Disturbance Rejection Specifications Research Articles

A Lyapunov-Based Approach for Recursive Continuous Higher Order Nonsingular Terminal Sliding-Mode Control

A recursive continuous higher order nonsingular terminal sliding-mode (TSM) controller is proposed in this article for nonlinear systems. A new integral TSM manifold is constructed in a recursive manner by modifying the tool of adding a power of integrator instead of exploring nonrecursive design directly. A super-twisting like reaching law is designed to achieve continuous control action without sacrificing disturbance rejection specification as that in boundary-layer approaches. By the new Lyapunov-based design, the proposed control method admits the following new features: first, rather than imposing some existence condition for nonrecursive design, the proposed method admits the certainty for chosen fractional power to guarantee the finite-time stability of the closed-loop system; second, an explicit Lyapunov function approach is proposed to establish finite-time stability of the closed-loop system; and, third, the proposed method is shown to be tunable to exhibit desired transient performance and control energy restriction.

Position control of an electro-hydrostatic asymmetric actuator operating in all quadrants

Pump-controlled actuators generally use single-rod cylinders in order to provide high output forces and reduce the installation space. According to the working principle of such systems, there are four possible circuit configurations, corresponding to four operational quadrants. This paper presents the design and experimental validation of a robust, fixed-gain, linear position controller for a newly developed single-rod pump-controlled actuator, i.e., electro-hydrostatic actuator (EHA) that operates in all quadrants. The actuator operates under different loading, being subjected to an alternating resistive-assistive load force. The controller has been built upon the quantitative feedback theory (QFT), and is designed to satisfy tracking, stability and disturbance rejection specifications, considering a wide range of parametric uncertainties. The ability of the proposed controller to maintain the actuator position within acceptable response envelopes, has been examined with the aid of an instrumented John Deere JD-48 backhoe. The experimental results show that oscillations in position responses are not observed during quadrant switch up to a load mass of 367 kg.

High-order moment stabilization for Markov jump systems with attenuation rate

This paper studies the high-order moment control problem for discrete-time Markov jump linear systems (MJLSs) with certain dynamic response performance and disturbance rejection specifications. An appropriate cumulant generating function is employed to express the original stochastic system in high-order component form. This facilities the high-order moment stabilization of MJLSs. Moreover, a pole region assignment approach is utilized to ensure desired dynamic response specifications with a certain attenuation rate. An arithmetic and geometric inequality approach is utilized to extract sufficient conditions ensuring the designed controller existence. These conditions ensure the high-order moment steady-state property and certain dynamic specifications for the MJLSs. The effectiveness of the proposed method is demonstrated through numerical and practical examples.

Disturbance Rejection Design for a Bank-to-Turn Missile using Decoupling Quantitative Feedback Theory

Multivariable Quantitative Feedback Theory (QFT) is applied to a bank-to-turn missile plant for disturbance rejection specifications. The plant is first partially decoupled over the plant uncertainty to reduce the interaction index to below unity for frequencies around and higher than the expected closed-loop system bandwidth. QFT methodology is then applied to design a diagonal controller to meet the disturbance rejection specifications. The resulting fully populated controller is able to meet the design specifications, which was not achievable using a diagonal controller because of the interaction and delay in the system.

Modeling of Atmospheric Turbulence as Disturbances for Control Design and Evaluation of High Speed Propulsion Systems

Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying integrated couplings between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms. Then a generalized formulation is developed in frequency domain for these scale models that approximates the fractional order with the products of first order transfer functions. Given the parameters describing the conditions of atmospheric disturbances and utilizing the derived formulations, the objective is to directly compute the transfer functions that describe these disturbances for acoustic velocity, temperature, pressure, and density. Utilizing these computed transfer functions and choosing the disturbance frequencies of interest, time domain simulations of these representative atmospheric turbulences can be developed. These disturbance representations are then used to first develop considerations for disturbance rejection specifications for the design of the propulsion control system and then to evaluate the closed-loop performance.

