Pointwise in frequency performance weight optimization in µ‐synthesis

A conceptually different approach to the µ‐synthesis robust performance problem is proposed in this article. The optimization problem posed maximizes the performance weights with respect to a suitable cost function that captures the desired closed‐loop performance. This maximization of performance weights is limited by the fact that there must exist some internally stabilizing controller that guarantees robust performance with respect to these maximized weights. Thus, performance weights and a controller that achieves an optimized level of robust performance are synthesized together by one algorithm in a systematic way. The designer is only required to specify the plant set and an optimization directionality. This directionality only appears in the cost function and reflects the desired closed‐loop properties in particular frequency regions. It is pointed out that choosing this directionality is much easier than choosing the performance weights directly. Correspondingly, this approach greatly simplifies the often long and tedious process of designing ‘good’ performance weights directly and gives an indication of what is the achievable performance. A pointwise in frequency solution to the posed optimization problem is also developed in this article. Copyright © 2005 John Wiley & Sons, Ltd.     

State‐space µ analysis for an experimental drive‐by‐wire vehicle

This paper considers the application of the skewed structured singular value to the robust stability of systems subject to strictly real parametric uncertainty. Three state‐space formulations that counteract the discontinuous nature of this problem are detailed. It is shown that the calculation of the supremum of the structured singular value over a frequency range using these formulations transforms into a single skewed structured singular value calculation. Similar to the structured singular value, the exact calculation of the skewed structured singular value is an NP‐hard problem. In this work, two efficient algorithms that determine upper and lower bounds on the skewed structured singular value are presented. These algorithms are critically assessed using a series of robustness analysis tests on a safety‐critical experimental drive‐by‐wire vehicle. Copyright © 2008 John Wiley & Sons, Ltd.     

Stability‐ and performance‐robustness tradeoffs: MIMO mixed‐µ vs complex‐µ design

We present a non‐trivial case study designed to highlight some of the practical issues that arise when using mixed‐µ or complex‐µ robust synthesis methodologies. By considering a multi‐input multi‐output three‐cart mass–spring–dashpot (MSD) with uncertain parameters and dynamics, it is demonstrated that optimized performance (disturbance‐rejection) is reduced as the level of uncertainty in one or two real parameters is increased. Comparisons are made (a) in the frequency domain, (b) by RMS values of key signals and (c) in time‐domain simulations. The mixed‐µ controllers designed are shown to yield superior performance as compared with the classical complex‐µ design. The singular value decomposition analysis shows the directionality changes resulting from different uncertainty levels and from the use of different frequency weights. The nominal and marginal stability regions of the closed‐loop system are studied and discussed, illustrating how stability margins can be extended at the cost of reducing performance. Copyright © 2008 John Wiley & Sons, Ltd.     

Development of a skew µ lower bound

Exploitation of the NP hard, mixed µ problem structure provides a polynomial time algorithm that approximates µ with usually reasonable answers. When the problem is extended to the skew µ problem an extension of the existing method to the skew µ formulation is required. The focus of this paper is to extend the µ lower bound derivation to the skew µ lower bound and show its direct computation by way of a power algorithm. Copyright © 2005 John Wiley & Sons, Ltd.     

Non‐smooth structured control design with application to PID loop‐shaping of a process

Feedback controllers with specific structure arise frequently in applications because they are easily apprehended by design engineers and facilitate on‐board implementations and re‐tuning. This work is dedicated to H_∞ synthesis with structured controllers. In this context, straightforward application of traditional synthesis techniques fails, which explains why only a few ad hoc methods have been developed over the years. In response, we propose a more systematic way to design H_∞ optimal controllers with fixed structure using local optimization techniques. Our approach addresses in principle all those controller structures which can be built into mathematical programming constraints. We apply non‐smooth optimization techniques to compute locally optimal solutions, and provide practical tests for descent and optimality. In the experimental part we apply our technique to H_∞ loop‐shaping proportional integral derivative (PID) controllers for MIMO systems and demonstrate its use for PID control of a chemical process. Copyright © 2007 John Wiley & Sons, Ltd.     

