Non-minimum Phase Property Research Articles

Zero Dynamic Active Suppression Control for Underactuated Reusable Launch Vehicles With Nonminimum Phase Property

Zero Dynamic Active Suppression Control for Underactuated Reusable Launch Vehicles With Nonminimum Phase Property

Koopman-operator-based learning control of air-breathing hypersonic vehicles with nonminimum phase properties

In this article, a prescribed learning controller is developed for nonminimum phase air-breathing hypersonic vehicles (AHVs) in the presence of parametric uncertainties and external disturbances. In comparison with the current state of the art, the most significant feature of our control design lies in introducing the Koopman operator to construct an intelligent output redefinition to overcome the nonminimum phase behavior. To evaluate the current control behavior and enhance the learning ability, an improved continuous-time performance index is developed under the actor–critic learning structure. Furthermore, combined with a nonlinear disturbance observer, prescribed learning control is proposed to design control commands, while compensating for lumped disturbances, including neural approximation errors and external disturbances. Numerical simulations have been performed to highlight the superiority of the proposed learning control.

Nonlinear finite time attitude control of flexible spacecraft based on a novel output redefinition method

A finite time attitude controller is designed for a flexible spacecraft based on a novel output redefinition method, in this paper. To make the flexible appendages vibration suppression effective, the appendage tip-point is selected as the output. First, a novel output redefinition method is proposed to overcome the non-minimum phase property of the dynamic model. The proposed method not only makes the system model minimum phase but also improves the attitude control system performance. Consequently, the precise attitude pointing and stabilization are achieved. Then, a nonlinear finite time H∞ controller is designed based on the backstepping approach. For the situation where the modal variables measurements are not available, a modal observer is also designed. The simulation results show the effectiveness of the proposed method in the presence of the model uncertainties and environmental disturbances.

Perfect control for nonminimum-phase unstable systems defined in the multivariable continuous-time state–space framework — An inverse-based approach

In this paper, a new perfect control law dedicated to nonminimum-phase unstable LTI MIMO systems governed in the continuous-time state–space domain is proposed. Two algorithms are investigated, one of which has turned out to be definitely accurate. Henceforth, the inverse model control-based formula can be applied to any right-invertible plants having more input than output variables. Last, not least, through the application of some generalized inverses, the perfect control procedure guarantees the structural stability behavior even for unstable systems. Thus, the notion of the nonminimum-phase property should be understood in terms of a possible achieveability covering the entire class of LTI MIMO continuous-time plants. Theoretical and practical simulation examples performed in the Matlab/Simulink environment confirm the feasibility of the newly introduced approach.

Robust Flight-Path Angle Consensus Tracking Control for Non-Minimum Phase Unmanned Fixed-Wing Aircraft Formation in the Presence of Measurement Errors

The robust flight-path angle consensus tracking control problem for multiple unmanned fixed-wing aircrafts is investigated in this paper, where the non-minimum phase properties and the presence of measurement errors are systematically addressed. A three-module control scheme is proposed for each aircraft: a Distributed Observer that obtains the available information from the reference system and the neighbor aircraft to provide the estimates of the reference states; a Casual Stable Inversion that calculates the bounded estimates of the desired input, desired external states, and most importantly, desired internal states to resolve the divergence issues caused by the non-minimum phase properties; and a Local Measurement Error Rejection Controller that includes a measurement error estimator (MEE) to actively compensate for the adverse effect of measurement errors to achieve robust consensus tracking control. Stability, convergence, and robustness of the proposed control are analyzed, showing that (1) the non-minimum phase issue can be systematically resolved by the designed Casual Stable Inversion to ensure aircraft internal stability and flight safety, and (2) the consensus tracking accuracy can be improved by tuning a single MEE parameter, which is favorable in practical applications to large-scale unmanned aircraft formations. Comparative simulation results with classic PID-based consensus control demonstrate the advantage of the proposed control in transient oscillations, steady-state tracking accuracy, and robustness against measurement errors.

On adjustable and lossless suppression to disturbances and uncertainties for nonminimum-phase laser pointing system

This paper focuses on the nonminimum-phase laser pointing system’s disturbances and uncertainties rejection problems on moving platforms. Moving platforms cause a variety of noticeable vibrations that substantially impair pointing accuracy. Additionally, the disturbance-observer-based control approaches currently in use sacrifice the desired disturbance suppression effects, stability margins, or tracking characteristics due to the nonminimum-phase laser pointing system. This paper suggests an adjustable disturbance-observer-based control strategy with dual filters to obtain lossless and adjustable disturbance suppression effects without sacrificing stability margins or tracking characteristics. The closed-loop controller and forward plant are presented to reduce the laser pointing system’s nonminimum-phase properties. An additional flexible filter is added to deal with the weakened nonminimum-phase system. Both filters are uniformly proposed depending on various disturbances brought on by moving platforms and work together to accomplish lossless desired disturbance suppression effects. The analyses and experiments show that the suggested approach can accomplish the lossless and adjustable disturbance suppression effects in the nonminimum-phase laser pointing system, which cancels out many more disturbances and uncertainties than the current methods.

