Showing papers in "International Journal of Robust and Nonlinear Control in 1994"
TL;DR: In this paper, the continuous and discrete-time H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI), and two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMI-based parametrization of all H ∞-suboptimal controllers, including reduced-order controllers.
Abstract: The continuous- and discrete-time H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMI-based parametrization of all H∞-suboptimal controllers, including reduced-order controllers.
The solvability conditions involve Riccati inequalities rather than the usual indefinite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of H∞ controllers and bear important connections with the controller order and the closed-loop Lyapunov functions.
Thanks to such connections, the LMI-based characterization of H∞ controllers opens new perspectives for the refinement of H∞ design. Applications to cancellation-free design and controller order reduction are discussed and illustrated by examples.
3,200 citations
TL;DR: In this article, the existence of solutions of a pair of Hamilton-Jacobi inequalities in n independent variables, associated with state feedback and output-injection design, was shown to be related to the existence and stability of the state feedback in affine nonlinear systems.
Abstract: This paper summarizes some recent results on the problem of disturbance attenuation via measurement feedback, with internal stability, for an affine nonlinear system. The solution of the problem is shown to be related to the existence of solutions of a pair of Hamilton-Jacobi inequalities in n independent variables, associated with state feedback and, respectively, output-injection design.
221 citations
TL;DR: In this article, the authors proposed a procedure for achieving approximate tracking for a nonlinear system whose linearization possesses real right-half plane zeros, which is guaranteed to remove the right half plane zero while the other zero remains in their previous location.
Abstract: An unstable zero-dynamics is a known obstruction to inducing exact asymptotic tracking for an open set of output trajectories with internal stability. This paper proposes a procedure for achieving approximate tracking for a nonlinear system whose linearization possesses real right-half plane zeros. The method is guaranteed to remove the right-half plane zeros while the other zeros remain in their previous location; moreover, it provides information on the class of signals for which good approximate tracking can be obtained. With other methods, the right-half plane zeros are eliminated but the final location of the remaining zeros is not known a priori. The design procedure is illustrated on a trajectory control problem of an aircraft in rapid manoeuvres. Simulations illustrate the computations involved and show that precise lateral and longitudinal manoeuvres can be performed, even in the presence of uncertainties.
112 citations
TL;DR: In this article, the authors consider the case in which a linear time-invariant (LTI) but uncertain plant suffers from nonlinearities y=n(x) which can be expressed as y=Kn+η(x), |η (x)|≤M, with K, a possibly uncertain scalar.
Abstract: This paper considers the case in which a linear time-invariant (LTI) but uncertain plant suffers from nonlinearities y=n(x) which can be expressed as y=Kn+η(x), |η(x)|≤M, with K, a possibly uncertain scalar. This covers a large and very important class of nonlinearities encountered in practice such as friction, backlash, dead zone and quantization.
Quantitative design techniques are presented for this class for the satisfaction of specifications. Special attention is paid to the avoidance of limit cycles using describing function theory, although the design method is also amenable of application using other stability criteria such as the circle criteria. Numerical examples are developed illustrating the design procedure.
73 citations
TL;DR: In this paper, a hierarchy of stability tests, including absolute stability, difference inclusions, and interval matrices, is presented, and it is shown that these tests are not, in general, polynomial-time tests.
Abstract: Stability concepts arising in the literature on absolute stability, difference inclusions and interval matrices are all shown to be equivalent to simultaneous asymptotic stability of a class of linear time-varying discrete systems and, in turn, to exponential stability. This enables the classification of an interval matrix stability test due to Bauer et al., a Lyapunov indicator test due to Barabanov and a constructive Lyapunov function test due to Brayton and Tong into a hierarchy of stability tests. Some applications of these tests are given and it is observed that they are not, in general, polynomial-time tests.
53 citations
TL;DR: In this article, the authors examined the ability of the H∞ design methodology to provide a solution to a gas- or oil-fired boiler control problem, and addressed the nontrivial application issues of the design.
Abstract: This paper examines the ability of the H∞ design methodology to provide a solution to a gas- or oil-fired boiler control problem, and addresses the nontrivial application issues of the H∞ design. The H∞ methodology is applied to an experimentally verified heating-cogeneration boiler model which exhibits nonlinearities, instability, time delays, non-minimum phase behaviour, and coloured noise disturbances with sensor noise in the frequency range of the significant plant dynamics. The design shows that, to satisfy performance criteria, a high order controller is needed. The paper also demonstrates a trade-off between the reduction of controller order and the loss of controller performance.
