An Iterative Algorithm Combining Model Reduction and Control Design

The present paper addresses the mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> norm analysis and feedback control design problem for structural systems with collocated actuators and sensors. The mixed norm formulation provides a trade-off measure of a system performance and robustness in the presence of uncertainties in the system model. First, we develop an explicit upper bound expression for the mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> norm of collocated structural systems and an explicit parametrization of output feedback control gains to guarantee such bounds. The results offer computationally efficient solutions for system analysis and multi-objective controller design that are especially suitable for large-scale collocated systems where traditional analysis and design methods fail. The second part of the paper uses the proposed bounds to address the simultaneous design of structural damping parameters and feedback control gains for optimized closed-loop mixed-norm performance. A linear matrix inequality (LMI) formulation is provided for the integrated damping and control gain optimization. Structural control design numerical examples are presented to demonstrate the advantages and computational efficiency of the proposed bounds and the integrated design approach.

This paper presents an integrated approach to the modeling and control of aircraft with exible wings. The coupled aircraft rigid body dynamics with a high-order elastic wing model can be represented in a nite dimensional state-space form. Given a set of desired output covariance, a model reduction process is performed by using the weighted Modal Cost Analysis (MCA). A dynamic output feedback controller, which is designed based on the reduced-order model, is developed by utilizing output covariance constraint (OCC) algorithm, and the resulting OCC design weighting matrix is used for the next iteration of the weighted cost analysis. This controller is then validated for full-order evaluation model to ensure that the aircraft's handling qualities are met and the uttering motion of the wings suppressed. An iterative algorithm is developed in CONDUIT environment to realize the integration of model reduction and controller design. The proposed integrated approach is applied to NASA Generic Transport Model (GTM) for demonstration.

Although control algorithms have been conceived for industrial chemical systems, their acceptance by industry has been slow due to a lack of direct experimental evidence of their effectiveness and to volumes of conflicting, or at least incompatible, recommendations on control structure design. This thesis provides the basis for a concerted theoretical and experimental program in multivariable process control structure design for packed bed chemical reactors by presenting an in-depth control analysis of a practical, multivariable, distributed parameter system-the heat conduction problem defined by the simple diffusion equation-using both frequency-domain and time-domain analyses and the formulation, numerical solution, and analysis of a detailed model for packed bed reactors, along with reduction to a low-order state-space representation suitable for on-line process control. The study of the heat conduction system allowed for consideration of various control design techniques and the relation between measurement structure and control system design. This study shows that the choice of measurements and their locations significantly affects the optimal control design and the usefulness of the different design techniques and the importance of an accurate process model and the necessity of model reduction to a low-order state-space representation for control structure design and implementation. The second portion of this study provides a detailed mathematical modeling analysis of packed bed catalytic reactors that significantly extends previous studies in the detail of the model and in the consideration of all aspects of the model development and reduction to a state-space control representation. The general view that modeling simplifications are desired since they lead to a reduction in numerical solution effort is contested, and it is shown that many simplifications are no longer necessary with today's advanced computational capabilities. A unified approach to dynamic reactor modeling is developed and its importance in the accurate description of dynamic and steady state reactor behavior, in the investigation of reactor start-up or the effects of process disturbances, and in the development of an accurate reduced state-space model for the design of control structures to stabilize the reactor under various disturbances or to provide optimal system recovery from input changes is shown.

This paper proposes design of dynamic out-put feedback controller feeding supplementary control signal to FACTS device for improving damping in system. Feedback controller design involves infinity control, model reduction, and closed loop pole-placements in addition to exposure to uncertainties in load conditions on system. A well designed controller satisfying infinity norm on the resulting closed loop system with output feedback meeting multiple objectives from pole-placements inside a conic sector in complex s-plane, robust to changing load conditions on system is attained. A Polytopic representation of system for changing operating point with load conditions called polytopic linear differential inclusion (PLDI) is considered in the design. The Proposed controller design simplifies steps otherwise involved in robust controller design. LMI framework is used in obtaining controller parameters. Controller designed is dynamic and is obtained by reducing the order of the original system to smaller value. The resulting feasible solution yields optimum values of matrix variables and hence a controller parameters both feasible and optimum.

This paper presents a model reduction and control approach for a class of active flow control problem. Computational fluid dynamics (CFD) has been used extensively to study fluid dynamic systems. It is a powerful tool to gain insight and understanding, but it is also extremely computationally intensive and thus unsuitable for control design and iteration. Various model reduction schemes have been proposed in the past to approximate the Navier-Stokes equation with a low-dimensional model. There are essentially two approaches: input/output model identification and modal decomposition based on snapshots of high-dimensional states such as proper orthogonal decomposition (POD). The former captures mostly the local behavior near a steady state and the latter is highly dependent on the snapshots of the flow state used to extract the projection. This paper presents a novel model reduction approach that attempts to combine the attractive features of the two approaches. The local behavior is first obtained through the identification of a linear (or semi-linear) time invariant model using the input/output data. To capture the large nonlinear structure, we project the difference between CFD response and the linear identified model response onto a set of POD basis. This trajectory is fit to a nonlinear dynamical model to augment the input/output linear model. The resulting linear+nonlinear model is used to design a feedback control law. The difference between the predicted trajectory and CFD simulated trajectory under this control law is further used to refine the POD basis, until a good match is obtained. The proposed method is applied to 2D compressible flow example with outlet flow rate control for a contraction section. Preliminary results for lift control of a 2D airfoil is also included.

