Closed-loop Poles Research Articles

Discrete Laguerre-based model predictive control for dynamic consensus of a vehicle platoon with time delay

Dynamic consensus of linear time-invariant multi-agent systems (MASs) using distributed model predictive control under the influence of input delay is addressed in this technical note. Model predictive control (MPC) is well suited to solve the consensus problem with its ability to handle multivariable systems and constraints. However, the increased computational complexity of MPC restricts its area of applications. An attempt to bridge this gap is made by proposing a Laguerre-based MPC design to bring down the computational load and make it viable for implementation. The effect of input delay on consensus is examined and the stability margin of a MAS with input delay is computed using the location of the closed-loop poles. A comparison of the proposed algorithm with conventional MPC establishes its superiority in convergence time, robustness to input delay and smoothness of the trajectories. The effectiveness of the proposed design is validated through the simulation of dynamic consensus on the benchmark problem of platoon configuration of vehicles. Abbreviations DLQR: discrete linear quadratic regulator; DMPC: distributed model predictive control; LMI: linear matrix inequality; LTI: linear time invariant; SISO: single-input single-output; MAS: multi-agent system; MIMO: multi-input multi-output; MPC: model predictive control

Design of gain-scheduling cascade control for a motion compensated gripper frame

The offshore wind market is growing, resulting in larger wind turbines being installed farther away from the coast and into deeper waters. This trend brings challenges to an industry strongly depending on the use of jack-up vessels. A floating vessel equipped with a Dynamic Positioning (DP) system and a Motion Compensated Gripper Frame (MCGF) provides a more efficient solution to guide XXL monopoles during the installation phase. According to strict regulations, the offset angle of monopiles shall not be over 0.25°. To ensure this, a robust control method is required to deal with gradual change in soil stifness, wave induced motions and sensor delays. The control force exerted by the gripper frame can significantly affect the floating vessel dynamics, hence, this should be optimized.Therefore, the research goal is to analyse the system and design a robustly stable control for the MCGF. In the context of this research, cascade PID control with gain-scheduling is chosen, which is able to control the Gripper Frame during all installation steps for different soil stiffness and to reject wave disturbances.With the use of the lumped multiplicative uncertainty structure, the changing and uncertain soil-characteristics are modelled. The sensor delay to measure the monopile inclination, has a significant impact on system stability. Robust stability criteria are validated using the Nyquist criterion and by analysing the system’s closed-loop poles. With the use of gain-scheduling it is possible to switch control settings during the installation. Time-domain results show that with this design approach the installation criteria are met such as the maximum monopile angle and the applied control force.Ultimately, it is shown that robust PID control with gain-scheduling for a MCGF can ensure safe, efficient and cost-effective installation of the next generation wind turbines. Future research should focus into the definition and implementation of the gain-scheduling switching criteria.

Robust decentralized control of interval DC linked hybrid microgrids network

Here, a robust sparse decentralized controller (RSDC) for uncertain DC-linked hybrid microgrids is designed. The robustness against load/generation uncertainty is guaranteed using Kharitonov's stability criteria and sparsity is promoted by appending an l1 term to the typical Linear Quadratic Regulator (LQR). To improve the convergence rate, the differentiable term of the composite cost function is second order approximated, the coordinate descent technique is adopted, and the “active set” idea which limits the search to the effective regions is employed. In addition, the level of sparsity is automatically and optimally adjusted not to compromise the system's stability and robustness. The algorithm is applied to a 69-bus (consist of 7 hybrid microgrid) distribution system and the controller sparsity percentage, design convergence rate, and performances are compared with the H2 and H∞ designs. The results indicate that the proposed method is superior to the others in all aspects, which are presented by the numerical indices, the time-domain transient responses, and the closed-loop poles map.

Performance Analysis of an Electromagnetic Frequency Regulator under Parametric Variations for Wind System Applications

The electromagnetic frequency regulator (EFR) device has proven to be an attractive solution for driving grid-connected electrical generators in distributed generation (DG) systems based on renewable energy sources (RES). However, the dynamic characteristic of the EFR has not yet been discussed for cases where its parameters vary from the nominal values. To evaluate this issue, this paper proposes a method for transient and steady-state performance analysis applied to the EFR device considering parametric variations. To perform this analysis, a dynamic model of the EFR device is derived, and its dynamic characteristics are discussed. Based on this model, the system’s controller gains are designed by using the root-locus method (RLM) to obtain the desired dynamic performance. Then, a sensitivity analysis of the closed-loop poles under the effect of parameters variation is performed. In addition, the paper also presents an analysis of the EFR-based system operating with the designed controllers. The proposed theoretical analysis is assessed using simulation and experimental results. The simulation program was developed using a Matlab/Simulink platform, while the experimental results were obtained through a laboratory setup emulating the EFR-based system.

