Horacio J. Marquez

IMC design for unstable processes with time delays

A modified IMC structure is proposed for unstable processes with time delays. The structure extends the standard IMC structure for stable processes to unstable processes and controllers do not have to be converted to conventional ones for implementation. An advantage of the structure is that setpoint tracking and disturbance rejection can be designed separately. A method is proposed to tune the modified IMC structure with an emphasis on the robustness of the structure. Design for some typical delayed unstable processes shows that the control structure can be tuned easily and achieve good tradeoff between time-domain performance and robustness.

Brief paper: LMI-based sensor fault diagnosis for nonlinear Lipschitz systems

The problem of sensor fault diagnosis in the class of nonlinear Lipschitz systems is considered. A dynamic observer structure is used with the objective to make the residual converge to the faults vector achieving detection and estimation at the same time. It is shown that, unlike the classical constant gain structure, this objective is achievable by minimizing the faults effect on the estimation error of the dynamic observer. The use of appropriate weightings to solve the design problem in a standard convex optimization framework is also demonstrated. An LMI design procedure solvable using commercially available software is presented.

Nonlinear observer design for one-sided Lipschitz systems

Control and state estimation of nonlinear systems satisfying a Lipschitz continuity condition have been important topics in nonlinear system theory for over three decades, resulting in a substantial amount of literature. The main criticism behind this approach, however, has been the restrictive nature of the Lipschitz continuity condition and the conservativeness of the related results. This work deals with an extension to this problem by introducing a more general family of nonlinear functions, namely one-sided Lipschitz functions. The corresponding class of systems is a superset of its well-known Lipschitz counterpart and possesses inherent advantages with respect to conservativeness. In this paper, first the problem of state observer design for this class of systems is established, the challenges are discussed and some analysis-oriented tools are provided. Then, a solution to the observer design problem is proposed in terms of nonlinear matrix inequalities which in turn are converted into numerically efficiently solvable linear matrix inequalities.

Comparison of some well-known PID tuning formulas

Criteria based on disturbance rejection and system robustness are proposed to assess the performance of PID controllers. A simple robustness measure is defined and the integral gains of the PID controllers are shown to be a good measure for disturbance rejection. An analysis of some well-known PID tuning formulas reveals that the robustness measure should lie between 3 and 5 to have a good compromise between performance and robustness.

Stabilization of remote control systems with unknown time varying delays by LMI techniques

In this paper, the stabilization of one class of remote control systems with unknown time varying delays is analysed and discussed using LMI techniques. A discrete time state space model under a static control law for remote control systems is first introduced based on some assumptions on the uncertain term. The time delay is unknown, time varying, and can be decomposed into two parts: one fixed part which is unknown and is an integer multiple of the sampling time; the other part which is randomly varying but bounded by one sampling time. Static controller designs based on delay dependent stability conditions are presented. This system is then extended to a more general case when the randomly varying part of the time delay is not limited to one sampling time. The derivative of the time delay is not limited to be bounded. Hence, the contributions are as follow: (i) for a given controller, we can use these stability criteria to test stability of the resulted system; (ii) we can design a remote controller to stabilize an unstable system. Finally, simulation examples are presented to show the effectiveness of the proposed method and to demonstrate remote stabilization of open loop unstable systems.

H ∞ observer design for lipschitz nonlinear systems.

The problem of observer design for Lipschitz nonlinear systems is considered. A new dynamic framework which is a generalization of previously used Lipschitz observers is introduced and the generalized sufficient condition that ensures asymptotic convergence of the state estimates is presented. The equivalence between this condition and an H/sub /spl infin// optimal control problem which satisfies the standard regularity assumptions in H/sub /spl infin// optimization theory is shown and a parameterization of all possible observers is also presented. A design procedure which is less restrictive than the existing design approaches is proposed, and a simulation example is given to illustrate the observer design.

Multivariable robust controller design for a boiler system

In an industrial boiler system, multiloop (decentralized) proportional-integral (PI) control is used because of its implementational advantages. We show that such control schemes sacrifice robustness and performance of the overall system. In particular, under normal boiler operating conditions, we design a robust multivariable controller using H/sub /spl infin// loop-shaping techniques; for consideration in implementation, we then reduce this controller to a multivariable PI controller. Both the H/sub /spl infin// controller and its PI approximation are tested extensively in letdown the frequency domain as well as in the time domain, using a valve complex nonlinear simulation software; the results show that the designed controllers are superior in robustness and performance to the existing multiloop controller.

H ∞ synthesis of unknown input observers for non-linear Lipschitz systems

The problem of unknown input observer design for non-linear Lipschitz systems is considered. A new dynamic framework which is a generalization of previously used linear unknown input observers is introduced. The additional degrees of freedom offered by this dynamic framework are used to deal with the Lipschitz non-linearity. The necessary and sufficient condition that ensures asymptotic convergence of the new observer is presented, and the equivalence between this condition and an H ∞ optimal control problem which satisfies the standard regularity assumptions in the H ∞ optimization theory is shown. Based on these results, a design procedure that is solvable using commercially available software is presented. A simulation example is given to illustrate the proposed design.

Design of unknown input observers for Lipschitz nonlinear systems

The problem of unknown input observer design for Lipschitz nonlinear systems is considered. A new dynamic framework which is a generalization of previously used linear unknown input observers is introduced. The additional degrees of freedom offered by this framework are used to deal with the Lipschitz nonlinearity. The necessary and sufficient condition that ensures asymptotic convergence of the new observer is presented, and the equivalence between this condition and an H/sub /spl infin// optimal control problem which satisfies the standard regularity assumptions in the H/sub /spl infin// optimization theory is shown. Based on these results, a design procedure that is solvable using commercially available software is presented.

Brief paper: Razumikhin-type stability theorems for discrete delay systems

In this paper, by employing the Razumikhin technique and Lyapunov functions, Razumikhin-type theorems that guarantee the uniform stability, uniformly asymptotic stability and uniformly exponential stability for the general discrete delay systems are established, respectively. Moreover, Razumikhin-type uniformly exponential stability theorem gives the estimation of the convergence speed. As theoretic application, the Razumikhin-type uniformly exponential stability result is further studied and used to show some well-known stability results for some kinds of discrete delay systems. Finally, examples are also worked through to illustrate our results.