43 citations
TL;DR: In this paper, the authors present new formulations for quantitative feedback theory that do not require the direct manipulation of templates in the classical sense and enable the explicit incorporation of highfrequency unstructured uncertainty into the problem statement, and allow for constructive existence conditions for the solvability of the QFT problem.
Abstract: New formulations are presented for quantitative feedback theory that do not require the direct manipulation of templates in the classical sense. This enables the explicit incorporation of high-frequency unstructured uncertainty into the problem statement, and allows for constructive existence conditions for the solvability of the QFT problem. Necessary and sufficient conditions for robust stability and robust performance are presented for plants with both parametric and high-frequency unstructured uncertainty, that parallel their corresponding H∞ counterparts. This work extends the recent contribution of Jayasuriya and Zhao to plants with more general non-minimum phase characteristics such as RHP poles and zeros and time delays.
43 citations
TL;DR: An original approach to the solution of the optimal state estimation problem by means of neural networks is proposed, which consists in constraining the state estimator to take on the structure of a multilayer feedforward network.
Abstract: Estimating the state of a nonlinear stochastic system (observed through a nonlinear noisy measurement channel) has been the goal of considerable research to solve both filtering and control problems. In this paper, an original approach to the solution of the optimal state estimation problem by means of neural networks is proposed, which consists in constraining the state estimator to take on the structure of a multilayer feedforward network. Both non-recursive and recursive estimation schemes are considered, which enable one to reduce the original functional problem to a nonlinear programming one. As this reduction entails approximations for the optimal estimation strategy, quantitative results on the accuracy of such approximations are reported. Simulation results confirm the effectiveness of the proposed method.
42 citations
TL;DR: In this article, a two-degree-of-freedom filter for the internal model control (IMC) method was proposed to improve the stability and robustness of the step response.
Abstract: In this paper we study the design of a new two-degree-of-freedom filter for the internal model control (IMC) method. The new filter alleviates some disadvantages of the standard IMC filter when the IMC method is applied to unstable plants that do not have non-minimum-phase zeros. We show that by employing the new filter, the resulting system has a flatter frequency response, better stability robustness, and little overshoot in the step response. Furthermore, one of its design parameters can be related directly to the closed-loop bandwidth and the other parameter can be used to control the recovery time after an overshoot has occurred in the step response. These features are important in the application of the IMC method to a new approach of adaptive robust control. Examples are given in the paper to illustrate the new filter design.
33 citations
TL;DR: In this article, sufficient and necessary conditions are given to resolve unambiguously the question of robust stability in SISO systems, which in fact confirms that a properly executed QFT design is automatically robustly stable.
Abstract: Quantitative feedback theory (QFT) has received much criticism for a lack of clearly stated mathematical results to support its claims. Considered in this paper are two important fundamental questions: (i) whether or not a QFT design is robustly stable, and (ii) does a robust stabilizer exist. Both these are precursors for synthesizing controllers for performance robustness. Necessary and sufficient conditions are given to resolve unambiguously the question of robust stability in SISO systems, which in fact confirms that a properly executed QFT design is automatically robustly stable. This Nyquist-type stability result is based on the so-called zero exclusion condition and is applicable to a large class of problems under some simple continuity assumptions. In particular, the class of uncertain plants include those in which there are no right-half plane pole-zero cancellations over all plant uncertainties. A sufficiency condition for a robust stabilizer to exist is derived from the well-known Nevanlinna-Pick theory in classical analysis. Essentially the same condition may be used to answer the question of existence of a QFT controller for the general robust performance problem. These existence results are based on an upper bound on the nominal sensitivity function. Also considered is QFT design for a special class of interval plants in which only the poles and the DC gain are assumed uncertain. The latter problem lends itself to certain explicit computations that considerably simplify the QFT design problem.
33 citations
TL;DR: In this paper, a new low-order matching method is presented to design robost crossfeed compensators for multi-input, multi-output (MIMO) systems.
Abstract: Control law design for rotorcraft fly-by-wire systems normally attempts to decouple angular responses using fixed-gain crossfeeds. This approach can lead to poor decoupling over the frequency range of pilot inputs and increase the load on the feedback loops. In order to improve the decoupling performance, dynamic crossfeeds may be adopted. Moreover, because of the large changes that occur in rotorcraft dynamics due to small changes about the nominal design condition, especially for near-hovering flight, the crossfeed design must be 'robust.' A new low-order matching method is presented here to design robost crossfeed compensators for multi-input, multi-output (MIMO) systems. The technique identifies degrees-of-freedom that can be decoupled using crossfeeds, given an anticipated set of parameter variations for the range of flight conditions of concern. Cross-coupling is then reduced for degrees-of-freedom that can use crossfeed compensation by minimizing off-axis response magnitude average and variance. Results are presented for the analysis of pitch, roll, yaw, and heave coupling of the UH-60 Black Hawk helicopter in near-hovering flight. Robust crossfeeds are designed that show significant improvement in decoupling performance and robustness over nominal, single design point, compensators. The design method and results are presented in an easily-used graphical format that lends significant physical insight to the design procedure. This plant pre-compensation technique is an appropriate preliminary step to the design of robust feedback control laws for rotorcraft.
