Reduced-order Output Feedback Controllers Research Articles

Design of reduced-order controllers for fluid flows using full-order controllers and Gaussian process regression

We propose a method to design reduced-order output-feedback controllers for fluid flows with the use of data produced by full-order controllers. First, the full-order controller is obtained by combining an ensemble Kalman filter (EnKF) and a model predictive controller (MPC) that are designed based on the Navier–Stokes equations. The full-order controller has high computational complexity and, therefore, is not suitable for real-time implementation. Hence, we use the full-order controller in offline numerical simulations to generate data for data-driven design of the reduced-order controller with low computational complexity. We find a reduced-order subspace of a closed-loop system under the full-order control from the data. This subspace underlies the reduced-order output-feedback controller. The reduced-order state-feedback law is obtained by approximating the full-order MPC with the use of its input/output data. The reduced-order observer is designed for a reduced-order model that is derived by using the Gaussian process regression (GPR). The GPR enables us to design the reduced-order observer which can evaluate uncertainty due to state-dependent residuals of the reduced-order model. We demonstrate the proposed method for a control problem of a flow around a cylinder at the Reynolds number 100. Numerical simulations reveal that the reduced-order controller performs as almost well as the full-order controller for a set of initial states. In addition, robustness of the reduced-order controller to a temporal disturbance that is not considered in the control design is confirmed in the simulations.

Finite-time Boundedness of Polytopic Uncertain Systems with Guaranteed Cost Output Feedback Control

A problem of designing robust guaranteed cost reduced-order output feedback controllers for finite-time boundedness of linear time-varying uncertain systems is considered in this paper. Assuming the system parameters to lie in a polytopic set, differential linear matrix inequality (DLMI) conditions for the design of reduced-order dynamic controllers to handle worst-case exogenous disturbances are derived. The designed controller guarantees the cost on considered disturbance attenuation performance on the system to be below an upper bound, while simultaneously satisfying the conditions for finite-time boundedness and finite L2 gain. Numerical simulations are carried out to demonstrate the applicability of the proposed method in bounding the system trajectories to a predefined set.

Global exponential stabilisation of nonlinear systems by reduced-order observer-based output feedback control via matrix inequality approach

In this paper, we consider the global exponential stabilisation problem by output feedback for a class of nonlinear systems with the extended structure of nonlinearity over the existing control scheme. The new feature is that we present a newly designed reduced-order observer-based output feedback controller with a gain-scaling factor. In our proposed method, we provide more flexibility in the selection of control parameters by utilising a matrix inequality approach under the extended structure of nonlinearity. Using examples, we illustrate the improved results of the proposed control scheme over the existing control scheme.

Quasi-Time-Dependent Output Control for Discrete-Time Switched System With Mode-Dependent Average Dwell Time

This paper is concerned with dynamic output feedback control for a class of switched systems with mode-dependent average dwell-time switching. By constructing a quasi-time-dependent Lyapunov function, the issues of global uniform asymptotic stability and $\ell _{2}$ -gain analysis for the switched system are addressed first. Then, a set of reduced-order output feedback controllers is designed, which is both mode-dependent and quasi-time-dependent. Compared with time-independent criteria, the new results greatly reduce the conservatism. The effectiveness and merits of the proposed method are illustrated with a numerical example.

Robust reduced-order output feedback stabilization for uncertain switched systems

The purpose of this paper is to design reduced-order output feedback controllers for stabilizing switched systems with average dwell-time switching and norm-bounded parameter uncertainties. The switching signals of the switched system and the controller can be either synchronous or asynchronous. In terms of linear matrix inequalities, a sufficient condition is presented, which ensures the closed-loop system to be robustly exponentially stable. Explicit expressions of the desired controller gain matrices can be constructed through the numerical solutions of linear matrix inequalities. An iterative algorithm is proposed for estimating the lower bound of the average dwell time. The effectiveness of the proposed design method is illustrated by two numerical examples.

Reduced-order controller synthesis with regional pole constraint

ABSTRACTA reduced order output feedback controller is designed for a linear time invariant system, which guarantees that the closed-loop poles are placed within some pre-specified stability region in the complex plane. A convex approximation of the non-convex constraints is used to pose a sequence of semi-definite programs, which provide the lowest order proper controller satisfying the approximate constraints. The proposed method is demonstrated on two practical controller design applications.

Reduced-order observer-based output feedback control of nonlinear time-delay systems with prescribed performance

This paper studies the problem of output feedback control for a class of nonlinear time-delay systems with prescribed performance. The system is in the form of triangular structure with unmodelled dynamics. First, we introduce a reduced-order observer to provide the estimate of the unmeasured states. Then, by setting a new condition with the performance function, we design the state transformation with prescribed performance control. By employing backstepping method, we construct the output feedback controller. It is proved that the resulting closed-loop system is asymptotically stable and both transient and steady-state performance of the output are preserved with the changing supply function idea. Finally, a simulation example is conducted to show the effectiveness of the main results.

