An interactive parameter space method for robust performance inmixed sensitivity problems

This paper presents an interactive graphical method to determine the set of fixed-order stabilizing controllers achieving robust performance, in the mixed sensitivity framework. The method is limited to single-input/single-output (SISO) systems but offers significant advantages over traditional loop gain shaping methods such as H^∞ and μ-synthesis. It can handle pure time delays in an exact manner and the weighting functions need not be rational. The technique translates frequency-domain weighting functions and stability constraints into the parameter space and thus gives the user more insights into the design than conventional methods. By virtue of producing the required parameter space region for the frequency response criteria, subsequent optimization of secondary objectives is possible. The controllers obtained are of lower order for comparable performance than those produced by current H^∞ and μ-synthesis techniques. The method is particularly well-suited to robust control problems where frequency-domain constraints emerge from the analysis of nonparametric uncertainties in the system and also to control problems where the frequency domain loop shaping is used to achieve time-domain specifications     

Robustness design of nonlinear dynamic systems via fuzzy linearcontrol

This study introduces a fuzzy linear control design method for nonlinear systems with optimal H^∞ robustness performance. First, the Takagi and Sugeno fuzzy linear model (1985) is employed to approximate a nonlinear system. Next, based on the fuzzy linear model, a fuzzy controller is developed to stabilize the nonlinear system, and at the same time the effect of external disturbance on control performance is attenuated to a minimum level. Thus based on the fuzzy linear model, H^∞ performance design can be achieved in nonlinear control systems. In the proposed fuzzy linear control method, the fuzzy linear model provides rough control to approximate the nonlinear control system, while the H^∞ scheme provides precise control to achieve the optimal robustness performance. Linear matrix inequality (LMI) techniques are employed to solve this robust fuzzy control problem. In the case that state variables are unavailable, a fuzzy observer-based H^∞ control is also proposed to achieve a robust optimization design for nonlinear systems. A simulation example is given to illustrate the performance of the proposed design method     

An H∞ approach to feedback design withtwo objective functions

The problem of tightly bounding and shaping the frequency responses of two objective functions T_i(s)( i=1,2) associated with a closed-loop system is considered. It is proposed that an effective way of doing this is to minimize (or bound) the function max {∥T₁(s)∥ _∞, ∥T₂(s)∥_∞} subject to internal stability of the closed-loop system. The problem is formulated as an H^∞ control problem, and an iterative solution is given     

A counterexample on continuous coprime factors

In Georgiou and Smith (1992), the following question was raised: Consider a linear, shift-invariant system on L₂[0, ∞). Let the graph of the system have Fourier transform (MN)H² (i.e., the system has a transfer function P=N/M) where M, N are elements of C_A={f∈H^∞: f is continuous on the compactified right-half plane}. Is it possible to normalize M and N (i.e., to ensure |M|²+|N|²=1) in C_A? The author shows by example that this is not always possible     

Interactive control system design by a mixedH∞-parameter space method

This paper presents an interactive graphical method to determine sets of stabilizing controllers satisfying any combination of constraints on the sensitivity, complementary sensitivity, and input sensitivity transfer functions. The method is limited to single-input/single-output systems but offers significant advantages over current H^∞ methods. It can handle pure time delays in an exact manner. The weighting functions need not be rational. By virtue of producing the required parameter space region for the frequency response criteria, subsequent direct time-domain optimization is possible. The controllers obtained are of lower order for comparable performance than those produced by current H^∞ techniques. The method is particularly well suited to robust control problems, where frequency domain constraints emerge from the analysis of uncertainties in the system, and also to suboptimal problems, where the frequency-domain loop shaping is used to achieve time-domain specifications     

H∞ control for linear time-varying systems:controller parameterization

In this correspondence, the H^∞ control problem is studied for finite-dimensional linear time-varying (FDLTV) systems. State-space formulas are derived for all FDLTV controllers solving the problem. These controllers are parameterized by the interconnection of the “central controller” with an exponentially stable, free system having H^∞ norm strictly less than γ. Our approach is drawn from some changes of variables, a time-varying version of a strict bounded real lemma, and Youla parameterization; thus, the proofs given are simple and clear     