360°‐viewable cylindrical integral imaging system using a 3‐D/2‐D switchable and flexible backlight

Abstract— A 360°‐viewable cylindrical three‐dimensional (3‐D) display system based on integral imaging has been implemented. The proposed system is composed of a cylindrically arranged electroluminescent (EL) pinhole film, an EL film backlight, a barrier structure, and a transmission‐type flexible display panel. The cylindrically arranged point‐light‐source array, which is generated by the EL pinhole film reconstructs 360°‐viewable virtual 3‐D images at the center of the cylinder. In addition, the proposed system provides 3‐D/2‐D convertibility using the switching of EL pinhole film from a point light source to a surface light source. In this paper, the principle of operation, analysis of the viewing parameters, and the experimental results are presented.     

Ten switched‐beams with 2 × 2 series‐fed 2.4 GHz array antenna and a simple beam‐switching network

This article presents a 2 × 2 series fed 2.4 GHz patch antenna array having multiple beam switching capabilities by using two simple 3 dB/90° couplers to achieve required amplitude and phase excitations for array elements with reduced complexity, cost and size. The beam switching performance with consistent gain and low side lobe levels (SLL) is achieved by exciting the array elements from orthogonally placed thin quarter‐wave (λ_g/4) feeds. The implemented array is capable to generate ten (10) switched‐beams in 2‐D space when series fed elements are excited from respective ports through 3 dB quadrature couplers. The dual polarized characteristics of presented array provide intrinsic interport isolation between perpendicularly placed ports through polarization diversity to achieve independent beam switching capabilities for intended directions. The implemented antenna array on 1.575 mm thick low loss (tan δ = 0.003) NH9450 substrate with ε_r = 4.5 ± 0.10 provides 10 dB return loss impedance bandwidth of more than 50 MHz. The measured beam switching loss is around 0.8 dB for beams switched at θ = ±20°, Ф = 0°, 90°, and 45° with average peak gain of 9.5 dBi and SLL ≤ ?10 dB in all cases. The novelty of this work is the capability of generating ten dual polarized switched‐beams by using only two 3 dB/90° couplers as beam controllers.     

IQC‐synthesis under structural constraints

A new controller synthesis technique enabling the design of control systems satisfying prescribed structural constraints as well as stability and performance specifications given in terms of integral quadratic constraints (IQC) is presented. The proposed approach relies on a nonsmooth optimization technique to solve the IQC feasibility problem directly in the frequency domain. As corroborated by the two numerical examples presented, the technique allows the synthesis of control laws of great practical utility (eg, PID, decentralized, and reduced‐order output feedback controllers) for a large class of systems presenting, for example, slope‐restricted nonlinearities, time‐varying delays, and uncertain parameters with bounded rates of variation.     

Robust multiple model adaptive control: Modified using ν‐gap metric

A new robust adaptive control method is proposed, which removes the deficiencies of the classic robust multiple model adaptive control (RMMAC) using benefits of the ν‐gap metric. First, the classic RMMAC design procedure cannot be used for systematic design for unstable plants because it uses the Baram Proximity Measure, which cannot be calculated for open‐loop unstable plants. Next, the %FNARC method which is used as a systematic approach for subdividing the uncertainty set makes the RMMAC structure being always companion with the µ‐synthesis design method. Then in case of two or more uncertain parameters, the model set definition in the classic RMMAC is based on cumbersome ad hoc methods. Several methods based on ν‐gap metric for working out the mentioned problems are presented in this paper. To demonstrate the benefits of the proposed RMMAC method, two benchmark problems subject to unmodeled dynamics, stochastic disturbance input and sensor noise are considered as case studies. The first case‐study is a non‐minimum‐phase (NMP) system, which has an uncertain NMP zero; the second case‐study is a mass‐spring‐dashpot system that has three uncertain real parameters. In the first case‐study, five robust controller design methods (H₂, H_∞, QFT, H_∞ loop‐shaping and µ‐synthesis) are implemented and it is shown via extensive simulations that RMMAC/ν/QFT method improves disturbance‐rejection, when compared with the classic RMMAC. In the second case‐study, two robust controller design methods (QFT and mixed µ‐synthesis) are applied and it is shown that the RMMAC/ν/QFT method improves disturbance‐rejection, when compared with RMMAC/ν/mixed?µ. Copyright © 2010 John Wiley & Sons, Ltd.     