Study on Angular Free Vibration Stability and Parameters Influence of Dry Gas Seal Based on the Characteristic Equation

Based on Laplace transform and Hurwitz stability criterion, the system characteristic equation and algebraic stability criterion of the two degree-of-freedom angular free vibration of dry gas seal are derived. The effects of rotational inertia, stiffness and damping parameters on the angular free vibration stability of dry gas seal are analyzed by using the root locus method and the concept of the closed-loop dominant pole. The results show that the constraint condition of rotational inertia is the most demanding of all stability conditions. Both the angular main damping and main stiffness are not simply the larger the better, but there are preferred values in the interval greater than the stability threshold. The approach of the absolute value of the cross coefficient to zero is beneficial to the suppression of angular free vibration. There is a threshold of rotational inertia, which makes the cross stiffness change from having only the lower limit value to both the upper and lower critical values at the same time.

Improved high order differential feedback control of quadrotor UAV based on improved extended state observer

Quadrotor unmanned aerial vehicle (QUAV) system is nonlinear, strongly coupled, and sensitive to unknown disturbances and uncertainties. The uncertainty, disturbance, and even unknown model function are the undesired force acting on the QUAV, so they must be totally estimated online. The ideal control scheme is that the total estimation is feedback in the opposite direction to the controller to compensate the model error or counteract the force caused by the unknown model and disturbance. An improved extended state observer (IESO), also called an improved high-order differentiator (IHOD), is designed to estimate the unknown model and disturbance of the QUAV. It is proved that the IESO is one type higher than the traditional ESO. Consequently, the estimation accuracy of IESO is higher than that of the ESO at the same bandwidth, and is verified through some typical functions. The IESO estimations for 2nd-order derivative of reference input and the total unknown model function are fed back to compensate the undesired force in opposite direction, and then an improved high-order differential feedback controller (IHODFC) is designed with the assigned closed-loop poles. The proof of the stability of the closed-loop system controlled by the IHODFC is given. The performance is verified by the tests using the Pixhawk-based DJI F450 frame experimental verification platform. The IHODFC superiority is demonstrated by comparing the classic model-free controller PID and active disturbance rejection control (ADRC).

A new digital resonant current controller for AC power converters based on the advanced Z-transform

In this paper, we present a new digital resonant current controller that can be applied in single-phase and three-phase alternating current (AC) power converters, based on voltage source inverters (VSI) with pulse width modulation (PWM). Since power converters based on PWM introduce fractional time delays regarding the sampling period (Ts), because of the current sampling and PWM command updating techniques that are employed, there is a need to develop analytical tools for precise modelling of these types of delays. To achieve this, the advanced Z-transform is applied in order to model the AC controllers in VSIs with PWM for the general case of a fractional time delay, including power converters with current sampling within a PWM period at any chosen time instance. This new approach to power converter modelling and current sampling allowed us to develop a modified resonant AC current controller for a VSI with RL load, based on the pole-placement parameter tuning method. It includes fractional time delays, which are conventionally employed in the power converter design, in the controller parameter derivations, and introduces the minimal order resonant controller that enables strict placement of all closed-loop control system poles. Simulations and experimental tests are carried out to show the improvements introduced by novel solution in this paper compared with conventional resonant current controllers. In the analysis of dynamic performance and robustness, in this paper conventional indices are applied to compare the proposed controller with a conventional design.

Mixed H2/H∞ Optimal Voltage Control Design for Smart Transformer Low-Voltage Inverter

The smart transformer has been widely applied for the integration of renewables and loads. For the smart transformer application, the voltage control of low-voltage inverter is important for feeding the load. In this paper, a multi-objective optimization control design approach which comprehensively considers all aspects of indexes, such as linear quadratic (LQ) index, H∞ norm, and closed-loop poles placement, is proposed based on the linear matrix inequality (LMI) solution. The proposed approach is able to alleviate the weight of the designer from the tedious design process of the multiple resonant controllers and the selection of the weighting matrix for the LQ control. Besides that, some excellent performances such as fast recovering time, low total harmonic distortion (THD) and high robustness are achieved by the proposed approach. The THD are 0.5% and 1.7% for linear and non-linear loads, respectively. The voltage drop for linear load step is reduced to 10 V. The proposed approach is applied to a 5 kVA three-phase inverter to yield an optimal control law. Results from the simulation and experiment presented herein will illustrate and validate the proposed approach.