TL;DR: In this article, a necessary and sufficient condition to test the robustness of a regulator of uncertain linear systems with constrained control is given, and the candidate regulator for this test is that stabilizing nominal systems.
Abstract: A necessary and sufficient condition to test the robustness of a regulator of uncertain linear systems with constrained control is given. The candidate regulator for this test is that stabilizing nominal systems. An illustrative example is also given.
TL;DR: In this article, it was shown that the H, control problem is solvable by a static output feedback controller if and only if there exists a positive definite matrix satisfying two quadratic matrix inequalities.
Abstract: SUMMARY In this paper we shall consider the H, control problem using static output feedback. The approach uses some recent results from linear algebra. The main result shows that the H, control problem is solvable by a static output feedback controller if and only if there exists a positive definite matrix satisfying two certain quadratic matrix inequalities. A parametrization of all static output feedback H, controllers is given. Many linear controller design analysis problems can be reduced to certain matrix linear algebra problems of the type studied in the covariance control literature ([4-61 and references therein.) For further motivation see the linear matrix inequalities discussed in Reference 3. In fact, the parametrization of all stabilizing controllers (of order equal to or less than the order of the plant) for a large variety of situations (continuous and discrete systems, with or without measurement noise) all reduce to the solution of just two linear algebra problems. In this paper we shall apply these linear algebra results to solve the standard H, control problem for static output feedback control [7-101. Using the linear algebra results we obtain necessary and sufficient existence conditions and a parametrization of all stabilizing static H, controllers. P+ will in the following denote the Moore-Penrose inverse of a matrix P. Everywhere, as usual, Q > 0 shall be taken to mean that Q is a positive definite, symmetric matrix. SVD stands for the singular value decomposition. 2. PRELIMINARIES
TL;DR: In this paper, a rigorous formulation for nominal and robust stability analysis of closed-loop linear, time-invariant, single-input single-output systems using Nichols charts is presented.
Abstract: A rigorous formulation is presented for nominal and robust stability analysis of closed-loop linear, time-invariant, single-input single-output systems using Nichols charts. This formulation is based on the Nyquist stability criterion, a simplified criterion that uses the notion of crossings and the properties of the mapping from the complex plane to the Nichols chart. >
TL;DR: In this article, the authors introduced some recently developed frequency-domain design techniques that are effective in the design of robust control systems that are required to be robust under parametric uncertainty.
Abstract: This paper introduces some recently developed frequency-domain design techniques that are effective in the design of control systems that are required to be robust under parametric uncertainty. We have extended the well-known classical control tools (i.e., Nyquist plot, Bode plot, and Nichols chart) developed for a fixed plant to the domain of families of plants where the uncertain parameter varies in intervals. Using this new family of plots, classical control design techniques can be used to design robust control systems. The technique is illustrated by examples.
TL;DR: In this paper, the zero placement capability of generalized sampled-data hold functions (GSHF) was explored and it was shown that the discretized plant can always be made minimum-phase.
Abstract: Loop transfer recovery (LTR) techniques are known to enhance the input or output robustness properties of linear quadratic gaussian (LQG) designs. One restriction of the existing discrete-time LQG/LTR methods is that they can obtain arbitrarily good recovery only for minimum-phase plants. A number of researchers have attempted to devise new techniques to cope with non-minimum-phase plants and have achieved some degrees of success.6-9 Nevertheless, their methods only work for a restricted class of non-minimum-phase systems. Here, we explore the zero placement capability of generalized sampled-data hold functions (GSHF) developed in Reference 14 and show that using the arbitrary zero placement capability of GSHF, the discretized plant can always be made minimum-phase. As a consequence, we are able to achieve discrete-time perfect recovery using a GSHF-based compensator irrespective of whether the underlying continuous-time plant is minimum-phase or not.
TL;DR: In this article, a nonparametric empirical transfer function estimate (ETFE) is employed to quantify the model uncertainty of any prespecified nominal model, from a sequence of measurement data of input and output signals from a plant.