A non‐smooth lower bound on ν

A non‐smooth optimization technique to directly compute a lower bound on the skew structured singular value ν is developed. As corroborated by several real‐world challenging applications, the proposed technique can provide tighter lower bounds when compared with currently available techniques. Moreover, in many cases, the determined lower bound equals the true value of ν. Thanks to the efficiency of the non‐smooth technique, the algorithm can be applied to problems involving even a significant number of uncertain parameters. Another appealing feature of the proposed non‐smooth approach is that the dimension of repeated scalar uncertainties in the overall structured uncertainty matrix has little impact on the computational time. The technique can be used to compute a lower bound on the structured singular value μ as well. Copyright © 2012 John Wiley & Sons, Ltd.     

ε‐Optimal Value and Approximate Multidimensional Dual Dynamic Programming

This paper develops an approximate dual dynamic programming for an ε? optimal multidimensional control problem governed by first order hyperbolic equations. The problem considered is of the Dieudonne‐Rashevsky type and contains as a particular case class‐qualified deposit and Capital theory problems. It is proven that each Lipschitz continuous function satisfying the dual Hamilton‐Jacobi inequality can be used to define an ε‐optimal value.     

Microrectangular‐coaxial phase shifter for microwave devices

This article reports the simulated performance of rectangular coaxial ferrite phase shifter at Ka‐band. The proposed technique exploits rectangular coaxial waveguide with a symmetrically placed inner signal conductor inside an outer conductor connected to the ground. Strontium ferrite‐SU8 composite is used as an anisotropic material of choice in the modeled design. Two model phase shifting structures were designed for reciprocal and nonreciprocal applications using High Frequency Structure Simulator, HFSS. The reciprocal model produced a tunable phase shift of almost across 0 to 400 kA/m applied field and at 1800 Gauss. The predicted simulated performance of the nonreciprocal phase shifter was from a reference phase of at 0 A/m at the same saturation magnetization. A return loss better than 20 dB and an insertion loss less than 1.5 dB were predicted for the two models. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:502–509, 2015.     

Efficient mapping and acceleration of AES on custom multi‐core architectures

Multi‐core processors can deliver significant performance benefits for multi‐threaded software by adding processing power with minimal latency, given the proximity of the processors. Cryptographic applications are inherently complex and involve large computations. Most cryptographic operations can be translated into logical operations, shift operations, and table look‐ups. In this paper we design a novel processor (called mu‐core) with a reconfigurable Arithmetic Logic Unit, and design custom two‐dimensional multi‐core architectures on top of it to accelerate cryptographic kernels. We propose an efficient mapping of instructions from the multi‐core grid to the individual processor cores and illustrate the performance of AES‐128E algorithm over custom‐sized grids. The model was developed using Simulink and the performance analysis suggests a positive trend towards development of large multi‐core (or multi‐ µ‐core) architectures to achieve high throughputs in cryptographic operations. Copyright © 2010 John Wiley & Sons, Ltd.     

New high‐luminance 50‐ and 43‐in. ACPDPs with an improved panel structure

New 50‐ and 43‐in. ACPDPs, which have been developed and commercialized in 2001, show high luminance with improved cell structure and higher Xe‐content gas. The specific features of the cell structure are “T”‐shaped electrodes and waffle‐structured ribs, which are same as those of the previous model. Both the cell structure and gas conditions have been optimized. New green and blue phosphors have also been adopted. As a result, the luminous efficacy has been improved up to 1.8 lm/W by using a black stripe. The peak luminance of the 50‐ and 43‐in. PDPs have reached 900 and 1000 cd/m², respectively, while the power consumption of the 50‐in. PDP has been decreased to 380 W, which is 20% lower than that of our previous 50‐in. PDP.     

A test for stability robustness of linear time‐varying systems utilizing the linear time‐invariant ν‐gap metric

A stability robustness test is developed for internally stable, nominal, linear time‐invariant (LTI) feedback systems subject to structured, linear time‐varying uncertainty. There exists (in the literature) a necessary and sufficient structured small gain condition that determines robust stability in such cases. In this paper, the structured small gain theorem is utilized to formulate a (sufficient) stability robustness condition in a scaled LTI ν‐gap metric framework. The scaled LTI ν‐gap metric stability condition is shown to be computable via linear matrix inequality techniques, similar to the structured small gain condition. Apart from a comparison with a generalized robust stability margin as the final part of the stability test, however, the solution algorithm implemented to test the scaled LTI ν‐gap metric stability robustness condition is shown to be independent of knowledge about the controller transfer function (as opposed to the LMI feasibility problem associated with the scaled small gain condition which is dependent on knowledge about the controller). Thus, given a nominal plant and a structured uncertainty set, the stability robustness condition presented in this paper provides a single constraint on a controller (in terms of a large enough generalized robust stability margin) that (sufficiently) guarantees to stabilize all plants in the uncertainty set. Copyright © 2008 John Wiley & Sons, Ltd.     

