Robust Feedback Controller Design Research Articles

ROBUST CONTROL OF CHAOTIC VIBRATIONS FOR IMPACTING HEAT EXCHANGER TUBES IN CROSSFLOW

A robust feedback controller design to suppress flutter-type chaotic vibrations in baffled heat exchanger tubes is presented. The vibrations are the result of the fluid dynamic forces on the tube which behave as a negative damping element. A consequence of these vibrations is that the heat exchanger tubes impact with the baffle plates thereby reducing the service life of the heat exchanger. To eliminate the resulting tube impacts, a feedback control strategy is proposed. The heat exchanger tube and the fluid dynamic forces acting on the tube are modeled with linear delayed differential equations. Due to the presence of the delay, these equations do not have a rational realization. The feedback controller is realized using a frequency domain loop shaping approach which is well suited for systems with transcendental transfer functions. The control effector is a magnetic force transducer that acts on the heat exchanger tube. The design strategy is based upon the premise that stabilizing the linear instability about the undeformed tube position will preclude the formation of the nonlinear chaotic vibrations that arise from impacting. The feedback controller is shown to provide robust stability and performance over a large flow velocity regime

Performance enhancement on the basis of identified model uncertainty sets with application to a CD mechanism

We address the design of robust feedback controllers based on nominal models and model error bounds that are obtained from measurement data. In order to keep controller complexity limited an approach is adopted where controller synthesis is performed on the basis of a low order (approximate) nominal model; prior to controller implementation the robust performance of the controller is evaluated based on a (highly accurate) system uncertainty set employing a dual Youla uncertainty structure. The procedure is based on an iterative scheme of identification and control design and is experimentally verified on the radial tracking control of a Compact Disc mechanism.

Iterative feedback control design for active vibration control

Model-based robust feedback control design is widespread: a parametric model is identified with some measure of the unmodeled dynamics present in the most advanced approaches. In off-line design, often open-loop experiments are used which can fail to provide satisfactory models because the identification criterion does not serve the aims of feedback robustness. Another frequent problem is possible large bias of the parametric part because of wrong model orders. In the best case large bias comes with large bounds of the unmodeled dynamics in the H-infinity or the L-1 norms. The conclusion is that the use of a plant model is the source of considerable problems while it has so far seemed a natural approach to controller design. In this paper a new ‘‘model-free’’ approach will be outlined for designing feedback vibration controllers. This will be based on a direct search using a sequence of iterative experiments. The experiments will alternate between two types: with and without the vibration source being active. The iterations of the controller parameters allowed by the sequence of experiments will lead to a sequence of improvements of control performance. This will be verified experimentally with reduction of sound-induced low-frequency vibration of a glass plate.

NARMAX modelling and robust control of internal combustion engines

Detailed in this paper is a SISO non-linear modelling and robust controller design methodology experimentally verified on an internal combustion engine. The methodology begins with the identification of a NARMAX model that captures the non-linear dynamics relating the input to the output of a system. This model is converted to a describing function representation for the purpose of robust feedback controller design. The ideology for the describing function recovery is developed in the form of an algorithm which can be extended to other NARMAX model structures not considered here. The controller design is executed in the frequency domain where the output performance specification is |y(t)|≤β∀t>0 and the actuator saturation constraint is |u(t)|≤K∀t>0. For the engine idle speed control application of this study, a SISO NARMAX model of the engine is developed between the by-pass idle air valve (BPAV) and engine speed. The performance objective for the controller design is the time domain tolerance of |Δ rpm| ≤ 100 rpm on idle speed perturbations despite a non-measurable 20 N m external torque disturbance. The controller is validated through numerical simulations as well as experimental verification.

LMI approach to suboptimal guaranteed cost control for uncertain time-delay systems

Results on the design of robust memoryless state feedback controllers for uncertain time-delay systems with norm bounded uncertainty are presented. It is proved that the feasibility of a linear matrix inequality (LMI) problem is necessary and sufficient for the quadratic stabilisation of an uncertain time-delay system. A robust state feedback controller can be constructed using the corresponding feasible solution of the LMI problem. A procedure is given to select a suitable state feedback controller that is also suboptimal in the sense of minimising a bound on a quadratic performance index.

Robust State Feedback Design of Parametric Uncertain Systems via Linear Matrix Inequality

This paper is devoted to the design of robust state feedback controllers for a class of linear uncertain systems. It is assumed that in the system and input matrices there are linear uncertain parameters, which satisfy no special restrictions, such as the matching condition or norm-bounded constraints. Through the matrix nonsingularity analysis, it is known that systems stabilized by a state feedback controller have robust stability bounds on the uncertain parameters, which can be computed from the structured singular value of a composite matrix. Based on this result and linear matrix inequalities, we form a convex optimization problem so that stabilizing controllers can be found to maximize the robust stability bounds.

