Loop Shaping Controller Research Articles

Development of real-time density feedback control on MAST-U in L-mode

In this paper we report on the development and demonstration of density feedback control for MAST-U. Sinusoidal perturbations are used to measure the frequency response from a deuterium gas valve (actuator) to line-integrated core electron density measured by the interferometer (sensor). In the frequency range relevant for control design, only two system-identification experiments were needed to regress a first-order dynamic model. This control-oriented model informs the offline design of a proportional integral controller with the established loop-shaping controller design method. After offline verification of the controller implementation, control is demonstrated by experimentally tracking a staircase reference for the line-integrated electron density. This paper demonstrates the efficiency of controller design using system-identification and loop-shaping, providing reliable density control for MAST-U.

Implementation Methods of Controllers Designed by $H_\infty$ Loop Shaping

When the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> loop-shaping controller is implemented as a unity feedback system, its step responses are sometimes unsuitable for tracking control, typically, displaying large overshoots. In this paper, the implementation method is studied for tracking control with small overshoots. Three implementation methods that are described by a unity feedback system, a previous simple two-degrees-of-freedom(2DoF) system, and a new simple 2DoF system proposed in this paper are examined. For the closed-loop transfer function of each system, the unstable zeros are analyzed and an upper bound of the peak gains is presented. These results show that the two simple 2DoF systems have adequate properties for tracking control with small overshoots. The new 2DoF system has good features that the system is minimum phase if the plant is minimum phase, and that the resonance peak gain is one. Their tracking performances are compared in several numerical examples.

Reliable current control for single‐phase pulse width modulation rectifiers based on H∞ loop shaping controller

AbstractIn this study, H∞ loop shaping is designed for single‐phase pulse width modulation (PWM) rectifier under current sensor gain faults. Pre‐compensator is used to obtain the desired loop shape at all frequencies and robust stabilization through the normalized coprime factorization. The mathematical model for the rectifier is developed to obtain the nominal plant transfer function, and two algebraic Riccati equations are used to solve the designed controller and obtain the loop shaping controller by combining the designed controller with the weights. ν‐gap metric is adopted to measure the magnitude of the current sensor gain fault that can be stabilized by the controller. The proposed controller is compared with H∞‐mixed sensitivity (H∞‐MS) controller. The robustness capability and dynamic performance is investigated and, hardware‐in‐loop experimental results show excellent balance between robustness and performance in the presence of current sensor gain faults.

H‐infinity loop shaping control of wireless power transfer system based on generalized state space averaging model

SummaryThe transmission distance and the output load of wireless power transfer (WPT) system are particularly prone to change, which results in higher requirements for the robustness and dynamic performance of the control. In order to reduce the influence of these characteristics, an H∞ loop shaping controller based on generalized state space averaging (GSSA) method is proposed in this paper. Based on the GSSA model, an appropriate compensation function is constructed for the WPT system to the target loop transfer function. The nominal coprime factorization of WPT system is carried out, and on this basis, H∞ controller is achieved by Riccati equation to minimize the infinite norm from disturbance to error output. The designed controller meets the requirements of robust. Furthermore, the obtained high‐order controller is discretized by a reasonable discretization method, and the details and limitations of its practical application are discussed based on the hardware computational capacity. The experimental results show that the proposed controller has better robustness and dynamic performance and flexibility than the mixed sensitivity H∞ controller and the Z‐N PI controller.

Dynamic performance improvement of proton exchange membrane fuel cell system by robust loop shaping and artificial intelligence optimized fractional order PI controllers

ABSTRACT Due to inherent nonlinear behavior, the Proton Exchange Membrane (PEM) Fuel Cell system yields in poor power quality. The sudden change in stack current causes uncertainty in PEMFC behavior resulting in degraded output. This necessitates the control of supply manifold pressure on the cathode side to prevent oxygen starvation. In this work, three techniques, namely, robust loop shaping, smith predictor, and Fractional Order Proportional Integral (FOPI) controllers, are designed after incorporating parametric uncertainty in system description. Further, the Particle Swarm Optimization (PSO) artificial intelligence technique is implemented to optimize the parameters of smith predictor and Fractional Order PI controllers. By stabilizing the system across the entire parameterized uncertainty range, the proposed control strategies, namely, loop shaping, PSO-Smith Predictor, and PSO-FOPI controller effectively compensate uncertainty effects. The simulation result shows that the PSO-tuned FOPI controller has best overshoot at operating points 3, 4, and 5 having a value of 0.505% in comparison with PSO-Smith Predictor where overshoot (ranging from 19.88% to 40.141%) is too high; and loop shaping controller having high values of overshoot (more than 40% at every operating point) Thus, PSO-FOPI controller exhibits the best performance with far superior overshoot and steady-state stability.