Parametric Robust Generalized Minimum Variance Control

This work presents a hybridization of the Generalized Minimum Variance control (GMVC) with Parametric Robust Control (RPC) for Linear Time Invariant (LTI) Uncertain Systems. A linear parametric uncertainties model is used to describe the system dynamic behavior. The controller synthesis is based on PID controller with a low-pass filter and formulated as a convex optimization problem which takes in account the desired closed-loop performance and the uncertainties on the model parameters. Then, the robust controller parameters, that represent the best solution for the all possible models and assign the closed-loop poles within the desired region in the s-plane, are transferred to GMVC by Tustin’s method, resulting in a parametric robust generalized minimum variance (PRGMV) controller, which was compared to two other approaches, carrying out several simulation essays in Matlab environment. In order to emphasize its performances and its efficiency, the performance index and sensitivity analysis were assessed. The results confirmed that the proposed controller ensures better robustness and performance for reference tracking and disturbance rejection.

A Generalized Analytical Tuning Approach for Model Predictive Controlled Grid-Tied Converters Under Wide Range of Grid Inductance Variation

In medium-high power applications, the LCL is the preferred filter topology to attain efficient power conversion. The filter provides a high damping attenuation of -60 dB/decade above the resonance frequency at the cost of a higher order plant, complex parameter design, and, increased vulnerability to un-modeled disturbances. Recently, model predictive control applied to power electronic converters has experienced great interest from researchers. The technique is tailored to the control of complex MIMO systems such as the LCL filter as it allows simultaneous regulation of several state-variables via a user defined cost function. However, the tuning of weighting factors (WFs) within the cost function is not trivial, and in most cases employs an empirical procedure. This paper presents an analytical procedure for tuning of WFs for indirect model predictive current controlled grid-tied converters. The method is based on using analytical closed-form expressions, that relate closed-loop poles of the filter with WFs via physical plant parameters. The presented expressions generalize the tuning of WFs to any arbitrary LCL design. The proposed method is validated by hardware-in-the-loop simulations conducted on PLECS RTBOX 3. Through experimental testing, it is shown that the controller is robust against a wide range of grid impedance variation.

Stability Assessment of A Radial Grid With Power Converters

The increase proportion of power converters causes stability problems in the radial grid. To address these issues, this paper firstly proposes a unified modeling procedure and applies it to two types of converters. Secondly, the impedance models are used to analyze the stability of a radial grid with converters under four cases. The influence of the short circuit ratio (SCR) and line impedance on system stability are investigated. Then, a comprehensive sensitivity analysis is performed in order to investigate the effects of parameters variations on the closed-loop poles of the system under different conditions. Finally, the accuracy of the model and theoretical analysis are verified by simulations and Hardware-in-the-Loop (HiL) tests.

Pole-zero analysis of a model-free and a model-based tuning strategy for Maglev system

This paper presents a different insight into stability analysis not only on the basis of steady state behaviour of the output response, but also the transient state behaviour caused due to the re-distribution of the poles and zeroes of the system and the controller in the closed loop configuration by the chosen tuning technique. This work establishes a correlation between theoretical analysis and experimental response by pole-zero analysis and the impact of tuning techniques of a PID controller on Maglev system, thus helping in better understanding of the designing and fabrication of the controller. The effectiveness of two popular industrial tuning techniques, one model-free and one model-based tuning strategy, has been analysed on the basis shifting of the root locus due to the placement of the closed-loop poles and zeroes, and the proximity of actual and desired dominant poles for this highly sensitive system.

Cooperative tracking control of single-integrator multi-agent systems with multiple leaders

In this paper, the cooperative tracking control of single-integrator multi-agent systems is investigated. The networked agents are partitioned into two groups, leaders and followers. Only the former have access to the state of an autonomous exogenous system and their role is to inject the control inputs into the network such that the followers track the predefined setpoint trajectories. The followers are controlled through local interaction rules based on the relative measurements from their neighbors. A novel distributed observer-based control strategy that solves the tracking control problem is proposed. Simple rules are provided for determining the controller and observer parameters which guarantee that the closed-loop system poles lie in the specified region. The effectiveness of the proposed approach is verified through numerical examples.

축소 차수 모델 기반 제어기와 결합한 PI 관측기 기반 제어 시스템의 안정성 해석

System model order reduction is a popular technique employed by control systems engineers due to its ability to reduce model complexity. However, control systems designed based on reduced-order model may cause closed-loop system instability when applied to the full-order model. In addition, conventional control system improvement methods such as increasing the controller gains or using robust control techniques in particular disturbance observers can further deteriorate system performance. In order to shade light on this phenomena, this paper presents an analytical study of the effects of high observer gain on the stability of observer compensated control systems whereby both the controller and the observer are designed using the reduced-order system model. The analysis is performed by carrying out stability analysis of the closed-loop system through root locus method and Routh-Hurwitz stability criterion. The paper also presents a comparative analysis between placing all the closed-loop poles of the controller at a single location or multiple locations using LQR technique for the aforementioned class of controller. The results obtained from the analysis have been validated through a DC motor position control system application.