H∞ Jitter Control for a Platform-Mounted Laser

AbstractThis paper presents a jitter control design for a platform-mounted laser. The controller reduces the transmission of platform jitter, modeled as a multi-tonal signal plus broadband noise, to the laser beam. The design utilizes the well-known H∞ loop shaping design procedure to ensure a balance between robust stability requirements and disturbance rejection specifications. Numerical simulation demonstrated at least a 20 dB (or, equivalently, > 90%) reduction at the tonal frequencies. Comparison to a previously implemented controller provides verification of a successful implementation of the proposed controller.

Modelling and robust μ-synthesis control of an intelligent self balancing two-wheel vehicle

A non-linear dynamic model is developed for a new type of two-wheel vehicles (B2). The B2 has two wheels side by side actuated via two DC motors and commanded through a controller card using a joystick. The vehicle can carry up to two passengers at a time. A first effort has been made to formulate a suitable set of requirements to be followed during the design phase. On the basis of such requirements, a reference linear dynamic model of the B2 has been derived. Then, a model matching H∞ control problem has been solved via the μ-synthesis approach, which allows disturbance rejection and robustness specifications to be taken into account. Finally, the designed control laws have been evaluated numerically both for the loaded and unloaded vehicle cases. The controller performed well even under maximum uncertainty and perturbation conditions.

Design and experimental evaluation of a QFT contact task controller for electro‐hydraulic actuators

AbstractThis paper presents design and experimental evaluation of a robust contact task controller for an electro‐hydraulic actuator that operates under significant system uncertainties and nonlinearities. The designed controller allows the actuator to follow a free space trajectory, and upon contact with an uncertain environment exert a desired force, by stably passing through the transition phase from free space to constrained space. The scheme is essentially the combination of two distinct control laws that are individually designed for position regulation in free space and force regulation during sustained contact. Both controllers are designed, using a nonlinear approach within the framework of quantitative feedback theory (QFT), to satisfy a priori specified stability, tracking and disturbance rejection specifications. They are then combined with a simple switching law to form a contact task controller. Due to the existence of a switching, the resulting control system is non‐smooth. The stability of the controller is then analysed using an extended version of Lyapunov's second method under the condition of existence and uniqueness of Filippov's solution. Experiments, performed on a typical industrial hydraulic actuator, include motion through free space, contact with the environment and the transition between the two. The proposed QFT contact task control scheme enjoys the simplicity of fixed‐gain controllers, is easy to implement, requires very little computational effort, is robust to the variation of hydraulic functions as well as environmental stiffness, and results in responses with good performance in both transient and steady‐state periods. Additionally, the controller only requires measured contact force and actuator position as feedback; this makes the controller attractive for industrial implementation. Copyright © 2006 John Wiley & Sons, Ltd.

A New Ratio Control Architecture

In this paper, a new ratio control architecture is proposed. It aims at providing high performance in both set-point following and load disturbance rejection specifications. A tuning procedure is given in order to set all the parameters in the control scheme so that the design effort required by the user is kept at a minimum level. Simulation and experimental results show the effectiveness of the methodology.

Robust and adaptive control: fidelity or an open relationship?

Robust and adaptive control are essentially meant to solve the same control problem. Given an uncertain LTI model set with the assumption that the controlled plant slowly drifts or occasionally jumps in the allowed model set, find a controller that satisfies the given servo and disturbance rejection specifications. Specifications on the transient response to a sudden plant change or “plant jump” are easily incorporated into the robust control problem, and if a solution is found, the robust control system does indeed exhibit satisfactory transients to plant jumps. The reason to use adaptive control is its ability, when the plant does not jump, to maintain the given specifications with a lower-gain control action (or to achieve tighter specifications), and also to solve the control problem for a larger uncertainty set than a robust controller. Certainly equivalence-based adaptive controllers, however, often exhibit insufficient robustness and unsatisfactory transients to plant jumps. It is therefore suggested in this paper that adaptive control always be built on top of a robust controller in order to marry the advantages of robust and adaptive control. The concept is called adaptive robust control. It may be compared with gain scheduling, two-time scale adaptive control, intermittent adaptive control, repeated auto-tuning, or switched adaptive control, with the important difference that the control is switched between robust controllers that are based on plant uncertainty sets that take into account not only the currently estimated plant model set but also the possible jumps and drifts that may occur until the earliest next time the controller can be updated.