Disturbance-Observer-Based Feedback Linearization Control for Stabilization and Accurate Voltage Tracking of a DC–DC Boost Converter

The nonminimum-phase property of the dc–dc boost converter can create difficulties in designing a stable, robust, and fast control for the output voltage. In this article, these difficulties are reduced by modifying the state model of the boost converter in such a way that it behaves like a minimum-phase system. More specifically, the control input entering the state equation for the output voltage is treated as an unknown disturbance to make the relative degree of the system equal the system’s order. As a result, the modified model does not exhibit zero dynamics, so that it can be treated as a minimum-phase system for the control design. The modified model is, then, used to derive a dynamic compensator for the output voltage regulation. More explicitly, the dynamic compensator is designed based on combining linearizing feedback control with a disturbance observer. The latter is employed to compensate for model uncertainties and unknown load with a view to ensure asymptotic regulation under the composite controller. The asymptotic regulation is achieved due to the integral action property characterizing the disturbance observer. More interestingly, after simple algebraic manipulation, it turns out that the composite controller reduces to a dynamic state feedback control plus an antiwindup scheme to mitigate the effect of control saturation during transients. The performance of the proposed controller is verified by experimental tests. The experimental results demonstrate the ability of the proposed controller to achieve good transient and steady-state performances.

On vibration rejection of nonminimum-phase long-distance laser pointing system with compensatory disturbance observer

This paper focuses on the vibration rejection problem for the nonminimum-phase long-distance laser pointing system on the moving platform. Due to the unstable approximate inverse of nonminimum-phase property, the disturbance-observer based control (DOBC) methods inevitably sacrifice numerous vibration rejection capabilities to stabilize the system. In this paper, a compensatory disturbance-observer-based control (CDOBC) method is proposed to ensure a much stronger vibration rejection performance. In this method, the stable nominal plant replaces the unstable approximate inverse. Limited by stability constraints, the primary filter still sacrifices performances to provide basic vibration rejection capabilities. In the premise of a stable primary filter, the proposed compensatory filter naturally and effectively satisfies its stability constraint. Thus, the novel compensatory filter has sufficient flexibility to make up for the sacrificed vibration rejection capabilities of the primary filter without breaking the system’s stability. The CDOBC method has quite enough capability to reject the vibrations of the nonminimum-phase long-distance laser pointing system, which is impossible for the DOBC methods. Furthermore, the analytical system’s stability and tuning laws for the proposed method are presented. The simulations and experiments demonstrated the effectiveness of the proposed method despite various vibrations.

On disturbance rejection control for inertial stabilization of long-distance laser positioning with movable platform

This paper focuses on the disturbance rejection control problem for inertial stabilization of long-distance laser positioning with the movable platform. Due to various disturbances of the movable platform, the positioning system has significant disturbances that affect the positioning accuracy. Moreover, the nonminimum-phase property of the inertial stabilization system leads to great challenges for designing traditional disturbance-observer-based as well as rejection control methods. In this paper, a dual-compensator disturbance-observer-based control algorithm is proposed to ensure a much stronger rejection of disturbances than those of conventional methods. In particular, it is proven that the two compensators in the proposed method effectively estimate disturbances in different frequency regions. Furthermore, the analytical tuning laws for the proposed dual-compensator disturbance-observer-based control method are presented. The experimental setup including the laser positioning platform demonstrated the validity of the proposed method, which effectively rejected various disturbances.

Hydrogen Fuel Cell and Ultracapacitor Based Electric Power System Sliding Mode Control: Electric Vehicle Application

Control of a perturbed electric power system comprised of a hydrogen fuel cell (HFC), boost and boost/buck DC–DC power converters, and the ultra-capacitor (UC) is considered within an electric vehicle application. A relative degree approach was applied to control the servomotor speed, which is the main controllable load of the electric car. This control is achieved in the presence of the torque disturbances via directly controlling the armature voltage. The direct voltage control was accomplished by controlling the HFC voltage and the UC current in the presence of the model uncertainties. Controlling the HFC and UC current based on the power balance approach eliminated the non-minimum phase property of the DC–DC boost converter. Conventional first order sliding mode controllers (1-SMC) were employed to control the output voltage of the DC–DC boost power converter and the load current of the UC. The current in HFC and the servomotor speed were controlled by the adaptive-gain second order SMC (2-ASMC). The efficiency and robustness of the HFC/UC-based electric power systems controlled by 1-SMC and 2-ASMC were confirmed on a case study of electric car speed control via computer simulations.