Abstract: Identification of linear models in view of robust control design requires the identification of a control-relevant nominal model, and a quantification of model uncertainty. In this paper a procedure is presented to quantify the model uncertainty of any prespecified nominal model, from a sequence of measurement data of input and output signals from a plant. By employing a nonparametric empirical transfer function estimate (ETFE), we are able to split the model uncertainty into three parts: the inherent uncertainty in the data due to data imperfections, the unmodelled dynamics in the nominal model, and the uncertainty due to interpolation. A frequency-dependent hard error bound is constructed, and results are given for tightening the bound through appropriate input design.
TL;DR: In this paper, the authors proposed a linear state feedback control law with a single tunable gain parameter that allows for local asymptotic stability and regulation to the origin for any initial condition in some a priori given (arbitrarily large) bounded set.
Abstract: We provide an alternative solution to the problem of semi-global stabilization of a class of minimum phase nonlinear systems which is considered in Reference 17. Our method yields a stabilizing linear state feedback law in contrast to a nonlinear state feedback law proposed in Reference 17. We eliminate the peaking phenomenon by inducing a specific time-scale structure in the linear part of the closed-loop system. This time-scale structure consists of a very slow and a very fast time scale. The crucial component in our method is the relation between the slow and the fast time scales. Our proposed linear state feedback control law has a single tunable gain parameter that allows for local asymptotic stability and regulation to the origin for any initial condition in some a priori given (arbitrarily large) bounded set.
TL;DR: A nonrecursive method is proposed for solving the general discrete-time algebraic Riccati equation related to the H∞ control problem (H∞-DARE) that reduces the computation involved in the recursive algorithms while giving much more accurate solutions.
Abstract: In this paper we propose a nonrecursive method for solving the general discrete-time algebraic Riccati equation related to the H∞ control problem (H∞-DARE). We have achieved this by casting the problem of solving a given H∞-DARE to the problem of solving an auxiliary continuous-time algebraic Riccati equation associated with the H∞ control problem (H∞-CARE) for which the well known nonrecursive methods of solving are available. The advantages of our approach are: it reduces the computation involved in the recursive algorithms while giving much more accurate solutions, and it readily provides the properties of the general H∞-DARE.
TL;DR: In this article, a circular arithmetic technique is developed for constructing value set of a characteristic polynomial and necessary and sufficient conditions for robust stability of disk polynomials and their simple combinations.
Abstract: Circular arithmetic technique is developed for constructing value set of a characteristic polynomial. It provides necessary and sufficient conditions for robust stability of disk polynomials and their simple combinations. In more complicated cases sufficient conditions can be obtained. Various examples including multilinear (real or complex) parameter perturbations are considered.
TL;DR: In this paper, a polynomial solution to the standard H∞-optimal control problem is presented, which is based on two J-spectral factorization problems, and a parameterization of all suboptimal compensators is obtained.
Abstract: The paper presents a polynomial solution to the standard H∞-optimal control problem. Based on two polynomial J-spectral factorization problems, a parameterization of all suboptimal compensators is obtained. A bound on the McMillan degree of suboptimal compensators is derived and an algorithm is formulated that may be used to solve polynomial J-spectral factorization problems.
TL;DR: In this article, the problem of system identification in ℋ∞ is investigated in the case when the given frequency response data are not necessarily on a uniformly spaced grid of frequencies.
Abstract: In this paper, the problem of ‘system identification in ℋ∞’ is investigated in the case when the given frequency response data are not necessarily on a uniformly spaced grid of frequencies. A large class of robustly convergent identification algorithms is derived. A particular algorithm is further examined and explicit worst case error bounds (in the ℋ∞ norm) are derived for both discrete-time and continuous-time systems. An example is provided to illustrate the application of the algorithms.
TL;DR: In this paper, the discrete-time H8 control problem with measurement feedback is studied and the structure of the H8 controllers is discussed, and it is shown that it is in certain cases possible to reduce the dynamical order of the controllers without loss of performance.
Abstract: This paper is concerned with the discrete-time H8 control problem with measurement feedback. We extend previous results by having weaker assumptions on the system parameters. We also show explicitly the structure of H8 controllers. Finally, we show that it is in certain cases possible, without loss of performance, to reduce the dynamical order of the controllers.
TL;DR: In this paper, the authors consider nonlinear control systems where the control and the state variables are submitted to explicit constraints, and investigate the problem of local controllability in a neighbourhood of an equilibrium point, while observing state and control constraints along the whole trajectory.
Abstract: We consider nonlinear control systems where the control and the state variables are submitted to explicit constraints. This paper has two objectives. First, for a class of nonlinear systems with constraints, an existence result of nontrivial admissible controls and some of their interesting properties are proved. Then, we investigate the problem of local controllability in a neighbourhood of an equilibrium point, while observing state and control constraints along the whole trajectory. An iterative procedure is also given, which allows one to compute the steering admissible control function. This procedure is illustrated with a classical example.