Identification of rational approximate models inH∞ using generalized orthonormal basis

Robust identification with FIR models fails to be successful when the number of coefficients to be estimated becomes large, caused by lightly damped modes of the plant or poles very close to the unit circle. The paper presents a two-stage algorithm to obtain a low-order approximate model in frequency domain in a generalized orthonormal basis with guaranteed H^∞ error bound for deterministic linear time-invariant stable systems, the first stage being an L^∞ rational approximation and the second nonlinear step being an H ^∞ rational approximation     

H∞ optimal and suboptimal controllers for infinitedimensional SISO plants

This paper presents a simple formula for H^∞ optimal and suboptimal controllers for unstable SISO distributed plants, with rational weighting functions. The controller is expressed in terms of i) inner and outer parts of the plant, ii) a finite dimensional spectral factor obtained from the weighting functions, and iii) a rational function satisfying certain interpolation conditions. Under certain genericity assumptions, this rational function is of dimension less than or equal to n₁+l-1 (n₁+l in the suboptimal case), where l is the number of unstable poles of the plant and n₁ is the order of the sensitivity weighting function. There are 2(n₁+l) (2(n₁+l+1) in the suboptimal case) linear equations, which determine this rational function. These linear equations can be written directly from the structure of the controller     

H∞ bounds for least-squares estimators

We obtain upper and lower bounds for the H^∞ norm of the Kalman filter and the recursive-least-squares (RLS) algorithm, with respect to prediction and filtered errors. These bounds can be used to study the robustness properties of such estimators. One main conclusion is that, unlike H^∞-optimal estimators which do not allow for any amplification of the disturbances, the least-squares estimators do allow for such amplification. This fact can be especially pronounced in the prediction error case, whereas in the filtered error case the energy amplification is at most four. Moreover, it is shown that the H^∞ norm for RLS is data dependent, whereas for least-mean-squares (LMS) algorithms and normalized LMS, the H^∞ norm is simply unity     

Alternating projection methods for mixed H2 andH∞ Nehari problems

In this paper, alternating convex projection methods along with fast Fourier transform techniques are used to solve some mixed H² and H^∞ Nehari problems     

A family of nonlinear H∞-output feedbackcontrollers

State-space formulas are derived for a family of controllers solving the nonlinear H^∞-output feedback control problem. The formulas given are expressed in terms of the solutions to two Hamilton-Jacobi inequalities in n independent variables. These controllers are obtained by interconnecting the “central controller” with an asymptotically stable, free system having L ²-gain ⩽γ. All proofs given are simple and clear and provide deeper insight in the synthesis of the corresponding linear H^∞ controllers     

Using scales in the multiobjective approach

Scales are used to reduce the conservatism encountered in most multiobjective approaches to control design. The most general case (i.e., matrix scales) results in a nonconvex problem, though the use of scalar scales leads to convex searches in the analysis and state feedback problems. Output feedback synthesis and other extensions are discussed. Numerical examples are provided to show the effectiveness of the suggested approach. The article considers, in particular, H^∞ control     

Memoryless H∞ controllers for state delayedsystems

In this note, a memoryless H^∞ controller for the state delayed system is presented. The controller is a delay independent stabilizer for the state delayed system, which also reduces the H^∞ norm of the closed loop transfer function, from the disturbance to the controlled output, to a prescribed level. The controller can be obtained by solving a modified Riccati equation     

Analysis of Parallel Algorithms for Matrix Chain Product and Matrix Powers on Distributed Memory Systems

Given N matrices A₁, A_2,...,A_N of size NtimesN, the matrix chain product problem is to compute A₁timesA₂times...timesA_N. Given an NtimesN matrix A, the matrix powers problem is to calculate the first N powers of A, that is, A, A², A³,..., A^N. We solve the two problems on distributed memory systems (DMSs) with p processors that can support one-to-one communications in T(p) time. Assume that the fastest sequential matrix multiplication algorithm has time complexity O(N^alpha), where the currently best value of a is less than 2.3755. Let p be arbitrarily chosen in the range 1lesplesN^alpha+1/(log N)². We show that the two problems can be solved by a DMS with p processors in T_chain(N,p)=O((N^alpha+1/p)+T(p))((N^2(2+1/alpha/p^2/alpha)(log+p/N)^1-2/alpha+log+((p log N)/N^alpha)) and T_power (N,p)=O(N^alpha+1/p+T(p)((N^2(1+1/alpha)/p^2/alpha)(log+p/2 log N)^1-2/alpha+(log N)²))) times, respectively, where the function log+ is defined as follows: log+ x=log x if xges1 and log+ x=1 if 0相似文献   