Non-minimum phase viscoelastic properties of soft biological tissues

Understanding the viscoelastic properties of biological tissues is important because they can reveal tissue structure. This study analyzes the viscoelastic properties of soft biological tissues using a fractional dynamics model. We conducted a dynamic viscoelastic test on several porcine samples, i.e., liver, breast, and skeletal muscle tissues, using a plate–plate rheometer. We found that some soft biological tissues have non-minimum phase properties, i.e., the relationship between compliance and phase delay is not uniquely related to the non-integer derivative order in the fractional dynamics model. The experimental results show that the actual phase delay is larger than that estimated from compliance. We propose an empirical model to represent these non-minimum phase properties; a fractional Maxwell model with the fractional Hilbert transform term is proposed. The model and experimental results were highly correlated in terms of compliance and phase diagrams, and complex mechanical impedance. We also show that the amount of additional phase delay, defined as the increase in actual phase delay compared to that estimated from compliance, differs with tissue type.

Byrnes-Isidori-based dynamic sliding-mode control for nonminimum phase hypersonic vehicles

This paper deals with the dynamic sliding-mode (DSM) control problem for nonminimum phase hypersonic vehicles (HSVs). When the elevator is the only control surface available for the altitude dynamics, the HSV model exhibits unstable zero dynamics, preventing the application of standard inversion-based control techniques. To solve this problem, a DSM control method based on Byrnes-Isidori (B-I) normalized form is proposed, achieving asymptotic tracking of velocity and Flight-Path-Angel (FPA) while stabilizing internal dynamics. First, for the pitch dynamics with nonminimum phase behavior, external dynamics and internal dynamics are determined by coordinate transformation to convert the longitudinal model to B-I normalized form, based on which a criterion of nonminimum phase property is given by the stability analysis of internal dynamics. Then, a DSM control method is proposed for the FPA subsystem of nonminimum phase, which transforms the output tracking problem into stabilization problem of an augmented system consisting of internal dynamics and dynamic compensator, making closed-loop pole adjustable, and thus improves the tracking performance. The principle of parameters determination is proposed, which is proved to achieve the stability of the system on the sliding surface. Besides, nonlinear disturbance observer is utilized to compensate the error caused by dynamic inversion control. The proposed method is compared with approximate backstepping control and is shown to have superior tracking accuracy as well as robustness from the simulation results. This paper may also provide a beneficial guidance for control design of other complex systems of nonminimum phase.

Design and application of nonlinear model‐based tracking control schemes employing DEKF estimation

SummaryThis paper deals with the design and application of nonlinear model‐based control schemes for stable and nonlinear benchmark industrial processes. The primary control objective is to facilitate set‐point (constant/time‐varying) tracking in the presence of external disturbances, process noise, measurement noise, parametric uncertainty, and model mismatch. We first propose a “noninferential‐type” model‐based control scheme which involves a finite‐dimensional, nonlinear, and deterministic process model to generate the model states. Secondly, an “inferential‐type” model‐based control scheme has been introduced particularly to take into account the stochastic uncertainties such as process noise and measurement noise. The second scheme exploits the dual extended Kalman filter for estimating the immeasurable states and the process parameters through which disturbance is injected. Unlike fixed‐parameter controllers, the proposed schemes update the controller gains at each step depending on the real‐time process gains. In order to demonstrate the usefulness of the proposed closed‐loop tracking control schemes, two exhaustive case studies have been carried out on the CSTR and Van de Vusse reactor processes, which are considered to be benchmark industrial processes due to highly nonlinear and unpredictable behaviour and due to nonminimum phase property. Finally, the performance of the proposed schemes are compared with an EKF‐based adaptive PI control framework and the simulation results reveal that the transient performance of the proposed schemes are better than that of the aforementioned PI technique especially in perturbed condition (ie, in presence of model mismatch and measurement noise).

A Generalized Input-output-based Digital Sliding-mode Control for Piezoelectric Actuators with Non-minimum Phase Property

In this paper, a generalized input-output-based digital sliding-mode control (GIODSMC) is developed for piezoelectric actuators (PEA) with non-minimum phase (NMP) property. First, the instability mechanism of the traditional input-output-based digital sliding-mode control (IODSMC) for NMP systems is analyzed. Then, a generalized approximate input-output model is established to cancel the effect of unstable zeros in NMP systems. The generalized model can be transformed into different forms, which represents a class of approximate models suitable for this situation. Based on this model, a controller, called the GIODSMC, is presented. Unlike existing works, the developed controller ensures precision motion control for PEA with NMP property. Moreover, additional control parameters are not required to stabilize the NMP systems, and neither a hysteresis model nor a state observer is needed for the developed method. Stability of the closed-loop system is theoretically analyzed. At last, the presented method is tested through numerical simulations and experimental investigations on a piezoelectric actuator device.

