Non-minimum Phase Characteristics Research Articles

Iterative flexibility compensation based high precision trajectory tracking for industrial manipulators

High precision industrial manipulators are widely demanded in precision machining and advanced manufacturing. To realize high precision trajectory tracking in task space, feedback plus model based feedforward control strategies are widely used in modern industrial manipulators. Furthermore, the accuracy of feedforward model determines the accuracy of trajectory tacking to a great extent, especially for elastic manipulators. In traditional feedforward controllers, the flexibilities out of the rotational plane are often neglected and thus the end-effector tracking performance can be degraded a lot. Therefore, an iterative flexibility compensation based feedforward controller is proposed to improve the end-effector trajectory tracking accuracy of industrial manipulators in this paper. First, the flexible deformations in all directions are described accurately by using the extended flexible joint model (EFJM) for industrial manipulators. Second, a feedforward controller is designed by using the dynamic inversion of EFJM. In the feedforward controller, an iterative flexibility compensation scheme is designed to transform the reference Cartesian trajectory into joint space and thus the limitation of the nonminimum phase characteristics of EFJM can be avoided. Moreover, the flexible deformations are predicted and compensated based on EFJM. After that, the feedforward torque is derived in joint space by using the efficient feedforward torque computation algorithm for EFJM. Simulation and experimental results demonstrate the effectiveness of the proposed method.

Robust sliding-mode observer for unbounded state nonlinear systems

Designing a full-state observer for nonlinear systems has always been accompanied by challenges and restrictive constraints. Mainly, applying a state observer in nonlinear systems with non-minimum phase characteristics is more challenging when the limiting constraints are not satisfied due to diverging internal dynamics. In this paper, a robust sliding-mode observer approach has been successfully employed to estimate the states of nonlinear systems with unbounded and diverging dynamics. The design principles of this observer are based on applying a classifying algorithm in single-input single-output and multiple-input multiple-output nonlinear systems. It is noteworthy that this observer is highly robust against disturbance, uncertainty and measurement noise, and its conditions are less conservative compared to previous nonlinear sliding-mode observers. One novel feature of the proposed observer is that while the system's state gets unbounded and diverged in fault-occurring scenarios or critical circumstances, this observer retains accuracy. The efficiency of the proposed observer is verified in the simulation results for two nonlinear industrial systems, including a hydro-turbine power generation plant and a continuous stirred tank reactor.

Adaptive Feedback Control of Nonminimum Phase Boost Converter with Constant Power Load

The inherent negative impedance characteristics of a Constant Power Load (CPL) pose a potential threat to the stability of the bus voltage in a DC microgrid consisting of a symmetrical parallel boost converter. We suggest an adaptive feedback control technique using the input–output exact feedback linearization theory for a boost converter integrated into a DC microgrid to improve the stability of the DC bus voltage. This approach involves a transformation of the model into a Brunovsky canonical form, effectively addressing the nonlinear challenges arising from the CPL and the nonminimum phase characteristics of the boost converter. Subsequently, guided by the Lyapunov approach, an adaptation law is established to fine-tune the controller’s gain vector, facilitating the tracking of a predefined linearizing feedback control. We methodically create a method to choose the gains of the adaptive controller in order to guarantee an adequate output response. We validate our suggested controller’s performance using simulation.

Tracking and Disturbance Suppression of the Radio Telescope Servo System Based on the Equivalent-Input-Disturbance Approach

