalman–Yakubovich–Popov (GKYP) lemma, the frequency-domain inequalities can be converted into linear matrix inequalities which are numerically tractable. Compared with the existing full frequency approaches, better results are obtained. Moreover, the selection methods of the cut-off frequencies in both low and high frequency ranges are extensively studied with a view to reduce the conservativeness in output feedback control design. Simulation results suggest the asymptotic validity of the main results in this paper.     

On stability, -gain and control for switched systems

This paper addresses the issues of stability, L₂-gain analysis and H_∞ control for switched systems via multiple Lyapunov function methods. A concept of general Lyapunov-like functions is presented. A necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized Lyapunov-like functions, which enables derivation of improved stability tests, an L₂-gain characterization and a design method for stabilizing switching laws. A solution to the H_∞ control problem for switched systems is also provided.