A new approach to robust control of hybrid systems over infinitetime

The paper presents a new approach to output feedback robust control synthesis problems for hybrid dynamical systems. The hybrid system under consideration is a composite of a continuous plant and a discrete-event controller. An output feedback H^∞-control problem on an infinite time interval is considered. The main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a Riccati algebraic equation of the H^∞-filtering type. These results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control     

H∞ control for more general nonlinear systems

The authors consider the standard H^∞-control problem for more general nonlinear systems modeled by equations in which the penalty output and the measured output are, in general, functions of the state, the exogenous input, and the control input. In particular, we characterize a family of H^∞ controllers via output feedback as well as state feedback, solving the problem. The results obtained generalize some recent results in the literature     

Persistent identification and adaptation: stabilization of slowlyvarying systems in H∞

In this paper, the problem of persistent identification and adaptive stabilization of time-varying systems is studied within the framework of deterministic worst case identification and slow H^∞ adaptation. The plants under consideration are unstable and time-varying and cannot be stabilized by a fixed robust controller. Starting from an initial well-designed operating point, the controller must persistently adapt to the time-varying plant to maintain uniform stability over all future time. A key property which guarantees uniform stability is that the identification-adaptation iteration satisfies a certain invariance principle. We demonstrate that the adaptive design using periodic external inputs, least squares identification, and slow H^∞ adaptation possesses such an invariance property, leading to a successful adaptive stabilization methodology. Generic natures of our findings are discussed     

Manganese(II)-selective PVC membrane electrode based on a pentaazamacrocyclic manganese complex

Manganese(II) complex of 14,16-dimethyl-1,4,7,10,13-pentaazacyclohexadeca-13,16-diene [Me₂(16)dieneN₅] (I) was synthesized and used in the fabrication of Mn²⁺-selective ISE membrane in PVC matrix. The membrane having Mn(II) macrocyclic complex as electroactive material along with sodium tetraphenylborate (NaTPB) as anion discriminator and dioctylphthalate (DOP) as plasticizer in poly(vinylchloride) (PVC) matrix was prepared for the determination of Mn²⁺. The best performance was observed by the membrane having Mn(II) complex–PVC–NaTPB–DOP in the ratio 1:5:1:3. The sensor worked well over a concentration range of 1.25 × 10⁻⁵ to 1.0 × 10⁻¹ M between pH 3.0 and 8.0 and had a fast response time of 20 s with a lifetime of 4 months. Their performance in partially non-aqueous medium was found satisfactory up to 30% (v/v) alcoholic content. Electrodes exhibited excellent selectivity for Mn²⁺ ion over other mono-, di-, trivalent cations. It can also be used as indicator electrode in the potentiometric titration of Mn²⁺ against EDTA.     

Robust stability and design of linear discrete-time SISO systemsunder l1 uncertainties

Shows how value sets and the zero exclusion principle can be used to obtain results on the robust stability and design of controllers against a special infinite-dimensional l₁ norm bounded parametric uncertainty in both numerator and denominator of scalar discrete-time plants. This parametric uncertainty has properties of both parametric and unstructured uncertainty and allows standard H^∞ design tools to be used without conservatism     

Dynamic admittance matrix of piezoelectric cantilever bimorphs

The matrix that relates the harmonically varying driving parameters: a moment M at the tip, a force F at the tip, a uniformly applied body force p and voltage V to their response parameters: the tip rotation α, the tip deflection δ, the volumetric displacement V and the electrode charge Q, have been determined. The electrical element of this matrix is the (4,4) element, which is the electrical capacitance, hence we call this the dynamic admittance matrix. It is a four by four symmetric matrix having a purely electrical part, a purely elastic part and a mixed (piezoelectric) part. A common factor in nearly all elements describes the resonance frequencies that are to be expected