Control design for nonlinear process models using linear robust control methods: An FCCU example

Recent advances in the area of computer-aided robust (i.e., uncertainty tolerant) multivariable feedback control design based on linear time invariant nominal plant models have so far had minimal impact on process control practice. This is partly because defining the uncertainty and performance requirements for a complex nonlinear model realistically and non-conservatively is difficult, and substantial expertise is required to set up a problem. In this paper, we focus on constructing a framework for generating suitable nominal model-uncertainty set pairs from nonlinear dynamic plant models with associated constraints and operating cost functions. We then demonstrate the effectiveness of the linear robust control approaches by performing robust analysis and synthesis for a fluidized catalytic cracking unit (FCCU), an economically important complex nonlinear, time varying exothermic process with multiple manipulated and regulated variables, and time domain constraints which is a prime candidate for advanced control design.

Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems

The design of robust state feedback controllers for a class of uncertain linear time-delay systems with norm-bounded uncertainty is presented. The state feedback results extend previous results on quadratic guaranteed cost control to the case of uncertain time-delay systems. This is done by the authors' definition of quadratic stability for uncertain time-delay systems with norm bounded uncertainty. It is shown that the state feedback controller can be constructed via the solution of a parameter dependent Riccati equation.

Robust multivariable control of an engine-dynamometer system

We present the robust multivariable feedback controller design of a highly coupled, nonlinear diesel engine-dynamometer system. The performance goal is to maximize the closed loop reference tracking of prespecified engine speed and torque curves by reducing the output variations due to system nonlinearities/uncertainty, and loop interactions through feedback control. The difficulties in controlling engine-dynamometer systems include the large degree of loop interactions, induction-to-power delays, combustion uncertainties, and engine nonlinearities. The performance goal is realized by balancing the bandwidths of the loop transfer functions to avoid excessive loop interactions in the closed-loop system. Standard high-gain and high-bandwidth solutions cannot be used for this design since the system contains pure delays and the controller implementation has sample rate limitations. The engine-dynamometer models used for controller design are developed from spectral estimation techniques and step responses where the effects of the system nonlinearities are captured in a parametric uncertain format. The controllers are designed using a sequential frequency domain approach. The controllers are implemented on an 8.3L turbocharged diesel engine and eddy current dynamometer maintained at Cummins Engine Company, Columbus, IN. The controllers are evaluated based upon the ability of the closed-loop system to track step inputs and a transient test cycle.

Optimal design of robust controllers for uncertain discrete-time systems

This paper presents a fast algorithm for the design of robust output feedback controllers for linear uncertain discrete-time systems. The algorithm utilizes a version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization method of conjugate directions and minimizes a performance index that includes a linear quadratic regulator (LQR) term to optimize performance and a robustness term based on recently developed bounds. The minimization of only the robustness term which corresponds to the maximization of the uncertainty bound is also studied. The case of unstructured perturbations in A has been the only one studied in the robust controller design literature; the present algorithm introduces a unified approach to both cases of unstructured and structured perturbations in the matrices of a state-space model. For the special case of unstructured perturbations in A only, the algorithm is shown to improve considerably the existing unstructured uncertainty bound. Several examples, including an aircraft cont...

Robust Control for Linear Systems with Markovian Jumping Parameters

This paper investigates the problem of robust control for a class of systems with both Markovian jumping parameters and parametric uncertainty. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process, and the parameter uncertainty is real time-varying norm-bounded. A methodology is proposed for the design of robust state feedback controllers. We show that the problem of robust control for linear systems with Markovian jumping parameters can be solved in terms of the solutions to a set of either int ercoupled Riccati differential equations, or algebraic Riccati equations.

Optimal guaranteed cost control of uncertain systems via static and dynamic output feedback

This paper is concerned with the design of robust static and dynamic output feedback controllers for a class of uncertain linear systems with norm-bounded uncertainty. The uncertainty is assumed to enter into both the state and input matrices. However, the output matrix is assumed to be free of uncertain parameters. Necessary conditions are given for the existence of a static output feedback controller that quadratically stabilizes the system and minimizes a bound on the quadratic function. Our results may be considered as an extension of the optimal output feedback LQR problem to the case of uncertain systems with norm-bounded uncertainty. The problem of full-order and reduced-order dynamic output feedback is also considered using the static output feedback results.

Quadratic guaranteed cost control with robust pole placement in a disk

The paper is concerned with the design of robust state feedback controllers for a class of uncertain systems with norm bounded uncertainty, where uncertainty enters in both the state and input matrices. The controller is designed to place the closed loop poles of the uncertain system in a specified disk and guarantees an upper bound on a quadratic cost function. A procedure is given for the construction of a controller which minimises a bound on an integral quadratic performance index.