This paper presents a composite control algorithm for the radio telescope servo control system to address the target tracking and matched/mismatched disturbance suppression problems. The algorithm consists of the equivalent-input-disturbance (EID) approach and the optimal control method. An EID estimator is developed using the difference between the estimated output of the state observer and the measurement output and then the estimate of the EID is fed forward into the control input to reject the disturbance. A cost function with clear physical meaning is selected and the weighting parameters are adjusted for the optimal controller to improve tracking performance. Considering the nonminimum phase characteristics of the radio telescope system, the state observer gain is computed using the linear matrix inequality (LMI) method. The system stability is analyzed using the small gain theorem, and the linear quadratic regulator (LQR) control method is utilized to determine the state feedback gain. Finally, the composite controller is designed for an identified telescope model. Simulation results show that for the tracking performance, the settling time of proposed method is 1.13 s and reduces by about 0.32 s and 0.87 s than that of the ADRC controller and PI controller, respectively. For the antidisturbance performance, the RMS value and the maximum error of the proposed method are 0.0039 and 0.0128, which are 42.86% and 40.38% of the ADRC controller and 30.71% and 27.77% of the PI controller, respectively, which indicates that the proposed method has better control performance. In addition, the proposed controller has certain robustness to systematic parameter perturbations.

Analysis of the non-minimum phase characteristics of the VSC system in a weak grid

Analysis of the non-minimum phase characteristics of the VSC system in a weak grid

High-Precision Tip Tracking of a Flexible Link Manipulator Using Two-Time Scale Adaptive Robust Control

A flexible link manipulator (FLM) has advantages of greater payload-to-manipulator-weight ratio, safer operation, and lower energy consumption compared with the rigid manipulator, which has promising demands in various industrial and aerospace applications. However, the internal dynamics of the system is easy to be unstable due to its nonminimum phase characteristics, and there exists severe parametric uncertainties and uncertain nonlinearities in its dynamics, which has brought many difficulties in the precise tip tracking control and effective vibration suppression. In this article, the entire mathematical model of the FLM is established with assumed mode method and actuator dynamics. Then, the system is decomposed into a slow subsystem and a fast subsystem through introducing an adjustable time-scale factor according to a new output redefined dynamics with uncertainties from truncated vibration modes and unknown disturbances of system. A two-time scale adaptive robust control (TTSARC) scheme, which consists of an adaptive robust control for the slow subsystem and a state feedback control for the fast subsystem, is proposed to effectively handle parametric uncertainties and uncertain nonlinearities as well as improve behavior of internal dynamics. Moreover, the clear connection of achievable performances and control parameters based on the stability analysis of the entire system is addressed. The experimental results indicate that precise tip tracking with small link deflection for the FLM working on different conditions can be achieved with the proposed TTSARC.

New Insights on Robust Control of Tilting Trains with Combined Uncertainty and Performance Constraints

A rigorous study on optimized robust control is presented for non-preview (nulling-type) high-speed tilting rail vehicles. The scheme utilizes sensors on the vehicle’s body, contrary to that of preview tilt (which uses prior rail track information). Tilt with preview is the industrial norm nowadays but is a complex scheme (both in terms of inter-vehicle signal connections and when it comes to straightforward fault detection). Non-preview tilt is simple (as it essentially involves an SISO control structure) and more effective in terms of (the localization of) failure detection. However, the non-preview tilt scheme suffers from performance limitations due to non-minimum-phase zeros in the design model (due to the compound effect of the suspension dynamic interaction and sensor combination used for feedback control) and presents a challenging control design problem. We proposed an optimized robust control design offering a highly improved non-preview tilt performance via a twofold model representation, i.e., (i) using the non-minimum phase design model and (ii) proposing a factorized design model version with the non-minimum phase characteristics treated as uncertainty. The impact of the designed controllers on tilt performance deterministic (curving acceleration response) and stochastic (ride quality) trade-off was methodically investigated. Nonlinear optimization was employed to facilitate fine weight selection given the importance of the ride quality as a bounded constraint in the design process.

PIDD2 Control of Large Wind Turbines’ Pitch Angle

The pitch control system has a profound impact on the development of wind energy, and yet a delay or non-minimum phase can weaken its performance. Thus, there is a strong incentive to enhance pitch control technology in order to counteract the negative effects of unidentified delays and non-minimum phase characteristics. To reduce the complexity of the parameter-tuning process and improve the performance of the system, in this paper, we propose a novel control method for wind turbine pitch angle with time delays. Specifically, the proposed control method is state-space PIDD2, which is based on internal model control (IMC) and the open-loop system step response. Then, considering the tracking, disturbance rejection and measurement noise, the proposed controller is verified through simulations. The simulation results demonstrate that the state-space PIDD2 (SS-PIDD2) can provide a trade-off between robustness, time domain performance and measurement noise attenuation and effectively improve pitch control performance in contrast to series PID and PI control methods.