On the Robust Multiple Objective Control with Simultaneous Pole Placement in LMI Regions

This article studies the problem of designing robust control laws to achieve multiple performance objectives for linear uncertain systems. Specifically, in this study we have selected one of the control objectives to be a closed-loop pole placement in specific regions of the left-half complex plane. As such, a guaranteed cost-based multi-objective control approach is proposed and compared with the H_2/H_∞ control by means of an application example.

Tracking Control of an Electro-Hydraulic Actuator System using LQR Controller

Electro-Hydraulic actuator (EHA) is a one type of application used in industry and building high performance of motion control process. Apparently, dealing with EHA behaviour is quite difficult and make the controlling process complicated. Designing Linear Quadratic Regulator (LQR) controller as a feedback controller require in selecting the weighting parameter Q and R. The result shows that the higher value of Q offers fast response and high stability by referring the placement of close-loop poles. However, the higher value of Q gives a higher error that can make position performance of hydraulic actuator become worst. In order to overcome this problem, the feedforward controller is developed by implementing the zero-phase error tracking control (ZPETC). It shows that both feedforward and feedback controller offers good tracking position performance in reducing gain and phase error.

Modeling and stability analysis of grid-tied VSC considering the impact of voltage feed-forward

The single-input and single-output (SISO) transfer functions are proposed in this paper to analyze the impact of voltage feed-forward (VFF) loop on the stability of grid-tied voltage-source converter (VSC). Based on the SISO transfer functions, the VFF’s impacts are analyzed by considering the influence of current control integral time constant (ITC) and the grid impedance ratio X/R. To be specific, the VFF can improve the stability when the VSC has a large ITC, while it can decrease the stability when the VSC has a small ITC. The impedance ratio X/R is another affecting factor to the VFF when the phase-locked loop (PLL) dynamics are included in the transfer function model. The closed-loop poles of the VSC without the VFF loop are sensitive to the decrease of X/R, while it is not very susceptible to the variation of X/R when the VFF loop is applied in VSC. The proposed SISO transfer functions and stability analysis are both verified through simulations.

LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of 𝒟 R -regions

This paper introduces an approach for the design of a state-feedback controller that achieves pole clustering in a union of -regions for linear parameter varying systems. The design conditions, obtained using a partial pole placement theorem, are eventually expressed in terms of linear matrix inequalities. In addition, it is shown that the approach can be modified in a shifting sense. Hence, the controller gain is computed such that different values of the varying parameters imply different regions of the complex plane where the closed-loop poles are situated. This approach enables the online modification of the closed-loop performance. The effectiveness of the proposed method is demonstrated by means of simulations.

Output Admittance Synthesizer for Synchronverters

This article proposes an “output admittance synthesizer” (OAS), a feedback block that enables the synchronverter (SV) to have specific values of output admittance (modulus and phase), at specified harmonic frequencies (and sequences) of the fundamental frequency of the grid voltage (including <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 1). The sequence discrimination enables the SV to have two different admittances at each frequency: A positive sequence and a negative sequence admittance. This feature is of interest for both treating harmonics and imbalance of the voltage at the point of common coupling. Additionally, using the OAS allows to place the closed loop poles of the resulting feedback system at arbitrary locations.

Modeling and Phase Synchronization Control of High-Power Wireless Power Transfer System Supplied By Modular Parallel Multi-Inverters

Modular parallel multi-inverters (MPMIs) with master-slave phase synchronization control is proposed for high-power wireless power transfer (WPT) where the MPMI output voltage phase is synchronized to suppress current circulation by compensating for the time delay of the slave inverters caused by signal propagation delay. Different power levels can be conveniently satisfied by flexibly adjusting the number of MPMIs. A modeling method based on the energy-amplitude and phase is developed and linearized to get the slowly changing phase variable and to analyze the system dynamic characteristics at its operating point. To achieve the required dynamic performance of the proposed model, the parameters of a PI controller are obtained by calculating the required settling time and overshoot of the closed-loop dominant poles. A 20.07 kW WPT prototype supplied by three MPMIs with an efficiency of 92.17% was designed and tested. Experimental results show that the proposed modeling method and controller design achieved both good performances of circulating current suppression and MPMIs output voltage phase synchronization.