Synchronised trajectory tracking for a network of MIMO non‐minimum phase systems with application to aircraft control

In this study, the problem of synchronised trajectory tracking for a network of multi-input–multi-output (MIMO) non-minimum phase (NMP) systems is addressed under a switching communication topology. First, an approach to convert the original system equation into a normal form is proposed, where a coordinate transformation matrix is introduced. Then, a control solution is developed, which is made up of a distributed observer network to generate an estimate of the reference system, a causal stable inversion to estimate the bounded state reference and feedforward term, and a local state-trajectory tracker to achieve simultaneously asymptotic output tracking and internal dynamics stabilisation. Finally, the solution is applied to the synchronised flight-path angle and velocity tracking problem of a network of F-16 aircraft, and further compared with the classic proportional–integral–derivative control-based approach used in many real-life applications. Simulation results demonstrate the effectiveness of the proposed solution, as well as the performance advantages owing to a systematic consideration of the NMP property.

Quasi-Natural Humanoid Robot Walking Trajectory Generator Based on Five-Mass With Angular Momentum Model

This paper proposes to develop a quasi-natural humanoid robot walking trajectory generator based on five-mass with angular momentum model using feedback–feedforward controller. This approach aims to minimize modeling error and improve the frequency characteristics from nonminimum phase properties so that walking performance and tracking accuracy are enhanced. This proposed model focuses on the angular momentum effects from arm and leg rotation to reduce modeling error to enhance walking performance. Based on pole-zero cancelation using series approximation method, it can overcome the sudden change of the natural zero-moment point reference due to the frequency characteristics in the nonminimum phase control system. The humanoid walking pattern generator is verified and demonstrated using a humanoid robot developed in our laboratory based on the proposed model.

Sliding Mode Control of Hydrogen Fuel Cell and Ultracapacitor Based Electric Power System: Electric Vehicle Application

The paper deals with controlling an electric power system comprised of a Hydrogen Fuel Cell (HFC), boost and boost/buck DC-DC power converters and the Ultracapacitor (UC) for an auxiliary power supply in order to control servomotor speed within a vehicle application. Relative degree approach is applied for direct control of the servomotor input voltage and speed, as well as the HFC and UC currents in the presence of the model uncertainties. The non-minimum phase property of the DC-DC boost converter is eliminated by controlling HFC and UC currents based on the power balance approach. The adaptive-gain second order sliding mode controllers (2-ASMC) control the current in HFC and the servomotor speed. The conventional Sliding Mode Controllers (SMC) are designed for controlling the output voltage of the converter and the load current of the UC. The efficiency and robustness of the proposed SMC and 2-ASMC are confirmed via computer simulations.

Observer-based attitude controller for lifting re-entry vehicle with non-minimum phase property

This article concentrates on the attitude control problem for the lifting re-entry vehicle with non-minimum phase property. A novel attitude control method is proposed for this kind of lifting re-e...

Regulation of a DC/DC Boost Converter Under Parametric Uncertainty and Input Voltage Variation Using Nested Reduced-Order PI Observers

DC/DC boost converters are known for presenting highly nonlinear and nonminimum phase properties. This paper combines a predesigned cascade controller and nested reduced-order proportional-integral observers (PIOs) to maintain the desirable voltage regulation performance of the cascade controller for a dc/dc boost converter subject to load change, parametric uncertainties, unmodeled dynamics, and input voltage variations. In the proposed cascade controller design, the fast inner current loop adopts proportional-integral control and the slow outer voltage loop employs integral-proportional control based on a linearized model at a single nominal operating point. Unified theoretical analysis is performed by applying singular perturbation theory, which confirms the desired approximation of the augmented system with the PIOs to the nominal closed-loop system using the cascade controller without accounting for the uncertainties. The validity of the proposed observer-based control scheme is tested via computer simulations and comparative experiments using a laboratory prototype. Both results show that the closed-loop performance remains nearly nominal under load change, parametric uncertainties, unmodeled dynamics, and input voltage variations, confirming the effectiveness of the proposed controller.

A robust adaptive control method for Wiener nonlinear systems

Summary This paper proposes a new robust adaptive control method for Wiener nonlinear systems with uncertain parameters. The considered Wiener systems are different from the previous ones in the sense that we consider nonlinear block approximation error, process noise, and measurement noise. The parameterization model is obtained based on the inverse of the nonlinear function block. The adaptive control method is derived from a modified criterion function that can overcome non-minimum phase property of the linear subsystem. The parameter adaptation is performed by using a robust recursive least squares algorithm with a deadzone weighted factor. The control law compensates the model error by incorporating the unmodeled dynamics estimation. Theoretical analysis indicates that the closed-loop system stability can be guaranteed under mild conditions. Numerical examples including an industrial problem are studied to validate the results. Copyright © 2016 John Wiley & Sons, Ltd.