A Multiobjective Feedback Linearization Control of a Cuk Converter

Cuk converter is one of the most common power electronic converters, but its controller design has always been a challenging problem due to its fourth-order nonlinear and nonminimum phase characteristics. In order to solve this problem, this paper proposes a multi-objective feedback linearization control method, which selecting the variables of interest to rebuild the output function to linearize the nonlinear system into a combination of a linear subsystem and a nonlinear subsystem. According to the structural characteristics of these two subsystems, the linear optimal control theory is adopted for the control design of the linear subsystem to make the original nonlinear system have a good output performance, while for the nonlinear subsystem, the coefficient of the output function is adjusted to ensure the stability of the original nonlinear system. The results of simulation and experiment show the feasibility and superiority of using the multi- objective feedback linearization control method to design the nonlinear control law of the Cuk converter.

Comparison of FCS-MPC Strategies in a Grid-Connected Single-Phase Quasi-Z Source Inverter

This paper compares two finite-control-set model predictive control (FCS-MPC) strategies in the context of a grid-connected single-phase quasi-Z source inverter (SP-qZSI). Both schemes use discrete-time models of the inductor current and capacitor voltage for the DC side, as well as the output current on the AC side. To enhance the converter’s performance, given the non-minimum phase characteristics of the DC side, a long prediction horizon is implemented for the predictive control. However, a horizon of this nature can be highly demanding in terms of processing load, rendering it inapplicable for some microcontrollers. To address this issue and mitigate the processing load, an alternative control strategy is presented that divides the total number of candidate solutions to be evaluated into smaller segments. The performance of the two control strategies is compared using total harmonic distortion (THD) and simulation times as evaluation metrics. The results indicate that the proposed strategy achieves significantly shorter simulation times than the compared control strategy when increasing the prediction horizon. Additionally, a reduction in the THD was observed in the proposed strategy, reaching an average of 2.8%, which is lower than the compared strategy that exhibited THD close to 3.5%.

Model Predictive Control of DC–DC Boost Converter Based on Generalized Proportional Integral Observer

Due to the nonminimum phase characteristics and nonlinearity of boost converters, the control design is always a challenging issue. A novel model predictive control strategy is proposed for the boost converter in this work. First, the Super-Twisting algorithm is applied to current control, and the input–output plant for voltage control is derived based on the linearization technique. All the model uncertainties are defined as lumped disturbances, and a generalized proportional integral observer is designed to estimate the lumped disturbance. Second, a composite predictive approach is developed on the basis of the predictive model and disturbance estimations. By solving the cost function directly, the optimal control law is derived explicitly. Lastly, the effectiveness of the proposed control strategy is verified by both simulation and experimental results.

Centralised fractional order LQI controller design for quadruple tank process — An optimisation approach

In this paper, a centralised Fractional Order Linear Quadratic Integral (FOLQI) controller is proposed for highly interacting Multi Input Multi Output (MIMO) system to reject the load disturbance conditions. An optimisation problem to minimise the control effort as an objective function is formulated in addition to meet the desired time domain inequality constraints. The parameters of the FOLQI controller are obtained by using sequential quadratic programming optimisation approach. For illustration, the quadruple tank process is considered as a case study which exhibits both minimum and non-minimum phase characteristics. To show the performance of the FOLQI controller, the simulation is performed under disturbance and parameter uncertainty conditions. The performance indices such as maximum peak overshoot, settling time and steady state error are computed for FOLQI controller. To show the superiority of FOLQI controller, these indices are compared with the responses obtained using the existing Integer Order Linear Quadratic Integral (IOLQI) and Linear Active Disturbance Rejection (LADR) controllers.

