Suboptimal Output Feedback Controller Research Articles

A separation theorem for guaranteed H2 performance through matrix inequalities

The usage of convex optimisation programs that leverage linear matrix inequalities allows for numerical solutions to the design of output-feedback controllers with guaranteed H2 performance. As decreed by the classical separation theorem for the related LQG control problem, the H2 control problem admits an optimal solution in terms of those of the separate optimal state-estimation and state-feedback design problems. This work details a new and alternative proof of this separation theorem. The proof builds on techniques for (linear) matrix inequalities and shows, in particular, that feasible but sub-optimal solutions of the state-feedback and the state-estimation problem yield a sub-optimal output feedback controller with guaranteed H2 performance.

Adaptive Suboptimal Output-Feedback Control for Linear Systems Using Integral Reinforcement Learning

Reinforcement learning (RL) techniques have been successfully used to find optimal state-feedback controllers for continuous-time (CT) systems. However, in most real-world control applications, it is not practical to measure the system states and it is desirable to design output-feedback controllers. This paper develops an online learning algorithm based on the integral RL (IRL) technique to find a suboptimal output-feedback controller for partially unknown CT linear systems. The proposed IRL-based algorithm solves an IRL Bellman equation in each iteration online in real time to evaluate an output-feedback policy and updates the output-feedback gain using the information given by the evaluated policy. The knowledge of the system drift dynamics is not required by the proposed method. An adaptive observer is used to provide the knowledge of the full states for the IRL Bellman equation during learning. However, the observer is not needed after the learning process is finished. The convergence of the proposed algorithm to a suboptimal output-feedback solution and the performance of the proposed method are verified through simulation on two real-world applications, namely, the X-Y table and the F-16 aircraft.

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.

Modal Testing and Suboptimal Vibration Control of Flexible Rotor Bearing System by Using a Magnetic Bearing

A suboptimal output feedback controller is designed based on a reduced order model and applied to a flexible rotor bearing system in order to control the unstable or lightly damped vibrations occurring during operation. The reduced order model is a truncated modal equation of the distributed parameter system obtained through the singular perturbation. The instability problem arising from the spillover effects caused by the uncontrolled high frequency modes is prevented through the constrained optimization by incorporating the spillover term into the performance index. The application of the matrix minimum principle yields a set of matrix equation similar to the unconstrained output feedback controller. The efficiency of the proposed method is demonstrated experimentally with a flexible rotor by using a magnetic bearing.

Vibration control of vehicle using the suboptimal output control with frequency-shaped cost functional.

The theory of linear suboptimal output feedback control with a frequency-shaped cost functional is applied to the vibration control of a vehicle model subjected to the input of the roughness of road surface. The feedback control gain is obtained with respect to a quadratic cost functional whose weighting matrices are functions of frequency. In the control using a frequency-shaped cost functional, the vibration frequency components can be reduced over specific bands of frequencies. Janeway and ISO human response curves with respect to acceleration are used to examine the vibration characteristics of a controlled vehicle model. The theory of the suboptimal control problem subjected to control structure constraints is applied to the synthesis of the output feedback control system. The theoretical and simulated results of the suboptimal output feedback control with a frequency-shaped cost functional are compared with those of the optimal control without a frequency-shaped cost functional and with state estimation using a Kalman filter.

Some new results on optimal and suboptimal regulators of the LQ problem with output feedback

The LQ (linear quadratic) regulator problem with output feedback is considered. In the problem studies an output feedback control is determined such that the cost is J*, the optimal cost for the LQ problem with state feedback, or beta j* with some constant beta >1. A set of sufficient conditions is given for determining such optimal and suboptimal output feedback control laws.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Sequential decentralized control with a prescribed degree of stability

In this paper, a new approach to decentralized stabilization and control is proposed. This approach combines a suboptimal high-gain output-feedback controller design with a sequential high-gain decentralized control scheme such that at each stage of the sequential scheme, the retained optimal closed loop eigenstructure has a prescribed degree of stability. This new algorithm is illustrated on a practical problem, the decentralized stabilization and control of a multi-machine power system.

Stochastic response analysis, order reduction, and output feedback controllers for flexible spacecraft

Real disturbances and real sensors have finite bandwidths. The first objective of this paper is to incorporate this finiteness in the 'open-loop modal cost analysis' as applied to a flexible spacecraft. Analysis based on residue calculus shows that among other factors, significance of a mode depends on the power spectral density of disturbances and the response spectral density of sensors at the modal frequency. The second objective of this article is to compare performances of an optimal and a suboptimal output feedback controller, the latter based on 'minimum error excitation' of Kosut. Both the performances are found to be nearly the same, leading us to favor the latter technique because it entails only linear computations. Our final objective is to detect an instability due to truncated modes by representing them as a multiplicative and an additive perturbation in a nominal transfer function. In an example problem it is found that this procedure leads to a narrow range of permissible controller gains, and that it labels a wrong mode as a cause of instability. A free beam is used to illustrate the analysis in this work.

Extensions of Suboptimal Output Feedback Control with Application to Large Space Structures

Active control for vibration suppression may be required with future large flexible spacecraft. Order reduction of the structural model needed to allow active controller design can lead to rank deficiency in the reduced-state observation matrix. This violates an assumption of the Kosut method of suboptimal output feedback. Such rank deficiency is equivalent to redundancy of the sensor configuration relative to the reduced-order system. To avoid the need for ignoring certain measurements or altering the sensor configuration, the Kosut method is extended so as to be applicable with arbitrary sensor configurations. The main result is the discovery that the linear equation for the output feedback gain matrix is algebraically consistent regardless of the rank of the reduced-state observation matrix. When the latter is rank-deficien t, a family of solutions to the gain equation exists. Free parameters generating this family are proportional in number to the rank-deficiency, and their values may be chosen to improve the performance of the full-order system driven by the reduced-order controller. A numerical example with a two-mass oscillator is given to demonstrate the application of the extensions and to indicate some of the possibilities for performance improvement.

Sub-Optimal Load Frequency Control for Interconnected Power System

This paper describes the application of infinite terminal time case to the load frequency control of a multiple-area interconnected power system. From the viewpoint of practical application, the linear feedback controller using the instantaneous values of output variables is proved to be effective.A number of different optimal or sub-optimal output feedback controllers can be designed by selecting different estimation functions of weighting factors, Q and R.The proposal sub-optimal output feedback controller is not significantly degraded by using the abbreviation of state covariance equation. And, it is deduced that this controller is promising as a candidate for on-line computer controls, because of the simplicity of the gain solution.

A Method for Adaptive Control Using a Minicomputer

This paper presents a method for adaptive control based on optimal or suboptimal output feedback control. The technique of least squares fit is applied to construct a mathematical model which is determined from directly measurable input and output data of the controlled plant. When an identified model of the original plant is used, an optimal output feedback solution is obtained by using this method. If a low-order approximate model is used, then a suboptimal output feedback solution is obtained. Since 1) a mathematical model is determined by using directly measurable input and output data, 2) the control structure is simple and easy to implement, and 3) the computational algorithm is simple, a minicomputer is available as a control instrumentation.