Gain-scheduled State Research Articles

Gain-Scheduled Structured Control in DC Microgrids

Power buffers are electronic converters that shield direct current (dc) microgrids from the effects of abrupt load changes. By promoting collective behaviors, distributed control solutions can improve the overall grid performance, as power buffers can collectively react to abrupt load changes. In this article, a novel gain-scheduled structured control scheme for power buffers is proposed. The control objective is to regulate both the stored energy and the input impedance of the power buffers in a distributed fashion, while guaranteeing, at the same time, the closed loop stability regardless of load changes occurring within predefined ranges. The proposed controller is expressed as a gain-scheduled state feedback law, whose coefficients depend affinely on the scheduling parameters. The structure of the controller gain is chosen to reflect the topology of the communication network implementing the distributed controller. In this article, the existing theory is extended to deal with such control problem, providing a novel strategy, which can be used to design gain-scheduled controllers for the considered class of structured feedback systems. Simulation results using a high-fidelity dc microgrid simulator verify the effectiveness of the proposed approach.

Design of a mixed ℋ2/ℋ∞ gain scheduling state derivative feedback controller for linear parameter-varying systems

In this paper, the mixed guaranteed cost for continuous-time linear parameter-varying (LPV) systems is proposed. In addition, the gain scheduling (GS) strategy and the state derivative feedback (SDF) were considered. The time-varying parameter is assumed to be available for online measurement, and the conditions are based on linear matrix inequalities (LMIs). To improve the behaviour of the system, the -stability is used. Examples show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and a mixed guaranteed cost minimisation.

Improved Embedding of Nonlinear Systems in Linear Parameter-Varying Models With Polynomial Dependence

In this article, the problem of automated generation of linear parameter-varying (LPV) state-space models to embed the dynamic behavior of nonlinear (NL) systems is addressed. The LPV model depends polynomially on an introduced set of scheduling variables. This set comprises linear combinations of residuals, the differences between NL functions in the original model description with their polynomial approximations, in addition to some of the states. The salient feature of the proposed method (PM) is that the LPV model complexity, LPV model accuracy, and LPV model conservativeness are jointly considered through the embedding procedure. To quantitatively evaluate the LPV model accuracy and conservativeness, two cost functions are introduced based on which the model complexity can be adjusted. Numerical studies reveal that the presented method is capable to deliver more accurate and less conservative LPV models in comparison with the available approaches. The effectiveness of the PM is shown in an empirical case study where the dynamic behavior of a 3DOF gyroscope is embedded into an LPV model. Exploiting the obtained LPV model, a gain-scheduled state feedback controller is designed and validated on the gyroscope, clearly demonstrating the applicability of the presented method.

Event-triggered output feedback consensus tracking control for nonlinear multiagent systems with sensor failures

This paper focuses on event-triggered consensus tracking control for nonlinear parametric strict-feedback multi-agent systems subject to unknown sensor failures. Different from existing state observer, a new gain-scheduled state observer is designed to estimate the unmeasured states and sensor failures simultaneously. On the basis of the adaptive observer, a sensor failure compensator is constructed to adaptively cancel the effects of sensor failures. Furthermore, the designed switching threshold event-triggered strategy effectively reduces the communication burden and balances system performance. Based on the Lyapunov function method and the backstepping technique, it is shown that output consensus tracking and global uniform boundedness of all the closed-loop signals are achieved. Additionally, the Zeno behavior is proven to be excluded. Finally, the obtained results are illustrated by means of two simulation examples.

Gain-scheduled state estimation for discrete-time complex networks under bit-rate constraints

In this paper, the gain-scheduled state estimation issue is investigated for a kind of complex networks subject to randomly occurring nonlinearities under bit-rate constraints. An array of random variables is introduced to govern the nonlinearities whose occurring probability is a time-varying but bounded value with known upper and lower bounds. A bit-rate constraint model is established and an encoding–decoding mechanism is proposed, under which an upper bound of the decoding error is acquired. The primary purpose of the issue considered in this paper is to design a gain-scheduled state estimator to obtain an estimate of the network state with an acceptable accuracy according to available output measurements. By means of the stochastic analysis and Lyapunov stability theory, a sufficient condition is provided such that the estimation error dynamics achieve the exponentially mean-square ultimate boundedness. The required estimator gain matrix is parameterized by solving a series of matrix inequalities. A numerical simulation is exploited to show the usefulness of the obtained gain-scheduled state estimator.