Application of Bispectrum Dimensionality Reduction Method in Ultrasonic Echo Signal Processing

Processing ultrasonic echo signals to obtain high-precision residual thickness information of the pipeline wall is the key to nondestructive testing of corrosion of a long-distance pipeline. The traditional power spectrum estimation method assumes that an analyzed echo signal is Gaussian, and the useful information is insufficiently extracted, which leads to errors in the processing results. In this paper, to solve this problem, the bispectrum, which requires the least amount of computation in higher-order spectral estimation, is proposed to process an echo signal with a non-minimum phase and non-Gaussian characteristics. The bispectrum is projected onto a one-dimensional frequency space using the dimensionality reduction method, and one-dimensional diagonal slices of the bispectrum are extracted to analyze the characteristics of the echo signal, which significantly improves the intuitiveness of data processing. The experimental results show that the bispectrum dimensionality reduction method has high accuracy in processing ultrasonic echo signals, and the relative error of the residua wall thickness is below 2%. A C-scan image displaying the shape, size, depth, and other characteristics of pipeline corrosion obtained by the proposed method is much better than that using the traditional power spectrum estimation method. Therefore, the proposed method is suitable for nondestructive testing of corrosion of long-distance pipelines.

Study on IMC-PID Control of Once-Through Steam Generator for Small Fast Reactor

The simplification of simulation inevitably leads to model mismatch. In this paper, a once-through steam generator (OTSG) for a small lead bismuth fast reactor (SLBFR) is established and verified, and the OTSG model is simplified by three different methods. Based on the simplified OTSG model, IMC and IMC-PID controllers are designed to verify the sensitivity of the controller to model mismatch. The results show that the sensitivity of the controller to model mismatch is related to the filter parameters. With the increase in λ, the IMC-PID controller becomes insensitive to model mismatch caused by model linearization, non-minimum phase characteristics, noise and time delay. However, the adaptability to model mismatch sacrifices the sensitivity of the system. When λ is too large, the inertia of the controller is too large, resulting in the deterioration of the fast power regulation. Through the research of this paper, the time domain response approximation method is recommended for OTSG model simplification, and λ is recommended to be between 5 and 10 for feedwater IMC-PID controller.

A Magnetically Coupled-Inductor Boost Converter with High Bandwidth and Fast Dynamic Response

Transient modeling analysis of the traditional DC/DC converters shows their worse effect of nonminimum-phase characteristics due to right-half-plane (RHP) zero existence in their plant transfer function. This RHP zero restricts the bandwidth of the switching converters and, that is the main reason for slower response. The motivation of this paper is to present a new technique for eliminating the RHP zero from the dynamics of a conventional boost converter that can solve the problems associated with the nonminimum phase converters and, to focus on its analysis, design and modeling to achieve a high voltage gain as well as the RHP zero cancellation. The proposed technique uses a transformer combined with switching capacitor cells. The striking feature of the suggested topology is its minimum-phase structure, further enhancement of the voltage gain, switching stress reduction, achievement of an improved frequency response and easiness for the design of a closed-loop control scheme to perform the voltage trajectory tracking task. First, the operation of the proposed converter is identified and then, the corresponding circuit performance is evaluated. By using a suitable design, the control-to-output-voltage transfer function is completely free from the RHP zero. The significant advantages of the proposed converter are established via comparisons. To confirm the design approach and theoretical findings, the simulations are introduced and, numerical experimental results such as Bode diagrams are presented.

An Active Disturbance Rejection Control of Large Wind Turbine Pitch Angle Based on Extremum-Seeking Algorithm

This paper proposes the analysis and design of the linear active disturbance rejection controller (LADRC) for the pitch angle model of a large wind turbine generator (WTG). Since the transfer function of the pitch control system exhibits nonminimum-phase characteristics, the parameters of LADRC are difficult to tune using the conventional bandwidth method. On the basis of PI controller parameters to first-order LADRC parameters, an optimization problem is proposed in this paper to find the parameters of an LADRC for the pitch control system under the constraint of robustness measure, and the extremum-seeking (ES) algorithm is used to solve the problem. Simulation results show that LADRC can achieve better tracking and disturbance rejection performance than traditional PI control without loss of robustness against time delay.