Robust Reduced-order H<sub>∞</sub> Output-Feedback Control of Retarded Stochastic Linear Systems

A method for designing reduced-order output-feedback controllers for linear time-invariant retarded systems with state-multiplicative Wiener-type noise is introduced, which achieves a minimum bound on the H∞ performance level. A cost function is defined that is the expected value of the standard H∞ performance cost with respect to the stochastic parameters. A solution is thus obtained, for the reduced-order H∞ output-feedback control problem, for the stationary case, via the input-output approach where the system is replaced by a non-retarded one, that contains deterministic norm-bounded uncertainties. The results achieved for the nominal case are extended to the uncertain case where the system matrices reside in a given polytope. A numerical example, taken from the field of aircraft control, is given that demonstrates the applicability of the theory developed.

Equivalent optimal compensation problem in the delta domain for systems with white stochastic parameters

The equivalent representation in the delta domain of the digital optimal compensation problem is provided and computed in this article. This problem concerns finding digital optimal full and reduced-order output feedback controllers for linear time-varying and time-invariant systems with white stochastic parameters. It can subsequently be solved in the delta domain using the strengthened optimal projection equations that we recently formulated in this domain as well. If the sampling rate becomes high, stating and solving the problem in the delta domain becomes necessary because the conventional discrete-time problem formulation and solution become ill-conditioned. In this article, by means of several numerical examples and compensator implementations, we demonstrate this phenomenon. To compute and quantify the improved performance when the sampling rate becomes high, a new delta-domain algorithm is developed. This algorithm computes the performance of arbitrary digital compensators for linear systems with white stochastic parameters. The principle application concerns nonconservative robust digital perturbation feedback control of nonlinear systems with high sampling rates.

An exterior-point approach to the robust D-stability control with output feedback

This paper deals with the robust D -stability (regional pole placement) control against time invariant polytopic uncertainties. It is known that such robust control problems can be described as parameter dependent bilinear matrix inequality (robust BMI) problems which are difficult to solve. In this paper, we propose an iterative approach to design a static or a reduced-order output feedback controller achieving the robust D -stability constraint. The feature of our approach is to construct a controller sequence approaching a feasible region from the outside. Numerical examples are given to show the efficiency of our approach.

Depth control of the INFANTE AUV using gain-scheduled reduced order output feedback

The paper addresses the problem of autonomous underwater vehicle (AUV) control in the absence of full state information. An application is made to the control of a prototype AUV in the vertical plane. The methodology adopted for controller design is nonlinear gain-scheduling control, whereby a set of linear, dynamic, reduced order output feedback controllers are designed and scheduled on the vehicle's forward speed. The paper summarizes the controller design steps, describes a technique for its practical implementation, and presents experimental results obtained with the INFANTE AUV during tests at sea.

Reduced order output feedback control design for PDE systems using proper orthogonal decomposition and nonlinear semidefinite programming

The design of an optimal (output feedback) reduced order control (ROC) law for a dynamic control system is an important example of a difficult and in general non-convex (nonlinear) optimal control problem. In this paper we present a novel numerical strategy to the solution of the ROC design problem if the control system is described by partial differential equations (PDE). The discretization of the ROC problem with PDE constraints leads to a large scale (non-convex) nonlinear semidefinite program (NSDP). For reducing the size of the high dimensional control system, first, we apply a proper orthogonal decomposition (POD) method to the discretized PDE. The POD approach leads to a low dimensional model of the control system. Thereafter, we solve the corresponding small-sized NSDP by a fully iterative interior point constraint trust region (IPCTR) algorithm. IPCTR is designed to take advantage of the special structure of the NSDP. Finally, the solution is a ROC for the low dimensional approximation of the control system. In our numerical examples we demonstrate that the reduced order controller computed from the small scaled problem can be used to control the large scale approximation of the PDE system.

DEPTH CONTROL OF THE INFANTE AUV USING GAIN-SCHEDULED REDUCED-ORDER OUTPUT FEEDBACK

The paper addresses the problem of autonomous underwater vehicle (AUV) control in the absence of full state information. An application is made to the control of a prototype AUV in the vertical plane. The methodology adopted for controller design is nonlinear gain scheduling control, whereby a set of linear, dynamic reduced order output feedback controllers are designed and scheduled on the vehicle's forward speed. The paper summarizes the basic controller design steps, describes a technique for practical implementation of the nonlinear control systems derived, and presents experimental results obtained with the INFANTE AUV during tests at sea.