TL;DR: In this article, a robust control design framework, model reference quantitative feedback design (MRQFD), is developed for the design of the MIMO parametric uncertain control systems, where an internal model reference loop is proposed to obtain the achievement of generalized diagonal dominance and the reduction of uncertainty in the resultant compensated internal loop system.
Abstract: A new decentralized robust control design framework, model reference quantitative feedback design (MRQFD), is developed for the design of the MIMO parametric uncertain control systems. An internal model reference loop is proposed to obtain the achievement of generalized diagonal dominance (GDD) and the reduction of uncertainty in the resultant compensated internal loop system. Based on nonnegative matrix theory, a useful design guide is derived to achieve the GDD condition for the internal model reference loop. Then a sensitivity-based quantitative feedback design (QFD) method is developed and used to solve the resulting series of single-loop QFD problems. The MIMO quantitative specifications are guaranteed to be satisfied by the proposed design framework for largely uncertain systems. A successful application to the design of a robust multivariable controller for the Allison PD-514 aircraft turbine engine is presented to demonstrate the effectiveness of the methodology developed here.
TL;DR: In this paper, the authors used nonlinear Quantitative Feedback Theory (QFT) and pilot compensation techniques to design a 2x2 flight control system for the YF-16 aircraft over a large range of plant uncertainty.
Abstract: : Nonlinear Quantitative Feedback Theory (QFT) and pilot compensation techniques are used to design a 2x2 flight control system for the YF-16 aircraft over a large range of plant uncertainty. The design is based on numerical input- output time histories generated with a FORTRAN implemented nonlinear simulation of the YF-16. The first step of the design process is the generation of a set of equivalent linear time-invariant (LTI) plant models to represent the actual nonlinear plant. It has been proven that the solution to the equivalent plant problem is guaranteed to solve the original nonlinear problem. Standard QFT techniques are then used in the design synthesis based on the equivalent plant models. A detailed mathematical development of the method used to develop these equivalent LTI plant models is provided. After this inner loop design, pilot compensation is developed to reduce the pilot's workload. This outer loop design is also based on a set of equivalent LTI plant models. This is accomplished by modeling the pilot parameters that result in good handling qualities ratings, and developing the necessary compensation to force the desired system responses.
TL;DR: In this paper, the existence of loop gain-phase shaping (LGPS) solutions for the design of robust digital control systems for SISO, minimum-phase, continuous-time processes with parametric uncertainty is addressed.
Abstract: This paper addresses the existence of loop gain-phase shaping (LGPS) solutions for the design of robust digital control systems for SISO, minimum-phase, continuous-time processes with parametric uncertainty. We develop the frequency response properties of LGPS for discrete-time systems using the Δ-transform, a transform method that applies to both continuous-time and discrete-time systems. A theorem is presented which demonstrates that for reasonable specifications there always exists a sampling period such that the robust digital control problem has a solution. Finally, we offer a procedure for estimating the maximum feasible sampling period for LGPS solutions to robust digital control problems.
TL;DR: This note concerns the adaptation of robust H∞ identification techniques to linear periodic discrete-time (LPDT) systems and the algorithm proposed by Helmicki et al.13 is based on a frequency-domain approach to LPDT systems.
Abstract: System identification algorithms for linear time-invariant (LTI) systems have been developed recently, which provide induced norm bounds on the difference between the true system and the identified one. The error bounds then allow the use of robust control design techniques with guarantees on performance of the real system. This note concerns the adaptation of robust H∞ identification techniques to linear periodic discrete-time (LPDT) systems. The paper focuses on the algorithm proposed by Helmicki et al.13 and is based on a frequency-domain approach to LPDT systems.
TL;DR: In this paper, the problem of minimax robust LQG controllers for linear systems with parameter and noise uncertainties is considered, and necessary and sufficient conditions for converting this problem to a two-person zero-sum continuous game problem are presented.
Abstract: The problem of design of minimax robust LQG controllers for linear systems with parameter and noise uncertainties is considered in this paper Necessary and sufficient conditions for converting this problem to a two-person, zero-sum continuous game problem are presented A simple procedure for design of a suboptimal minimax robust LQG controller, ie, the LQG controller for least-favourable model, is proposed Necessary and sufficient conditions for the existence of a saddle point are established Under these conditions, the controller obtained is exactly the minimax LQG controller When there does not exist a saddle point, the worst-case error between the controller obtained and the minimax robust LQG controllers under described uncertainties is bounded