Time domain constrained H∞‐synthesis

Structured H_∞‐synthesis subject to time domain performance specifications is introduced. Our method allows to control trajectories of the linearized system and the underlying nonlinear dynamics simultaneously. A non‐smooth bundle optimization method for this class of programs is proposed and discussed. Our approach is tested against two benchmark studies: control of a rotational actuator to attenuate vibration noise, and control of a continuous crystallizer. Our algorithm gives a local convergence certificate and is suited for systems with large state dimension. Copyright © 2010 John Wiley & Sons, Ltd.     

IQC‐synthesis with general dynamic multipliers

Analogously to the existing μ‐synthesis tools, we propose an alternative algorithm for the systematic design of robust controllers based on an iteration of standard nominal controller synthesis and integral quadratic constraint (IQC) analysis with general dynamic multipliers. The suggested algorithm enables us to perform robust controller synthesis for a significantly larger class of uncertainties if compared with the existing methods. Indeed, while the classical approaches are restricted to the use of real/complex time invariant or arbitrarily fast time‐varying parametric uncertainties, the IQC framework also offers, for example, the possibility to efficiently handle sector‐bounded and slope restricted nonlinearities or time‐varying parametric uncertainties and uncertain time‐varying time‐delays, both with bounds on the rate‐of‐variation. Secondly, in contrast to the classical approaches, the proposed techniques completely avoid gridding and curve‐fitting. We present new insights that allow us to reformulate the robust IQC analysis LMIs into a standard quadratic performance problem. This enables us to generate suitable initial conditions for each subsequent iteration step. Depending on the size of the problem, this can significantly speed up the synthesis process. The results are illustrated by means of two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.     

Multiple robust H∞ controller design using the nonsmooth optimization method

This paper proposes a systematic technique to design multiple robust H_∞ controllers. The proposed technique achieves a desired robust performance objective, which is impossible to achieve with a single robust controller, by dividing the uncertainty set into several subsets and by designing a robust controller to each subset. To achieve this goal with a small number of divisions of the uncertainty set, an optimization problem is formulated. Since the cost function of this optimization problem is not a smooth function, a numerical nonsmooth optimization algorithm is proposed to solve this problem. This method avoids the use of Lyapunov variables, and therefore it leads to a moderate size optimization problem. A numerical example shows that the proposed multiple robust control method can improve the closed‐loop performance when a single robust controller cannot achieve satisfactory performance. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust nonlinear ship course‐keeping control by H∞ I/O linearization and μ‐synthesis

In this paper, the H_∞ input/output (I/O) linearization formulation is applied to design an inner‐loop nonlinear controller for a nonlinear ship course‐keeping control problem. Due to the ship motion dynamics are non‐minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H_∞ I/O linearization is proposed to obtain a nonlinear H_∞ controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a μ‐synthesis method is employed to design an outer‐loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed‐loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd.     

Local input‐to‐state stabilization and ℓ ∞ ‐induced norm control of discrete‐time quadratic systems

This paper addresses the problems of local stabilization and control of open‐loop unstable discrete‐time quadratic systems subject to persistent magnitude bounded disturbances and actuator saturation. Firstly, for some polytopic region of the state‐space containing the origin, a method is derived to design a static nonlinear state feedback control law that achieves local input‐to‐state stabilization with a guaranteed stability region under nonzero initial conditions and persistent bounded disturbances. Secondly, the stabilization method is extended to deliver an optimized upper bound on the ? _∞ ‐induced norm of the closed‐loop system for a given set of persistent bounded disturbances. Thirdly, the stabilization and ? _∞ designs are adapted to cope with actuator saturation by means of a generalized sector bound constraint. The proposed controller designs are tailored via a finite set of state‐dependent linear matrix inequalities. Numerical examples are presented to illustrate the potentials of the proposed control design methods. Copyright © 2014 John Wiley & Sons, Ltd.