Two-Degree-of-Freedom Optimal Preview Tracking Control: A Mechatronic Design Example

A design method for digital tracking control is described and applied to control an arm robot with structured uncertainties. A two-degree-of-freedom control system configuration provides the desired feedback and input-output performances independently. Regarding controller design, first, sampled-data H∞ control and linear matrix inequality approaches are used to design a reduced-order output feedback controller. Then, the feedforward controller is parameterized based on the feedback controller, with the free parameter being chosen based on a preview strategy.

An Interior Point Constrained Trust Region Method for a Special Class of Nonlinear Semidefinite Programming Problems

In this paper, an interior point trust region algorithm for the solution of a class of nonlinear semidefinite programming (SDP) problems is described and analyzed. Such nonlinear and nonconvex programs arise, e.g., in the design of optimal static or reduced order output feedback control laws and have the structure of abstract optimal control problems in a finite dimensional Hilbert space. The algorithm treats the abstract states and controls as independent variables. In particular, an algorithm for minimizing a nonlinear matrix objective functional subject to a nonlinear SDP-condition, a positive definiteness condition, and a nonlinear matrix equation is considered. The algorithm is designed to take advantage of the structure of the problem. It is an extension of an interior point trust region method to nonlinear and nonconvex SDPs, with a special structure which applies sequential quadratic programming techniques to a sequence of barrier problems and uses trust regions to ensure robustness of the iteration. Some convergence results are given, and, finally, several numerical examples demonstrate the applicability of the considered algorithm.

Experimental Investigation of Vibration Suppression Control for 2 Link Flexible Robot Arm by Sliding Mode Control.

A reduced order output feedback control algorithm based on a low order modeling methodology for suppressing the vibration and obtaining the high speed, high precision positioning of flexible robot arm is proposed and discussed. The proposed low order modeling methodology gives no modal truncation error and makes it possible to vary the mode shapes of the link according to the change of the boundary conditions due to the feedback gains and the payload at the tip of the arm. Furthermore, this methodology can take into account not only the flexibility of links but also the flexibility of joints. The reduced order output feedback control algorithm is designed by the combination of sliding mode controller and suboptimal output feedback controller so as to achieve both the damping of the system vibration and the stabilization at the same time. The results of numerical simulation and of experiment for a two-link robot arm model are compared. And they prove that the proposed modeling methodology is able to describe the dynamic behaviors of the arm, and the controller designed applying the suboptimal output feedback sliding mode control is able to control the arm quite well.

Vibration Suppression Control of 2 Link Flexible Robot Arm by Sliding Mode Control.

A low order modeling methodology and a reduced order output feedback control algorithm for suppressing the vibration and obtaining the high speed, high precision positioning of flexible robot are presented and discussed. The low order modeling methodology gives no modal truncation error and make it possible to vary the mode shapes of the link according to the change of the boundary conditions due to the feedback gains and the payload at the tip of the arm. The reduced order output feedback sliding mode control algorithm is designed by the combination of sliding mode controller and suboptimal output feedback controller so as to achieve both the damping of the system vigration and the stabilization at the same time. According to the presented method, the vibration suppression control of the two-link robot arm is realized by only 6 sensors, that is, this robot arm model is reduced to 6 output and 2 control input noncollocated system in spite of 34 state variables system.

Design and Implementation of a Robust Controller for a Free Gyro-Stabilized Mirror System

In this paper, we consider the problem of designing a robust controller for a multivariable servomechanism of a free gyro-stabilized mirror system where there exists cross-coupling between the axes. The nonlinear dynamics of the system are first linearized and reformulated into an H∞ problem. A reduced order output feedback controller is then designed using the asymptotic time-scale and eigenstructure assignment (ATEA) technique. The overall design has been implemented using a personal computer with C++ and tested on the actual gyro-stabilized mirror system. Our simulation and implementation results show that the design is very successful.

Disturbance Attenuation and Trajectory Tracking via a Reduced-order Output Feedback Controller for Robot Manipulators

This paper presents a solution to the problem of trajectory tracking with external disturbance attenuation in robotics systems via a reduced-order output feedback controller, without velocity measurement. The proposed control law ensures both semi-global asymptotic stability of the closed-loop system and external disturbance attenuation. The approach is based on the notion of the L 2 -gain and requires to solve two algebraic Riccati inequalities. The proposed controller design is illustrated by a simulation example.

H∞ Reduced-Order Output Feedback Controller For Trajectory Tracking Of Robot Manipulators

This paper is dedicated to trajectory tracking problem with disturbance attenuation (L2) in robotics systems via a reduced-order output feedback controller, without velocity measurement. This controller ensures both semi-global asymptotic stability of the closed-loop system and external disturbance attenuation.