Vibration and Position Tracking Control of Piezoceramic-Based Smart Structures Via QFT

This paper presents robust vibration and position tracking control of a flexible smart structure featuring a piezoceramic actuator. A cantilever beam structure with a surface-bonded piezoceramic actuator is proposed, and its governing equation of motion and associated boundary conditions are derived from Hamilton’s principle. The transfer function from control input voltage to output displacement is then established in Laplace domain considering the hysteresis behavior as a structured plant uncertainty. A robust QFT (quantitative feedback theory) compensator is designed on the basis of a stability criterion which prescribes a bound on the peak value of an M-contour in the Nichols chart (NC). In the formulation of the compensator, disturbance rejection specification and tracking performance bounds are specified to guarantee the robustness of the system to the plant uncertainty and external disturbance. A prefilter is also designed for the improvement of step and sinusoidal tracking control performances. Forced-vibration and tracking control performances are investigated through computer simulation and experimental implementation in order to demonstrate the efficiency and robustness of the proposed control methodology.

Feedback design for robust tracking and robust stiffness in flight control actuators using a modified QFT technique

The problem of dynamic stiffness of hydraulic servomechanisms has often been recognized as a significant performance issue in a variety of applications, the most notable of which includes flight control actuation. When a hydraulic actuator such as this is operated in position control, an aerodynamic flutter load on the control surface manifests itself as a force disturbance on the system. Although this would appear to be a standard disturbance rejection problem, the disturbance does not enter the system as in the classical sense (i.e. at the plant output) and hence, this problem must be considered in a modified formulation. A hydraulic servomechanism is said to be 'stiff' if it exhibits acceptable rejection of force disturbances within the control bandwidth. In this paper, an approach to feedback design for robust tracking and robust disturbance rejection is developed via the quantitative feedback theory (QFT) technique. As a result, it is shown that reasonable tracking and disturbance rejection specifications can be met by means of a fixed (i.e. non-adaptive), single loop controller. The methodology employed in this development is the sensitivity-based QFT formulation. As a result, robust tracking and robust disturbance rejection specifications are mapped into equivalent bounds on the (parametrically uncertain) sensitivity function; hence, the frequency ranges in which tracking or disturbance rejection specifications dominate become immediately obvious. In this paper, a realistic non-linear differential equation model of the hydraulic servomechanism is developed, the linear parametric frequency response properties of the open loop system are analysed, and the aforementioned QFT design procedure is carried out. Analysis of the closed loop system characteristics shows that the tracking and disturbance rejection specifications are indeed met.

分母系列表現のパデ近似による低次元２自由度制御系の設計法

Having advantages of setting independently feedback characteristics such as disturbance rejection specification and reference response characteristics, two-degree-af-freedom (2DOF) control is widely utilized to improve the control performance. The ordinary design method such as model matching usually derives high-ordered feedforward element of 2DOF controller.In this paper, we propose a new design method for low order feedforward element which is based on Pade approximation of the denominator series expansion. The features of the proposed method are as follows: (1) it is suited to realize reference response characteristics in low frequency region, (2) the order of the feedforward element can be setected apart from the feedback element. These are essential to the 2DOF controller design.With this method, 2DOF reactor power controller is designed and its control performance is evaluated by numerical simulation with reactor dynamics model. For this evaluation, it is confirmed that the controller designed by the proposed method possesses equivalent control characteristics to the controller by the ordinary model matching method.

H∞ control for a sensorless permanent-magnet synchronous drive

A robust two degrees of freedom speed controller for a permanent-magnet synchronous motor (PMSM) drive system without using shaft sensor is proposed. The feedback controller and the prefilter are designed in a simple way by extending the utility of the H∞ optimisation procedure. The feedback controller is designed to meet robust stability and disturbance rejection specifications by using the H∞ loop shaping design procedure. For the prefilter the free contractive parameter resulting in H∞ control is used to improve the robust model matching properties of the feedback system. A DSP-based sensorless PMSM drive under the field-oriented control framework is established for experimentally verifying controller performance.