Unified Closed-Loop Control and Parameters Design of Buck–Boost Current-Fed Isolated DC–DC Converter With Constant Power Load

The bidirectional buck–boost current-fed isolated dc–dc converter suffers from the instability when feeding the constant power load (CPL). The mathematical models of buck and boost subsystems of the converter with CPL are derived. It is proven that CPL leads to the instability of the both subsystems and the system cannot be stabilized by the single output voltage closed-loop control. The active damping method is introduced to ensure the closed-loop stability of the converter. An optimal design method of the active damping feedforward coefficient is proposed to keep the open-loop stability of the two subsystems and ensure a good dynamic response. An input voltage feedforward is used to overcome the influence of nonminimum-phase characteristics between dynamic response and the stability of the boost mode. The unified design method of the closed-loop controller parameters based on Hurwitz criterion and frequency response is proposed to keep the closed-loop stability of the two subsystems. The correctness and feasibility of the parameter design method are verified by detailed experimental results.

Novel Passive Controller Design for Enhancing Boost Converter Stability in DC Microgrid Applications

Boost converters have nonminimum phase (NMP) characteristics, which makes the stable closed-loop control design difficult. Based on the passive theory, this article proposes to add a feedforward loop in the conventional double-loop closed loop to compensate for the NMP effect. Therefore, the potential instability caused by NMP can be avoided. Such compensation is especially useful for dc microgrid applications where boost converters are widely used as interface converters. Two types of feedforward gain are discussed and compared. The gain of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> with a high-pass filter is used eventually for integrating with conventional droop control because it does not change the low-frequency quiescent operation point. The stability of the proposed controller is analyzed through loop gain on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula> plane. Besides, how the output impedance of the converter is shaped by the passive controller is analyzed. The experimental results validate the effectiveness of the proposed passive controller.

A Multi-Index Feedback Linearization Control for a Buck-Boost Converter

Due to the nonlinear and nonminimum phase characteristics of the buck-boost converter, the design of its controller has always been a challenging problem. In this paper, a multi-index feedback linearization control strategy is proposed to design the controller of the buck-boost converter. Firstly, by constructing an appropriate output function, the original nonlinear system is mapped into a combination of a linear subsystem and a nonlinear subsystem. Then, according to the structural characteristics of these two subsystems, the linear optimal control theory is adopted for the control design of the linear subsystem to make it have a good output performance, while for the nonlinear subsystem, the coefficient of the output function is adjusted to ensure its stability. Finally, based on the Hartman–Grobman theorem, the internal mechanism and coefficient adjustment basis of the proposed method are revealed; that is, by adjusting the coefficient of the output function and the feedback coefficient of the linear control law, the poles of the system are configured to achieve the purpose of adjusting the static and dynamic performance of the system. The simulation results show the feasibility and superiority of using the multi-index feedback linearization control strategy to design the nonlinear control law of the buck-boost converter.

Modified preactuation tracking control for LPV systems with application to boost converters

Boost converters are usually employed as constant or discrete variable voltage sources. They are expected as a continuously variable voltage source for electric drives (based on pulse-amplitude modulation control), or for reduction of the size of energy buffer components for mass motor drives. When changing the output voltage of boost converters according to the duty ratio, the nonlinear and nonminimum phase characteristics of boost converters cause undershoots. This study was devoted to extending the technique known as preactuated multirate feedforward (PMF), which can effectively compensate for the effects caused by nonminimum phase characteristics in boost converters. PMF was originally considered for linear time-invariant systems. In this study, the technique was extended to linear parameter-varying systems by the interpolation method. Simulation and experimental results verified the effectiveness of the proposed approach.