1,721,043 research outputs found
Nonlinear scheduled anti-windup design for linear systems
No full textThe nonlinear L2 anti-windup framework introduced in Teel and Kapor (1997) reduces the anti-windup synthesis problem to a state feedback synthesis problem for linear systems with input saturation and input matched L2 disturbances. In this note, based on the structure proposed in that previous paper, we provide a linear matrix ineqaulity (LMI) formulation of high-performance anti-windup design for control systems with linear asymptotically stable plants. In particular, we first give a linear quadratic-based formulation of linear anti-windup compensation, in terms of the solution of a set of (always feasible) LMI constraints. Then, we propose a nonlinear scheduling technique, where hysteresis switching among a family of linear gains is employed for performance improvement. Both design techniques are demonstrated on an academic example
On a performance-robustness trade-off intrinsic to the natural anti-windup problem
No full textAny natural definition of the anti-windup (AW) control problem requires the design of an add-on compensator which, connected to a saturating closed loop system (which would be well-behaved in the absence of saturation), guarantees stability and, as long as the saturation limits are never exceeded, preservation of the original linear behaviour. Three main contributions are given in this paper. First, it is shown that the "model-matching" requirement implied by the preservation of the linear response can be incompatible with the achievement of robust stability in the presence of large uncertainties, even if the controlled plant is robustly open loop stable. Then, a reasonable "weakened" AW problem is introduced, in which the "model-matching" requirement is considered just as a performance requirement (instead of a hard constraint) whose relaxation can be traded off with robustness to larger uncertainties. Finally, the approach proposed in Teel and Kapoor [(1997a). In Proceedings of the fourth European control conference] is extended to deal with the new problem, leading to a family of state feedback compensators parameterized in terms of a state feedback gain (already present in the original approach) and a stable linear time invariant filter. A detailed design procedure for determining suitable values of the parameters is also described. (c) 2006 Elsevier Ltd. All rights reserved
The L2 (l2) bumpless transfer problem for linear plants: Its definition and solution
No full textA novel characterization of bumpless transfer among alternative controllers, both in continuous and discrete time, is introduced. The bumpless transfer problem is to design a compensation scheme guaranteeing an L2 (respectively, l2) bound on the mismatch, after the switching time between the actual plant output and a particular target, ideal response. Minimization of the gain from initial plant state mismatch to L2 (respectively, l2) plant output mismatch provides improved transients. A solution to the bumpless transfer problem is given, both for plants without input saturation and for plants with input saturation. The solution guarantees anti-windup features in the latter case
Stability properties of reset systems
No full textStability properties for a class of reset systems, such as systems containing a Clegg integrator, are investigated. We present Lyapunov based results for verifying L2 and exponential stability of reset systems. Our results generalize the available results in the literature and can be easily modified to cover Lp stability for arbitrary p∈[1,∞]. Several examples illustrate that introducing resets in a linear system may reduce the L2 gain if the reset controller parameters are carefully tuned
Analytical and numerical Lyapunov functions for SISO linear control systems with first-order reset elements
No full textStability analysis for stochastic hybrid systems: A survey
No full textThis survey addresses stability analysis for stochastic hybrid systems (SHS), which are dynamical systems that combine continuous change and instantaneous change and that also include random effects. We re-emphasize the common features found in most of the models that have appeared in the literature, which include stochastic switched systems, Markov jump systems, impulsive stochastic systems, switching diffusions, stochastic impulsive systems driven by renewal processes, diffusions driven by Lévy processes, piecewise-deterministic Markov processes, general stochastic hybrid systems, and stochastic hybrid inclusions. Then we review many of the stability concepts that have been studied, including Lyapunov stability, Lagrange stability, asymptotic stability, and recurrence. Next, we detail Lyapunov-based sufficient conditions for these properties, and additional relaxations of Lyapunov conditions. Many other aspects of stability theory for SHS, like converse Lyapunov theorems and robustness theory, are not fully developed; hence, we also formulate some open problems to serve as a partial roadmap for the development of the underdeveloped pieces
Adaptive output regulation for linear systems via discrete-time identifiers
Full text linkThe problem of output regulation for general multivariable linear systems has been solved in the 70s, in the seminal works of Francis, Wonham and Davison, under the assumption that the reference signals and the disturbances acting on the system are generated by a known exogenous linear system (the exosystem). The regulator is designed to embed an internal model of the exosystem, which ensures that asymptotic regulation is maintained under arbitrary plant perturbations that do not destroy linearity and closed-loop stability. This robustness property, however, is inexorably lost whenever the internal model does not match exactly the exosystem. In this paper we endow the linear regulator with a discrete-time adaptive unit that adapts the regulator's internal model on the basis of the closed-loop evolution. Compared to existing approaches, adaptation here is cast as an identification problem, and the corresponding optimal predictor is designed independently from the underlying control system. This permits to separate stabilization and adaptation, thus naturally handling general non-square multivariable non minimum-phase plants. Closed-loop stability is guaranteed and, if the dimension of the internal model is large enough and a persistency of excitation condition is fulfilled, asymptotic regulation is achieved for references and disturbances generated by an unknown exosystem. Robustness to parametric uncertainties is inherited by the linear regulator and robustness to additional unmodeled disturbances is proved to hold
Stability and performance for saturated systems via quadratic and nonquadratic Lyapunov functions
No full textIn this paper, we develop a systematic Lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration. The only assumptions we make about the system are well-posedness of the algebraic loop and local stability. Problems to be considered include the estimation of the domain of attraction, the reachable set under a class of bounded energy disturbances and the nonlinear L2 gain. The regional analysis is established through an effective treatment of the algebraic loop and the saturation/deadzone function. This treatment yields two forms of differential inclusions, a polytopic differential inclusion (PDI) and a norm-bounded differential inclusion (NDI) that contain the original system. Adjustable parameters are incorporated into the differential inclusions to reflect the regional property. The main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain Lyapunov function where the PDI or the NDI is valid. With quadratic Lyapunov functions, conditions for stability and performances are derived as linear matrix inequalities (LMIs). To obtain less conservative conditions, we use a pair of conjugate non-quadratic Lyapunov functions, the convex hull quadratic function and the max quadratic function. These functions yield bilinear matrix inequalities (BMIs) as conditions for stability and guaranteed performance level. The BMI conditions cover the corresponding LMI conditions as special cases, hence the BMI results are guaranteed to be as good as the LMI results. In most examples, the BMI results are significantly better than the LMI result
On weakened anti-windup and the design of state-feedback solutions
No full textA weakened anti-windup problem was introduced in (Galeani and Teel, 2004) to overcome the robustness limits inherent in the definition of the natural anti-windup problem, and its solution was given in terms of a parameterized family of state-feedback compensators. Two new contributions are presented in this paper. First, a quantitative measure of the performance-robustness trade-off involved in the weakened anti-windup definition is given. Then, a procedure for selecting suitable values for the parameters of the weakened anti-windup compensator is described. Simulations illustrate the effectiveness of the proposed approach
Constructive nonlinear anti-windup design for exponentially unstable linear plants
No full textIn this paper we give a constructive method for anti-windup design for general linear saturated plants with exponentially unstable modes. The constructive solution is independent of the controller dynamics so that the size of the (necessarily bounded) operating region in the exponentially unstable directions of the plant state space is large. Desirable properties of the closed-loop are formally proved and shown to induce a very desirable behavior on a MIMO example with two exponentially unstable modes. (C) 2006 Elsevier B.V. All rights reserved
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