Part 1 Computers in control systems: historical development digital computer interfacing structure of a digital control loop interface units data representation and aliasing. Part 2 The z-transformation: definition of the z-transform z-transform properties inverse z-transform pulse of z-transfer functions of systems discrete approximations numerical integration pole-zero mapping modified z-transform multi-rate sampling systems analysis of multi-rate systems fast-slow multi-rate systems closed-loop multi-rate systems. Part 3 Analysis of sampled-data control systems z-transformation of systems stability in discrete systems time domain analysis root locus analysis frequency domain analysis. Part 4 Digital compensator design: continuous domain design digital design digital root locas design state feedback design digital PID control disign deadbeat response design optimal control design controller design in the presence of noise. Part 5 Real-time computer control systems: hardware requirements the digital computer and peripheral equipment the real-time clock interface units software aspects controller implementation programming languages system design co-ordination sampling rate selection and quantization errors computer/device communications interrupt handling multi-tasking and background/foreground. Part 6 Advances in computer control: artificial intelligence expert systems examples of expert systems knowledge based systems in control engineering conventional controller design methods manual control methods fuzzy sets and rule-based control basic fuzzy operations fuzzy relations fuzzy control algorithms parallel processing techniques parallel computers algorithms for parallel (MIMD) computers programming parallel computers performance of parallel computers parallel processing in control engineering matrix algebra numerical integration fault tolerance. Appendices: Table of laplace and z-transforms continuous second-order systems response specifications frequency response characteristics the transputer and occam occam overview transputer systems and occam configuration vibration control of a flexible cantilever system simulation modelling and state estimation controller design user interface solutions.

In the past decade, Absolute Nodal Coordinate Formulation (ANCF), which is kind of a finite element method, has been developed for flexible multibody systems with large deformation and large rotation. Almost all studies for ANCF are dedicated to the development of expression ability of flexible multibody system’s behaviors, for example, a study of expansion of ANCF to three dimensional beam, the improvement of computational performance for numerical analysis and so on. On the other hand, there are few studies which extract controllers from the mathematical expressions derived by ANCF. The main aim of this study is to propose a controller design procedure by the use of the mathematical expression which is derived by ANCF. A flexible beam is introduced as a controlled object and the control torque is applied to the one end of the beam. Control objective is to rotate the beam to the desired position and suppress the residual vibration of the beam. In order to derive the mathematical expression for controller design, a kind of ANCF which uses continuum mechanics approach is employed. It is shown that some assumptions and manipulations of the mathematical expression derived by that method result in the linear equation of motion with some uncertainties and the resultant equation has a form suitable for controller design based on μ synthesis framework which is one of the robust control design method. Using μ synthesis framework, controllers are derived for some design parameters and the derived controllers are applied to the controlled object. The validity of the procedure for controller design is shown by numerical simulations and the possibilities and future works of the proposed controller design procedure by the use of mathematical expression by ANCF is discussed.

This paper will discuss the experimental evaluation of a structural control system designed using a combination of Frequency Weighted LQG and Maximum Entropy. The experimental implementation was performed on an experimental truss structure, the Sandia Truss, which is described in the paper. The control design model was obtained via experimental system identification using the eigensystem realization algorithm with data correlation. The control design used frequency weighting to stabilize the unstructured uncertainty of the system due to low signal-to-noise and uncertain system dynamics in various frequency ranges. Maximum entropy is used to provided robustness for structured uncertain system dynamics within the controller bandwidth. The experimental implementation of the controllers designed with this approach show the ability to design controllers with a specified bandwidth, gain stabilization of unstructured uncertainty, and robustness to structured uncertainty within the controller bandwidth.

This paper presents a new algorithm for the design of linear controllers with special structural constraints imposed on the control gain matrix. This so called SLC (structured linear control) problem can be formulated with linear matrix inequalities (LMI's) with a nonconvex equality constraint. This class of problems includes fixed order output feedback control, multi-objective controller design, decentralized controller design, joint plant and controller design, and other interesting control problems. Our approach includes two main contributions. The first is that many design specifications are described by a similar matrix inequality. A new matrix variable is introduced to give more freedom to design the controller. Indeed this new variable helps to find the optimal fixed-order output feedback controller. The second contribution is to propose a linearization algorithm to search for a solution to the nonconvex SLC problems. This has the effect of adding a certain potential function to the nonconvex constraints to make them convex. The convexified matrix inequalities will not bring significant conservatism because they will ultimately go to zero, guaranteeing the feasibility of the original nonconvex problem. Numerical examples demonstrate the performance of the proposed algorithms and provide a comparison with some of the existing methods.