Feedback Ratiometric Control of Two Microbial Populations in a Single Chemostat

We address the problem of controlling the dilution rate in a chemostat to regulate the ratio between the concentrations of two microbial populations growing in continuous culture. After analyzing the open-loop dynamics of this multicellular system, we present two alternative feedback control strategies, one based on a gain-scheduled state feedback controller, the other on a switching control strategy. We show that both strategies are effective in solving the problem and illustrate the results by a set of representative in-silico experiments.

Design of an gain scheduling state derivative feedback controller for linear parameter-varying systems

ABSTRACT This paper is devoted to the guaranteed cost of continuous-time linear parameter-varying (LPV) systems, considering the gain scheduling (GS) strategy and the state derivative feedback (SDF). The main contribution of the paper is to derive linear matrix inequalities (LMIs) conditions for the -SDF problem for LPV systems, taking into account the GS controller. For the good behaviour of the controller, we assume that the time-varying parameters are available for online measurement. In some cases, the -GS-SDF controller obtained high control signals, and as we intend to apply the proposed method in practical situations, we introduce the concept of -stability in the problem approach. Examples and a practical implementation show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and guaranteed cost minimisation.

Artificial Neural Network-Based Gain-Scheduled State Feedback Speed Controller for Synchronous Reluctance Motor

Abstract This paper focuses on designing a gain-scheduled (G-S) state feedback controller (SFC) for synchronous reluctance motor (SynRM) speed control with non-linear inductance characteristics. The augmented model of the drive with additional state variables is introduced to assure precise control of selected state variables (i.e. angular speed and d-axis current). Optimal, non-constant coefficients of the controller are calculated using a linear-quadratic optimisation method. Non-constant coefficients are approximated using an artificial neural network (ANN) to assure superior accuracy and relatively low usage of resources during implementation. To the best of our knowledge, this is the first time when ANN-based gain-scheduled state feedback controller (G-S SFC) is applied for speed control of SynRM. Based on numerous simulation tests, including a comparison with a signum-based SFC, it is shown that the proposed solution assures good dynamical behaviour of SynRM drive and robustness against q-axis inductance, the moment of inertia and viscous friction fluctuations.

Online Estimation and Control for Feed Drive Systems With Unmeasurable Parameter Variations

This paper develops an online parameter estimation and control method for both rigid and flexible feed drive systems with unmeasurable parameter variations. The perturbations of the state-space model caused by the parameter variations are formulated, thereby making it possible to obtain the parameter variations in real-time by estimating the perturbations. To estimate the perturbations, they are regarded as the extended states and estimated through the extended-state-observer. With the estimation method, a novel state feedback control structure with double integrators is further proposed, which can eliminate the steady-state tracking error at constant velocities. The H$_\infty $ optimization technique is used to design the proposed state feedback controller. A simulation is conducted that integrates the estimator and the controller for a ball screw setup with mass-dependent resonant modes, where several proposed state feedback controllers are linearly interpolated into a gain-scheduling controller and scheduled by the estimated mass. The results demonstrate that the designed gain-scheduling state feedback controller outperforms a linear-time-invariant state feedback controller and an adaptive backstepping sliding mode controller. The proposed method is experimentally validated on a rigid linear-motor-driven motion stage, of which the results indicate the proposed estimation method can accurately estimate the parameter variations.

Gain‐scheduled constrained state feedback control of DC–DC buck power converter

A gain-scheduled constrained state feedback controller (SFC) for a SiC MOSFET direct current (DC)-DC buck power converter with a non-synchronous control strategy is presented. First, the synthesis process of a gain-scheduled SFC for a control system with a state-dependent parameter is proposed. Next, constraints of important states and control variables are a posteriori introduced into control algorithm to provide satisfactory dynamic behaviour and safe operation of the plant. The boundary values of control signals which provide permissible values of the future state-space variables are derived from the models of power converters that take into account two modes of operation (i.e. charging and discharging mode). The novelty of the proposed approach lies in efficient control algorithm that utilises the gain-scheduled SFC with the parameter-dependent constraint handling method. The designed control algorithm is extensively tested through simulation and experiments at a switching frequency of 36 kHz. The proposed solution is further compared with a conventional cascade control structure based on two proportional integral controllers for voltage and current loops as well as with a non-constrained state feedback control structure to illustrate its performance and low computational complexity.

