Institute for Systems Research Technical Reports

Permanent URI for this collectionhttp://hdl.handle.net/1903/4376

This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.

Browse

Author: search.filters.author.Zafiriou, E.Subject: search.filters.subject.nonlinear systems

Search Results

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    A Local Small Gain Theorem and Its Use for Robust Stability of Uncertain Feedback Volterra Systems
    (1993) Zheng, Q.; Zafiriou, E.; ISR
    The requirement to evaluate a gain over the whole signal space is one of the restrictions in the well-known small gain theorem. Using the concepts of local gain and strict causality a local form of small gain theorem is proposed, which can be used to analyze input magnitude dependent stability problems of feedback nonlinear systems, such as a Volterra system. Since only finite order Volterra series can be handled in practice, an uncertainly model is derived to address the robustness issue of approximating a nonlinear system by a finite Volterra series in the context of closed-loop control. The local small gain theorem is then used to analyze the feedback properties of the uncertain Volterra system and a sufficient condition for robust stability is obtained.
  • Thumbnail Image
    Item
    Stability Analysis of Inverse Volterra Series
    (1993) Zhang, Q.; Zafiriou, E.; ISR
    Among various nonlinear control methods, the one based on the Volterra series expansion is a promising approach for chemical process control. Almost all compensator design methods based on Volterra series system models utilize the inverse or some type of pseudo-inverse of the models. It is well known that this inverse is usually stable only for a limited amplitude of input signals, and this limited range is not understood quantitatively. Traditional input-output stability analysis methods cannot be used to analyze such an input amplitude dependent stability problem. Under the assumption of the open-loop system being strictly causal, Local Small Gain Theorem (LSGT) is first developed in the paper, which states a sufficient condition for the stability of the closed-loop nonlinear system. Using the new theorem, not only can one determined the local stability of the closed-loop system but also obtain a bound on the external input signal which guarantees BIBO stability. Then, this theorem is used to analyze the stability problem of inverse Volterra series. It so happens that for the Volterra series models an approximation of the local system gain can be easily obtained. By solving a simple single-variable optimization problem, a bound on the external input signal can be obtained, which guarantees the stability of the inverse Volterra series. Both mathematical analysis and simulation results are presented.
  • Thumbnail Image
    Item
    Optimization-based Tuning of Nonlinear Model Predictive Control with State Estimation
    (1993) Ali, Emad; Zafiriou, E.; ISR
    Nonlinear Model Predictive Controllers determine appropriate control actions by solving an on-line optimization problem. A nonlinear process model is utilized for on-line prediction, making such algorithms particularly appropriate for the control of chemical reactors. The algorithm presented in this paper incorporates an Extended Kalman Filter, which allows operations around unstable steady-state points. The paper proposes a formalization of the procedure for tuning the several parameters of the control algorithm. This is accomplished by specifying time-domain performance criteria and using an interactive multi- objective optimization package off-line to determine parameter values that satisfy these criteria. Three reactor examples are used to demonstrate the effectiveness of the proposed on-line algorithm and off-line procedure.
  • Thumbnail Image
    Item
    On the Tuning of Nonlinear Model Predictive Control Algorithms
    (1993) Ali, Emad; Zafiriou, E.; ISR
    Nonlinear Model Predictive Controllers determine appropriate control actions by solving an on-line optimization problem. A nonlinear process model is utilized for on-line prediction, making such algorithms particularly appropriate for the control of chemical reactors. The algorithm presented in this paper incorporates an Extended Kalman Filter, which allows operations around unstable steady-state points. The paper proposes a formalization of the procedure for tuning the several parameters of the control algorithm. This is accomplished by specifying time-domain performance criteria and using an interactive multi- objective optimization package off-line to determine parameter values that satisfy these criteria. A reactor example is used to demonstrate the effectiveness of the proposed on-line algorithm and off-line tuning procedure.