Disturbance rejection with bounded control action: Loop-shaping methodology

Suppressing the influence of external disturbances on a process is the most common objective of a controller in a chemical plant. A control system that can keep the controlled variables at or near their set point and the manipulated variables lower than their prespecified maximum bounds in the face of load disturbances is wanted. A method is presented to design controllers with disturbance rejection specifications and limits over the control energy. This methodology is based on a special strategy to shape the structured singular value of a closed-loop transfer function matrix.

Robust feedback synthesis for margins at the plant input

In its present form, the Quantitative Feedback Theory (QFT) for uncertain MIMO feedback systems is a tool to design the two degree-of-freedom of a feedback system. It satisfies demands of robustness, performance, and gain and phase margin at the plant input for diagonal controllers. The method is now extended to meet the requirements of gain and phase margin specifications (including as a function of frequency) at the plant input for non-diagonal controllers. The advantages are: (1) elimination of underdamped closed loop transfer function from any plant input into itself and elimination of underdamped closed loop poles in the effective bandwidth of the system. In the most general terms the time response at the plant input owing to disturbances, sensor noise and/or tracking commands is improved and long-duration ‘ringing’ is avoided; (2) the margins fit the conditions of the circle criterion of guarantee stability for memoryless elements at one of the plant inputs; and (3) the design can be tailored to meet disturbance rejection specifications at the plant input for a given disturbance spectrum.

On the design of robust two degree of freedom controllers

The aim of this paper is to introduce two methods of designing robust two degree of freedom (TDF) controllers. Both design procedures will be illustrated and evaluated on a high purity distillation column example. In the first approach the feedback controller and the prefilter are designed in a single step using an H ∞ optimization procedure. The second method optimizes the feedback controller and prefilter in two separate design stages. Roughly speaking, the feedback controller is designed to meet robust stability and disturbance rejection specifications, while the prefilter is used to improve the robust model matching properties of the closed loop system. The single step approach has the advantages that it is easy to use, and that the resulting controller degree is the same as that of the plant. The two stage approach offers greater design flexibility and it may produce robust stability and robust performance margins which are significantly bigger than those achievable with the single stage approach. Set against that, the two stage technique is more difficult to use and it produces controllers which may have an order which is significantly bigger than that of the plant.

Linear-quadratic Gaussian with loop-transfer recovery methodology for the F-100 engine

The design of a multivariable feedback control system for the F-100 turbofan jet engine is a challenging task for control engineers. This paper employs a linearized model of the F-100 engine to demonstrate the use of the newly developed linear-quadratic Gaussian with loop-transfer recovery design methodology that adopts an in- tegrated frequency and time-domain approach to multivariable feedback control synthesis so as to meet stability robustness, command following, and disturbance rejection specifications. ODERN turbofan jet engines represent an important multiple-input/multiple-output (MIMO) control ap- plication area since the dynamic coordination of fuel flow and several engine geometry variables can lead to improved performance and efficiency, while maintaining safe fan and compression stall margins. Indeed, the MIMO feedback con- trol of turbofan and turboshaft engine has received a great deal of attention in the past few years.18 The F-100 turbofan engine was used as a main design exam- ple for which different MIMO control methodologies were employed. The so-called linear-quadratic-regulator (LQR) ap- proach9'10 was the basis of engineering designs and evaluations14 that required the feedback of several F-100 state variables. In the past five years significant advances have been made in integrating time-domain optimization-based approaches (such as LQR and linear-quadratic Gaussian (LQG)) with fre- quency domain approaches. Such an integrated frequency- domain and state-space approach to MIMO control systems design was pioneered by Stein and his colleagues1114 and has culminated to the so-called linear-quadratic Gaussian with loop-transfer recovery (LQG/LTR) methodology for MIMO feedback control synthesis. The primary objective of this paper is to illustrate the LQG/LTR design methodology using a four-input/fou r- output linear model of the F-100 engine. Specifically, we stress how MIMO command following and disturbance rejection performance specifications, as well as stability robustness specifications are naturally posed in the frequency domain us- ing the singular values of suitably defined loop-transfer matrices. Then, we demonstrate how the LQG/LTR design procedure is used to meet the posed specifications. Further-