A new extended LMI-based robust gain scheduled state feedback H 2 controller design

This paper proposes an improved robust H 2 state feedback control synthesis for the Linear Parameter Varying (LPV) systems by attaining the affine quadratic stability. In place of standard H 2 computation in the literature, a new H 2 computation based on extended Linear Matrix Inequality (LMI) is improved by means of the slack variable, where it is obtained by separation Lyapunov matrix from system matrix. State feedback H 2 synthesis is improved for the systems, and is more effective and less conservative than the common ones in the literature. Therefore, the less conservative results are obtained for gain scheduling controller design for LPV systems. The numerical examples are presented to show the superiority of the proposed controller design.

Gain scheduled state feedback velocity control of hydrostatic drive transmissions

In this paper, a velocity tracking controller for hydrostatic drive transmissions is developed. The solution is based on a state-dependent model that incorporates nonlinear characteristics of the system. A full state feedback controller is devised and the gains are scheduled on measured speed and pressures, together with approximated volumetric flow. The effects of uncertainties, especially those related to equilibrium values of pressures, are eliminated by utilizing so-called D-implementation. This technique eliminates the need for equilibrium values, which are model based and thus uncertain.To demonstrate the efficacy of the controller, the solution is implemented on a 4.5-ton wheel loader. For comparison purposes, a constant gain state feedback controller with integral action is devised, and also a linear PID controller is tuned. The results show that the benefits of the devised controller are significant when it is compared to these two controllers. Moreover, the controllability of the machine is maintained in every situation.

Stabilization of linear time-varying systems with state and input constraints using convex optimization

The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched(gain-scheduled) state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.

Gain-Scheduled State Feedback Controllers for Discrete-Time LPV systems Using Scheduling Parameters Affected by Absolute and Proportional Uncertainties

This paper is concerned with the design problem of Gain-Scheduled State Feedback (GSSF) controllers for discrete-time Linear Parameter-Varying (LPV) systems. By considering that exact scheduling parameters are not available in many practical systems, the scheduling parameters provided to GSSF controllers are supposed to be affected by absolute as well as proportional uncertainties. We introduce a set covering the admissible set for the pair of scheduling parameters and the inexact ones, and propose a design method of GSSF controllers using the set. Numerical examples illustrate the effectiveness and possible conservatism of our method.

LPV Modeling of Buck Converter and Gain Scheduling Control

A kind of gain scheduling control is designed for Buck converter. The small signal model of the Buck converter is translated into the Linear Parameter-Varying (LPV) dynamic equation with the load and the line voltage as the scheduled parameters. Based on it, the closed-loop system poles assignment is taken to the specific area with gain scheduled state feedback via linear matrix inequalities (LMIs) technique, the gain scheduled state feedback is designed to regulate the duty cycle of the switch conduction. Compared with robust state feedback control, it has better disturbance rejection performance.

A BMI approach for ℋ︁∞ gain scheduling of discrete time‐varying systems

AbstractThe problem of gain‐scheduled state feedback control for discrete‐time linear systems with time‐varying parameters is considered in this paper. The time‐varying parameters are assumed to belong to the unit simplex and to have bounded rates of variation, which depend on the values of the parameters and can vary from slow to arbitrarily fast. An augmented state vector is defined to take into account possible time‐delayed inputs, allowing a simplified closed‐loop analysis by means of parameter‐dependent Lyapunov functions. A gain‐scheduled state feedback controller that minimizes an upper bound to the ℋ︁∞ performance of the closed‐loop system is proposed. No grids in the parametric space are used. The design conditions are expressed in terms of bilinear matrix inequalities (BMIs) due to the use of extra variables introduced by the Finsler's lemma. By fixing some of the extra variables, the BMIs reduce to a convex optimization problem, providing an alternate semi‐definite programming algorithm to solve the problem. Robust controllers for time‐invariant uncertain parameters, as well as gain‐scheduled controllers for arbitrarily time‐varying parameters, can be obtained as particular cases of the proposed conditions. As illustrated by numerical examples, the extra variables in the BMIs can provide better results in terms of the closed‐loop ℋ︁∞ performance. Copyright © 2009 John Wiley & Sons, Ltd.

