Full-state Feedback Controller Design Research Articles

Fractional‐order filter‐based enhanced full state feedback control design with multi‐objective formulation using grey wolf optimization algorithm

AbstractA perturbed fractional‐order filter (FOF)‐based LQR control design with multiple performance indices is proposed in this paper. Three variants of the FOF‐based linear quadratic regulator (LQR) system have been proposed along with choices on the commensurate order of state feedback law. The multi‐objective problem formulation has been done with three performance objectives to address the different issues of design. The first performance index constitutes a weighted sum of ITAE (Integral Time of Absolute Error) and the difference between the eigenvalues of the plant and the LQR controlled plant, chosen to minimize the large oscillations as well as relative stability with respect to eigenvalues. A new lower bound of the singular values have been addressed to ensure the robust stability of the system through the formulation of a second performance objective. It is the minimization of singular values of the return ratio matrix at the plant's input. The third and the last performance index aims minimization of maximum singular values of the perturbation transfer function at the plant's output, so as to guarantee no closed‐loop right half plane zeros. The multi‐objective optimization problem is solved and the optimal solutions are obtained via Grey Wolf Optimization Algorithm. The simulation results validate the performance and effectiveness of the proposed control design.

Prescribed performance tracking for a class of uncertain nonlinear systems with actuator failures

AbstractIn this article, we consider the design of a tracking controller for a class of uncertain nonlinear systems with external disturbances and actuator failures and achieve predesignated performance results on the tracking error. First, since the existing prescribed performance strategies are unable to specify performance bounds in an arbitrary way, we propose a new tool to address the prescribed performance issue by constructing chained first‐order filters and an input switching method. With the aid of the new and flexible prescribed performance tool, any predesignated continuous bounds can be formed by setting the reference coordinate values, sufficiently small coordinate value intervals and the gain parameters of the filters. Second, a full state feedback controller design scheme based on the prescribed performance bounds, which describe the convergence rate and maximum overshoot of the tracking error, is proposed. It is proven that the tracking error always satisfies the prescribed performance bounds. Finally, simulation studies are used to illustrate the effectiveness of the proposed tool and the correctness of the established theoretical results.

Position-Based Impedance Control Design for a Hydraulically Actuated Series Elastic Actuator

Series elastic actuators (SEAs) have become a common actuation method in torque-controlled electric lightweight arm applications that physically interact with the environment in assembly tasks. Compared to traditional actuators, SEAs can provide high force fidelity, shock tolerance, and force sensing for interaction control. Considering inherent system dynamics and the variable stiffness of the fluid, the control design for hydraulic SEAs (HSEAs) that lead into fifth-order system is a challenging task. As a novelty, a full state feedback controller design for the developed fifth-order HSEA system is presented to serve as an inner-loop controller to handle highly nonlinear dynamics behavior. In addition, as an outer-loop impedance controller for HSEAs in heavy-duty applications, the position-based impedance controller is designed to handle control of the HSEA system during the contact motion. Experimental results with a one-degree-of-freedom real-size experimental setup with a payload of 200 kilos demonstrates the effectiveness of the proposed HSEA control methods both in the free-space motion and in a contact impedance motion.

Full-State Feedback Control Design for Shape Formation using Linear Quadratic Regulator

This study investigated the capability of a group of agents to form a desired shape formation by designing the feedback control using a linear quadratic regulator. In real application, the state condition of agents may change due to some particular problems such as a slow input response. In order to compensate for the problem that affects agent-to-agent coordination, a robust regulator was implemented into the formation algorithm. In this study, a linear quadratic regulator as the full-state feedback of robust regulator method for shape formation was considered. The result showed that a group of agents can form the desired shape (square) formation with a modification of the trajectory shape of each agent. The results were validated through numerical experiments.

Fuzzy Logic Control of an Uncertain Manipulator With Full-State Constraints and Disturbance Observer

In this paper, a fuzzy logic control strategy is proposed for solving trajectory tracking control issues of an uncertain manipulator. Fuzzy logic is utilized to compensate for nonlinear uncertainties in manipulator dynamics and full-state constraints are involved in full-state feedback controller design for ensuring motion constraints during movement processes. Disturbance observer (DO) is designed to counteract the effects of unknown nonlinear disturbances caused by friction force or other various forms of disturbance. Combining with Lyapunov theory and back-stepping method, the proposed method can guarantee error signals in closed-loop system semi-globally uniformly bounded (SGUB). In view of safe operation, tangent barrier Lyapunov functions (tBLFs) are chosen to maintain joint angle and velocity in a predefined constrained region in tracking processes. Finally, simulation results are carried out to show the effectiveness of our proposed control strategy.