Optimizing Lyapunov functions for systems with structured uncertainties

The robust stability problem of a nominally linear system with nonlinear, time-varying structured perturbationspj,j=1,...,q, is considered. The system is of the form $$\dot x = A_N x + \sum\limits_{j = 1}^q {p_j A_j x} .$$ When the Lyapunov direct method is utilized to solve the problem, the most frequently chosen Lyapunov function is some quadratic form. The paper presents a procedure of optimization of Lyapunov functions. Under some simple conditions, the weak convergence of the procedure is ensured, making the procedure effective in solving the robust stability problem. The procedure is simple, requiring only numerical routines such as inverting positive-definite symmetric matrices and determining the eigenvalues and eigenvectors of symmetric matrices. It is expected that the optimal Lyapunov function may be used in a robust linear feedback controller design. The examples demonstrate the effectiveness of the method. As shown when considering a system of dimension 24, the method is effective for large-scale systems.

Optimal guaranteed cost control and filtering for uncertain linear systems

The paper presents results on the design of robust state feedback controllers and steady-state robust state estimators for a class of uncertain linear systems with norm bounded uncertainty. The state feedback results extend the linear quadratic regulator to the case in which the underlying system is dependent on uncertain parameters. The state estimation results extend the steady-state Kalman filter to the case in which the underlying system is also uncertain.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Construction of optimal Lyapunov function for systems with structured uncertainties

The robust stability problem for nominally linear system with nonlinear, time-varying structured perturbations p/sub j/, j=1,...,q, is considered. The system is of the form x/spl dot/=A/sub N/x+/sup q//spl Sigma//sub j=1/p/sub j/A/sub j/x. When Lyapunov direct method is utilized to solve the problem, usually some quadratic form is chosen as a Lyapunov function. The note presents a procedure of selection of optimal Lyapunov function from the class of quadratic forms. Under some weak conditions the procedure is effective in solving the robust stability problem. The procedure is simple, requires only such numerical routines as inverting positive definite symmetric matrices and determining the eigenvalues and eigenvectors of symmetric matrices. It is expected that when optimal Lyapunov function is used for a robust linear feedback controller design, the resulting controller will have the smallest in some sense gains. The examples demonstrate the effectiveness of the method. The method is effective for large scale systems, it worked well for 24 dimensional system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust feedback design for nonlinear high-purity distillation column control

The critical issues of uncertainty estimation and robust feedback controller design for nonlinear systems are addressed in this paper. Using a high-purity distillation column as an example, a set of linear models representing the dynamics of the column at different operating conditions around the initial steady state are identified and utilized to assess the nonlinearity-induced uncertainty. A robust controller design using singular values and eigenvalues of the closed-loop system based on the estimated uncertainty is also presented. Effectiveness of the designed linear control systems in controlling both end products of the column is also analyzed.

Observers for stabilization of systems with matched uncertainty

In this article, we study the design of observer-based robust linear feedback controllers. The uncertainty, which can enterA, and either theB orC matrices, is assumed to satisfy certain matching conditions. Lyapunov techniques are used to establish sufficient conditions for stability, given an uncertainty bound. In particular, sufficient conditions are obtained that, if met, result in stabilizing controllers regardless of the size of the uncertainty entering the system matrix, as long as the standard constraints on the uncertainty entering the input or output matrices are met. As with the case of more general forms of uncertainty, the resulting observers often have high gains. To study performance, the problem of disturbance rejection is considered. Sufficient conditions are presented for obtaining control laws that stabilize the closed loop system, regardless of the size of the uncertainty entering the system matrix, while simultaneously guaranteeing arbitrarily small infinity norm for the transfer function from the plant disturbances to the outputs.

ROBUST CONTROL OF BATCH REACTORS

Abstract The design of robust nonlinear feedback controller is analysed for a trajectory tracking in a single-input single-output nonlinear state variable system x = f(x) + g(x)u, y=cx which arises in nonlinear chemical processes particularly in batch reactor control problems. Simulation results for the batch reactor temperature tracking problem show the effectiveness of the control scheme and its robustness to modelling errors. The method is also applicable to multi-input multi-output system where the number of inputs is equal to that of outputs. The controller design is also analyzed for situations wrier: the kinetics, the activation energy and Ihe heat of reaction are unknown and also only limited measurement of state-variables are available. The method of Youcef-Toumi and Ito (1987) is applied to such problems and the effectiveness of control system is shown by simulation.

A COMPUTATIONAL PROCEDURE FOR MULTIVARIABLE STATE FEEDBACK ROBUST CONTROLLER DESIGN

This paper describes a procedure for multivariable state feedback robust controller design. The plant in state space is given by the operational point description or in terms of a vector of slow varying physical parameters. Through solution of the Sylvester matrix equation, a nonunique static feedback controller, which assigns the prespecified closed-loop spectrum, is calculated. In addition, all the remaining feedback degrees of freedom are utilized to optimize a multiobjective function that reflects further design properties. The robust feedback gains is calculated through a three-phase computational algorithm. Numerical examples show that under the robust state feedback control, the closed-loop systems can both achieve satisfied transient characteristics and greatly reduce state trajectory sensitivity to small or large parameter variations in the plant. The pro-posed procedure is still applied to a VTOL aircraft model.