Stability analysis and gain-scheduled state feedback control for continuous-time systems with bounded parameter variations

The problems of robust stability analysis and state feedback control based on gain-scheduling for continuous-time systems with time-varying parameters that have bounded rates of variation and lie inside a polytope are addressed in this article. With respect to previous results in the literature, two main contributions of the article are: (i) the robust stability analysis conditions are less conservative and demand less computational effort than the existing ones; (ii) the conditions can be extended to cope with the problem of control design for this class of system. Parameter-dependent linear matrix inequality (LMI) conditions are given for the existence of a parameter-dependent Lyapunov function quadratic in the state and homogeneous polynomially of arbitrary degree in the parameter assuring robust stability. Two convex procedures based on LMIs exhibiting distinct complexities are proposed to solve the problem of robust stability. An extension to deal with the computation of a stabilising parameter-dependent state feedback gain for this class of time-varying systems is also provided, as a sequence of LMIs of increasing precision. Examples illustrate the results, including comparisons with other techniques from the literature.

Design of a Gain-Scheduled Flight Control System Using Bifurcation Analysis

A method for identifying regions of instability in closed-loop systems has been developed for flight dynamics applications. This forms a novel approach in which a surface of equilibria is generated in the region of interest as the influence of the control system is increased. In this way, the creation and destruction of equilibria in the controlled system can be easily found and visualized. This systematic approach allows the stability of the closed- loop system to be directly related to that of the open loop. Results are given for a highly nonlinear aircraft model and demonstrate the power of a combined analytical and graphical approach to control system synthesis. flight dynamics model. We believe that there is great deal of poten- tial in the use of continuation methods in the design and analysis of gain-scheduled feedback control systems. They allow us to address systems with significant nonlinearity and in particular multivalued steady states. The essence of this paper is to consider the application of a gain-scheduled state feedback controller to an aircraft. Contin- uation algorithms are used for two purposes within this paper: 1) to create pseudocontinuous gain schedules throughout a wide oper- ating region and 2) to create surfaces of state equilibria that show changes in the global behavior of the system ranging from the open- loop to the closed-loop configurations. The first step in this approach is to create pseudocontinuous gain functions that satisfy the design criteria at equilibrium throughout the desired operating region of the nonlinear system. Given suf- ficient control authority, these allow the dynamic response of the desired branch of equilibria to be specified. This paper formalizes a continuation approach to gain scheduling using standard feedback control design terminology. The second step is to determine the global implications of this gain-scheduled controller. A novel approach is adopted in which three-dimensional bifurcation surfaces of equilibria are found as both the reference signal and the controller gains are varied. This powerful technique illustrates graphically the influence of the con- trol system and is shown to be invaluable in the evaluation of the global stability of the system. These bifurcation surfaces can be used to indentify undesired attractors within the closed-loop system. The creation of equilibrium surfaces in terms of the variation in control system gain is an entirely new concept in aircraft controller design and allows a tradeoff between local and more global properties of the closed-loop system. These methods are demonstrated using a highly nonlinear air- craft model, the hypothetical high angle of incidence research model (HHIRM). 8 Aircraft dynamics are complex, incorporating nonlin- earities as a result of many factors such as inertial coupling be- tween the different degrees of freedom and aerodynamic forces and moments. 9

Gain-scheduled ℋ2 controller synthesis for linear parameter varying systems via parameter-dependent Lyapunov functions

This paper deals with the problem of gain-scheduled ℋ2 control for linear parameter-varying systems. The system state–space model matrices are affinely parameterized and the admissible values of the parameters and their rate of variation are supposed to belong to a given convex bounded polyhedral domain. Based on a parameter-dependent Lyapunov function, a linear matrix inequality methodology is proposed for designing a gain-scheduled state feedback ℋ2 controller, where the feedback gain is a matrix fraction of polynomial matrices with quadratic dependence on the scheduling parameters. Copyright © 2005 John Wiley & Sons, Ltd.

H2 gain scheduled state feedback for LPV system with new LMI formulation

The H2 gain scheduled state feedback problem is considered by using the parameter-dependent Lyapunov function for linear parameter varying system, in which the dependent parameter is assumed to be measurable on-line in a polytope space. First, a new linear matrix inequality (LMI) representation provides a type of H2 cost computation for this system. With the introduction of the extra variable, this condition provides a decoupling between Lyapunov function matrix and system matrices and will be useful for a synthesis problem study. Secondly, using a polytopic characteristic of the dependent parameter, based on this representation gain scheduled state, the feedback synthesis problem can be transformed into finite-dimensional LMIs formulation. In addition, by using the parameter-dependent Lyapunov function, it can reduce the conservatism that occurred before in the H2 performance synthesis problem with a fixed Lyapunov function. Finally, a numerical example is included to illustrate the efficiency of the proposals.