Robust state-feedback control design for active suspension system with time-varying input delay and wheelbase preview information

This paper develops a robust state-feedback controller for active suspension system with time-varying input delay and wheelbase preview information in the presence of the parameter uncertainties. By employing system augmentation technique, a multi-objective control optimization model is first established and then this controller design is converted to a static full-state feedback controller design with robust H∞ and generalized H2 performance, wherein the model-dependent control gain is evaluated by transforming the related nonlinear matrix inequalities into their corresponding linear matrix inequality forms based on Lyapunov theory, and then LMI (Linear-Matrix-Inequality) technique is applied to solve and obtain the desired controller. A numerical simulation case is finally provided to reveal the effectiveness and advantages of the proposed controller.

A self-tuning robust full-state feedback control design for the magnetic levitation system

In this study, a self-tuning robust integral of signum of error (RISE) based controller is designed and used to control a magnetic levitation (maglev) system. In the control design, unlike the classical RISE controller, ‘tanh’ function is used instead of ‘signum’ function to obtain a more smooth control signal. The gains of the controller are updated according to a time-varying update rule. Convergence of the error under the closed-loop operation is proven via Lyapunov-based stability analysis. The controller is tested on an experimental maglev system and successful results are obtained.

Single-step full-state feedback control design for nonlinear hyperbolic PDEs

ABSTRACTThe present work proposes an extension of single-step formulation of full-state feedback control design to the class of distributed parameter system described by nonlinear hyperbolic partial differential equations (PDEs). Under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear state feedback law, both feedback control and stabilisation design objectives given as target stable dynamics are accomplished in one step. In particular, the mathematical formulation of the problem is realised via a system of first-order quasi-linear singular PDEs. By using Lyapunov's auxiliary theorem for singular PDEs, the necessary and sufficient conditions for solvability are utilised. The solution to the singular PDEs is locally analytic, which enables development of a PDE series solution. Finally, the theory is successfully applied to an exothermic plug-flow reactor system and a damped second-order hyperbolic PDE system demonstrating ability of in-domain nonlinear control law to achieve stabilisation.

H-infinity Based Full State Feedback Controller Design for Human Swing Leg

In this paper, the robustness properties of H-infinity control to produce a dynamic output feedback controller is applied to a human swing leg system. The double pendulum structure is usually used to model this system. The pendulum links will represent the thigh and shank of a human leg. The upper body will be connected to the thigh and then the shank via hip and knee joints. The muscles of thigh and shank are moved by applied two external (servomotor) torques at the hip and knee joints. The mathematical model of the system is developed. The results show that the proposed controller can robustly stabilize the system and achieve a desirable time response specification. The results are obtained by using Matlab program and the achieved time response specifications are rise time tr=0.18 seconds, settling time ts=0.25 seconds and maximum over shoot Mp=0.03 for hip joint and tr=0.13 seconds, ts=0.21 seconds andMp=0.01 for knee joint.

Three-Stage Feedback Controller Design With Applications to Three Time-Scale Linear Control Systems

This paper presents a new technique for design of full-state feedback controllers for linear dynamic systems in three stages. The new technique is based on appropriate partitioning of the linear dynamic system into linear dynamic subsystems. Every controller design stage is done at the subsystem level using only information about the subsystem (reduced-order) matrices. Due to independent design in each stage, different subsystem controllers can be designed to control different subsystems. Partial subsystem level optimality and partial eigenvalue subsystem assignment can be achieved. Using different feedback controllers to control different subsystems of a system has not been present in any other known linear full-state feedback controller design technique. The new technique requires only solutions of reduced-order subsystem level algebraic equations. No additional assumptions were imposed except what is common in linear feedback control theory (the system is controllable (stabilizable)) and theory of three time-scale linear systems (the fastest subsystem state matrix is invertible)). The local full-state feedback controllers are combined to form a global full-state controller for the system under consideration. The presented results are specialized to the three time-scale linear control systems that have natural decomposition into slow, fast, and very fast subsystems, for which numerical ill conditioning is removed and solutions of the design algebraic equations are easily obtained. The proposed three-stage three time-scale feedback controller technique is demonstrated on the eighth-order model of a fuel cell model.