This paper is concerned with control design for a generalized discrete-time Takagi-Sugeno fuzzy system. The Takagi-Sugeno fuzzy system generally describes nonlinear systems by employing local linear system representations. It is a great tool to analyze a nonlinear system and to design a stabilizing controller for it. However, there is a case where a controller design for a nonlinear system based on the Takagi-Sugeno fuzzy system becomes difficult due to its representation. A generalized fuzzy system to be considered in this paper describes even a wider class of nonlinear systems by representing locally nonlinear systems, and gives a different representation from the standard Takagi-Sugeno fuzzy system, which leads to a rather easy controller design. For such a generalized system, a stabilizing controller design method is proposed by introducing a new class of nonlinear controllers. Then, the resulting closed-loop system becomes a fuzzy system with linear system structures locally, which makes the control design easier. Stabilizing controller design conditions are given in terms of a set of linear matrix inequalities(LMIs), which are easily numerically solvable. A relaxation method is used to reduce the conservatism of design conditions. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.

There are three kinds of algorithms(2-ARE, mu-synthesis, LMI) for controller design using closed-loop shaping method. This paper provides the summary of background theory of three algorithms and controller design results for spacecraft attitude control using the three controller design tools of Matlab Toolbox for comparison. As a result, it reveals that LMI design method is more reliable as well as easier than others for spacecraft attitude control design. Comparison results are as follow: 2-ARE method and LMI method provide almost same results in robust stability, robust performance and control authority level. But 2-ARE method is more sensitive than LMI method with respect to proper design of weighting functions: 2-ARE method is more difficult than LMI method in weighting function design. The design result of mu-synthesis method shows worse performance and requires bigger control authority than others.

&lt;div class="htmlview paragraph"&gt;The feasibility of frame vibration control in automotive vehicles using active hydraulic engine mounts is investigated. The focus of the study is on engine idle conditions. A 38&lt;sup&gt;th&lt;/sup&gt; dynamic model of a simplified vehicle system is used. The simplified system consists of a powertrain and a bare chassis supported by air pillow mounts at four corners. A modified LQG (linear-quadratic-Gaussian) control design method was used to synthesize a reduced order controller with improved robustness to harmonic disturbances. This modified LQG controller design is compared to a standard LQG controller.&lt;/div&gt; &lt;div class="htmlview paragraph"&gt;First, the conceptual implementation of active hydraulic mounts is proposed. The proposed mounts use a close-coupled servo-valve for high-speed fluid injection. The active mounts are capable of producing either attractive or repulsive forces between the powertrain and chassis.&lt;/div&gt; &lt;div class="htmlview paragraph"&gt;Predictions are made for levels of frame vibration reduction and actuator power consumption from simulation of closed-loop system responses. These results provide an estimate of hardware requirements for the implementation of an active mount system.&lt;/div&gt; &lt;div class="htmlview paragraph"&gt;Various issues in control design for flexible structures are addressed. Chief among these are the issues of model order reduction and controller order reduction. Other issues addressed are disturbance robustness and parameter robustness.&lt;/div&gt;

Traditional structural feedback control systems are centralized systems. The applications of these systems to large scale structures usually encounter a number of difficulties regarding system reliability, cost, and feedback latency. Decentralized control strategies offer promising alternatives that can address some of these difficulties. When making control decisions, decentralized controllers may only require data from sensors located in the neighborhood of a control device. Control decentralization lowers the demand on communication range in the sensing and control network, reduces feedback latency, and removes the risk associated with a centralized controller where single-point failure can paralyze the entire control system. This paper presents a time-delayed decentralized structural control strategy that aims to minimize the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> norm of the closed-loop system. Feedback time delay is included in the formulation for the decentralized controller design, which employs a homotopy method through linear matrix inequalities (LMI). Corresponding to certain decentralized feedback patterns, the homotopy method gradually degenerates a centralized control design into a decentralized control scheme. At each homotopy step, LMI constraints are satisfied to guarantee the performance requirement for the closed-loop H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> norm. The proposed algorithm is validated through numerical simulations with an example structure.

A two-stage Active Disturbance Rejection Control (ADRC) design procedure is presented for the output trajectory tracking control problem in Single Input Single Output (SISO) nonlinear systems. Aside from the given scalar system output, the plant is assumed to exhibit a second, physically measurable, internal scalar output variable. The system output is controlled in an ADRC manner from an implicit static, or dynamic, nonlinear feedback controller using, in general, a nonlinear differential expression of the internal output variable. A desired internal output trajectory is thus generated. The internal output variable, in turn, is controlled from the original input and forced to track the desired trajectory synthesized in the previous step by the auxiliary controller. Each ADRC controller design is based on a simplified model of the corresponding subsystem, usually relegating interaction variables and additive nonlinearities to be part of a local (total) disturbance input term. The control scheme is reduced to a set of linear ADRC controllers with, possibly, cancellation of nonlinear input gains which are assumed to be known. Two illustrative aerospace examples are presented where the proposed procedure is illustrated via digital computer simulations.

Extremum seeking control for the trajectory tracking of a skid steering vehicle via averaged sub-gradient integral sliding-mode theory