Survey Constructive nonlinear control: a historical perspective

We propose a new feedback controller architecture. The distinguished feature of our new controller architecture is that it shows structurally how the controller design for performance and robustness may be done separately which has the potential to overcome the conflict between performance and robustness in the traditional feedback framework. The controller architecture includes two parts: one part for performance and the other part for robustness. The controller architecture works in such a way that the feedback control system can be solely controlled by the performance controller when there is no model uncertainties and external disturbances and the robustification controller can only be active when there are model uncertainties or external disturbances.

A new controller architecture for high performance, robust, and fault-tolerant control

Bifurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input. Typical bifurcation control objectives include delaying t...

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Bifurcation control: theories, methods, and applications

Gas turbines have become increasingly popular in the different power systems, due to their lower greenhouse emission as well as the higher efficiency, especially when connected in a combined cycle setup. With increasing installations of gas turbines scheduled in different countries, the dynamics of the gas turbines become increasingly more important. In order to study such dynamics, accurate models of gas turbines are needed. This paper presents a comparative analysis and an overview of various models of gas turbines published in different literature.

Overview and Comparative Analysis of Gas Turbine Models for System Stability Studies

Model reduction methodologies for the partial differential equations modeling distributed parameter systems constitute an important first step in controller design. A systematic computer-assisted study illustrating the use of two such methodologies (Approximate Inertial Manifolds and the Karhunen-Loeve expansion) in controlling (stabilizing) a nonlinear reaction-diffusion problem is presented. The approximation quality of the models, issues of computational implementation of the reduction procedure, as well as issues of closed-loop stability are addressed.

Nonlinear model reduction for control of distributed systems: A computer-assisted study

Nonlinear control of surge in axial compression systems

A one-dimensional unsteady compressible viscous flow model of a generic compression system previously developed by the authors is applied to a multistage axial compressor experimental rig configured for single-stage operation. The required model parameters and maps are identified from experimental data. The resulting model is an explicit system of nine first-order ODEs. The model inputs are compressor speed, nozzle area, compressor discharge bleed area, plenum bleed area, inlet total pressure and entropy, and nozzle and bleed exit static pressures. The model and experimental data are compared with respect to both open-loop uncontrolled and closed-loop controlled behaviors. These comparisons focus on (i) forced transients and (ii) global nonlinear dynamics and bifurcations. In all cases the agreement between the model and experimental data is excellent. Of particular interest is the ability of the model, which does not include any hysteretic maps, to predict experimentally observed hysteresis with respect to the onset and cessation of surge. This predictive capability of the model manifests itself as the coexistence of a stable equilibrium (rotating stall) and a stable periodic solution (surge) in the model at a single fixed set of system input values. Also of interest is the fact that the controllers used for closed-loop comparisons were designed directly from the model with no a posteriori tuning of controller parameters. Thus, the excellent closed-loop comparisons between the model and experimental data provide strong evidence in support of the validity of the model for use in direct model based controller design. The excellent agreement between the model and experimental data summarized above is attributed in large part to the use of effective lengths within the model, as functions of axial Mach number and nondimensional compressor rotational speed, as prescribed by the modeling technique. The use of these effective lengths proved to be far superior to the use of physical lengths. The use of these effective lengths also provided substantial improvement over the use of physical lengths coupled with fixed first-order empirical lags, as proposed by other authors for the modeling of observed compressor dynamic lag. The overall success of this model is believed to represent a positive first step toward a complete experimental validation of the approach to control-oriented high-frequency turbomachinery modeling being developed by the authors

Control-Oriented High-Frequency Turbomachinery Modeling: Single-Stage Compression System One-Dimensional Model

In this paper, an approach for control-oriented high-frequency turbomachinery modeling previously developed by the authors is applied to develop one-dimensional unsteady compressible viscous flow models for a generic turbojet engine and a generic compression system. We begin by developing models for various components commonly found in turbomachinery systems. These components include: ducting without combustion, blading, ducting with combustion, heat soak, blading with heat soak, inlet, nozzle, abrupt area change with incurred total pressure losses, flow splitting, bleed, mixing, and the spool. Once the component models have been developed, they are combined to form system models for a generic turbojet engine and a generic compression system. These models are developed so that they can be easily modified and used with appropriate maps to form a model for a specific rig. It is shown that these system models are explicit (i.e., can be solved with any standard ODE solver without iteration) due to the approach used in their development. Furthermore, since the nonlinear models are explicit, explicit analytical linear models can be derived from the nonlinear models. The procedure for developing these analytical linear models is discussed. An interesting feature of the models developed here is the use of effective lengths within the models, as functions of axial Mach number and nondimensional rotational speed, for rotating components. These effective lengths account for the helical path of the flow as it moves through a rotating component. Use of these effective lengths in the unsteady conservation equations introduces a nonlinear dynamic lag consistent with experimentally observed compressor lag and replaces less accurate linear first-order empirical lags proposed to account for this phenomenon. Models of the type developed here are expected to prove useful in the design and simulation of (integrated) surge control and rotating stall avoidance schemes.

Aircraft Engine Committee Best 1993 Paper Award: Control-Oriented High-Frequency Turbomachinery Modeling: General One-Dimensional Model Development

A simplified approach for control of rotating stall. II - Experimental results

In this article the theoretical foundations of a simplified approach for control of rotating stall are presented. This approach requires two-dimensional sensing, but only a single one-dimensional axisymmetric effector with relatively low bandwidth requirements. The reduced actuation requirements of this approach are a consequence of the fact that in this approach one does not require or act upon rotating stall phase information. This is due to the fact that one does not seek to extend the theoretical stable axisymmetric flow range of the compressor. Rather, one seeks to directly address persistent disturbances that would otherwise throttle the equilibrium into the unstable axisymmetric flow range of the compressor. In addition, one seeks to enlarge the domains of attraction of linearly stable axisymmetric equilibria, thereby addressing impulsive disturbances that would otherwise perturb the system state beyond the domain of attraction of the stable axisymmetric equilibrium. Experimental validation of this approach on a single-stage low-speed axial compressor rig is discussed in Part 2 of this article.

O. O. Badmus

Papers

Nonlinear control of surge in axial compression systems

Control-Oriented High-Frequency Turbomachinery Modeling: Single-Stage Compression System One-Dimensional Model

Aircraft Engine Committee Best 1993 Paper Award: Control-Oriented High-Frequency Turbomachinery Modeling: General One-Dimensional Model Development

A simplified approach for control of rotating stall. II - Experimental results

Simplified approach for control of rotating stall. I - Theoretical development