Full state feedback controller design for active engine mounting system using PID, pole placement and LQR

Design, implementation and comparison of full state feedback controller (FSFC) with proportional integral derivative (PID) controller to attenuate the engine–body disturbance is presented in this paper. The methods discussed in this paper for FSFC design are linear quadratic regulator (LQR) and pole placement (PP). These control techniques are implemented on two degree of freedom engine–body vibration model so that vibration isolation is achieved by controlling the actuator force placed between engine mounts which rejects the disturbance so as to minimise vibrations that are harmful to the vehicle body and passengers in order to increase comfort level in automobiles. Comparison is done between LQR, PP and PID and which reflects their performances on our engine vibration model.

Controller and observer design for a class of discrete-time nonlinear switching systems

The main contribution of this paper is to present some controller synthesis results for the discrete-time nonlinear (Lipschitz-like) switching systems. Under the assumption that the discrete state of switching systems is known, three related problems are considered, which are full-state feedback controller design, continuous state observer design, and observer-based output feedback controller design. The basic idea of the proposed approaches is to construct the different types of Hybrid Lyapunov function to guarantee the stability, and all of these methods are given in terms of linear matrix inequalities. The results obtained in this paper are only dependent on the Lipschitz-like constant matrices without regard to the specific nonlinear forms. Finally, a numerical example made up of two subsystems is given to show the applicability of theoretical results.

Robust Adaptive Output Feedback Control Design for a Multi-Input Multi-Output Aeroelastic System

In this paper, robust adaptive control design problem is addressed for a class of parametrically uncertain aeroelastic systems. A full-state robust adaptive controller was designed to suppress aeroelastic vibrations of a nonlinear wing section. The design used leading and trailing edge control actuations. The full state feedback (FSFB) control yielded a global uniformly ultimately bounded result for two-axis vibration suppression. The pitching and plunging displacements were measurable; however, the pitching and plunging rates were not measurable. Thus, a high gain observer was used to modify the FSFB control design to become an output feedback (OFB) design while the stability analysis for the OFB control law was presented. Simulation results demonstrate the efficacy of the multi-input multi-output control toward suppressing aeroelastic vibrations and limit cycle oscillations occurring in pre- and post-flutter velocity regimes.

Model-Free Control Design for Multi-Input Multi-Output Aeroelastic System Subject to External Disturbance

In this paper, a class of aeroelastic systems with an unmodeled nonlinearity and external disturbance is considered. By using leading- and trailing-edge control surface actuations, a full-state feedforward/feedback controller is designed to suppress the aeroelastic vibrations of a nonlinear wing section subject to external disturbance. The fullstate feedback control yields a uniformly ultimately bounded result for two-axis vibration suppression. With the restriction that only pitching and plunging displacements are measurable while their rates are not, a high-gain observer is used to modify the full-state feedback control design to an output feedback design. Simulation results demonstrate the efficacy of the multi-input multi-output control toward suppressing aeroelastic vibration and limit cycle oscillations occurring in pre and postflutter velocity regimes when the system is subjected to a variety of external disturbance signals. Comparisons are drawn with a previously designed adaptive multi-input multi-output controller.

Full-state feedback controller design with “delay scheduling” for cart-and-pendulum dynamics

A new approach is proposed to design fixed full-state feedback controllers for linear-time-invariant (LTI) systems with multiple time-delays. This approach takes advantage of the recently introduced “delay scheduling” concept, which opens a new direction in synthesizing the control. “Delay scheduling” strategy suggests further prolonging the existing (and unavoidable) delays in the feedback in order to recover stability or to improve the control performance features. To be able to do this, however, system should have large (and maybe multiple) stable operating zones in the domain of the delays. The main contribution of this paper is to develop a methodology for designing a control law to create this feature. The operation starts with a selection of the feedback gains for a stable non-delayed system. We then utilize a recent paradigm, Cluster Treatment of Characteristic Roots (CTCR), to examine the stability outlook when the delays are present in the dynamics. A scheme is also introduced to modify this gain structure so that the system exhibits a desirably large stable pocket(s) to enable the “delay scheduling”. The paper describes the methodology, without loss of generality, on a fully-actuated cart–pendulum system. Relevant experiments are carried out to show the viability of the proposed idea.

Modeling and Simulation for Control in Carding

The purpose of this work is to further study the transfer function model for carding introduced in a previous paper. Our goal is to develop mathematical and computational tools that will ultimately lead to the design of real-time controllers for carding. In this paper, we discuss a linear, time-variant version of the model presented for one carding group. We also present a reduced order, linear model and use it to build a linear estimator (observer) as part of a full-state feedback controller design. Computer sim ulations and experimental results are shown.