Ripple Voltage Suppression of Dual Active Bridge Converter in Electric Locomotive Using H∞ Loop Shaping Control Method

The next-generation electric locomotive drive system has the problem of double grid frequency ripple voltage in the DC side of a single-phase PWM rectifier. In this paper, the intermediate stage dual-active-bridge DC-DC converter is studied, and an H∞ loop shaping ripple voltage suppression control strategy is proposed to restrain the harmonic voltage and optimize the dynamic and robust performance of the closed-loop system. Firstly, the mathematical model of the DAB closed-loop control system with fluctuating input voltage is established. Then, based on the H∞ loop shaping control theory, the dynamic performance, the ability of ripple voltage suppression, and the robust performance of the system are analyzed in the frequency domain. According to the results, a reasonable compensator is selected to reconstruct the magnitude frequency characteristic curve of the nominal system. After reconstruction, the solution of the robust stability margin of the corrected object is transformed into the H∞ robust control problem under the coprime factor uncertainty. The suboptimal H∞ robust controller is solved to obtain the best robustness boundary of the constructed system. Finally, the H∞ loop shaping ripple voltage suppression controller is obtained by combining the H∞ controller with the compensator. The experimental environment is set up in MATLAB-Simulink software. Compared with the traditional voltage loop control method and the input voltage feedforward control method, the dynamic performance of the proposed control strategy is slightly improved, and while within the allowable robust boundaries of the system, it has better ripple voltage suppression performance. When the system magnitude frequency curve is outside the tolerant robust stability margin, the ripple voltage suppression performance fails, but the harmonic content of output voltage is still far less than the other two control methods. The experiment results also prove the correctness of the theoretical analysis and that the proposed control method is effective and proper.

Performance assessment of tripping and drilling operations controllers on an experimental drilling rig prototype

Oil well drilling towers have different operating modes during a real operation, each mode involves certain external disturbances and uncertainties. Performance evaluation of robust or adaptive Cascade PID, Active Disturbance Rejection, Loop Shaping, Feedback Error Learning, and Sliding Mode torque controllers, during the tripping and drilling operations, and their practical comparison are studied and evaluated by constructing a drilling rig prototype. The modeling of the experimental setup is extracted by mathematical modeling, and system identification. The practical performance of the controllers and their stabilities against the uncertain forces including the parametric uncertainties and the external disturbances are studied during the operations, by loading and unloading a disturbance weight. It has been shown that the effects of uncertain forces are successfully eliminated by the controllers. The Loop Shaping controller has the best performance among all the designed controllers, and all of them roughly consume the same control energy. A desired speed profile is designed to shape the vertical speed reference during the tripping operation, then its effect on the system behavior is analyzed to prevent the slackening problem in the drilling cable. Also, the behavior of control architectures in two modes of autonomous drilling is studied and analyzed. By analyzing and optimizing the performance efficiency in a controlled environment, along with enhancing the performances of the controllers, what we learn in this research could presumably be applicable in the field to have an accurate and safe operation.

Linear Parameter-Varying Control of a Power-Synchronized Grid-Following Inverter

This article proposes a linear parameter-varying loop-shaping controller for a power-synchronized grid-following inverter (PSGFLI). This control strategy regulates the inverter output active and reactive powers at the terminal instead of the point of connection and does not require a phase-locked loop (PLL) for extracting the voltage phase angle. Hence, the prevalent stability issues exhibited when GFLIs are connected to weak grids are not present, and the proposed PSGFLI control strategy can work under both very weak and strong grid conditions without being prone to instability. In this approach, the controller parameters are functions of the operating point and are changed during the real-time operation such that the closed-loop performance is preserved in all operating points. Furthermore, since the grid impedance is a factor in the design process, a robustness analysis against grid impedance estimation error is conducted, and it is shown that discrepancies in the estimated and real grid impedances are unlikely to make the system unstable. The performance of the proposed control design is validated in MATLAB/PLECS and experiments for both strong and weak grids.

A Design Synthesis Method for Robust Controllers of Active Vehicle Suspensions

This paper presents a design synthesis method for robust controllers of active vehicle suspensions (AVSs). Various control techniques have been applied to the design of AVSs for enhancing ride comfort and handling performance of ground vehicles. However, most of these model-based controller designs show poor robustness when the vehicle models are not accurate and operating conditions vary. To address the poor robustness problem of AVSs, a new controller is designed using the H∞ loop-shaping control technique. The controller targets robustness issues on vehicle models with parametric uncertainties and unmodelled dynamics. To facilitate the robust controller design, a design synthesis method is proposed: the H∞ loop-shaping controller design is formulated as a multi-objective optimization problem, the weighting functions’ parameters of the controller are treated as design variables, the expensive computing loads are handled by a parallel computing technique, and the solution of the optimization problem is the desired robust AVS controller. Simulation results demonstrate the benefits of the proposed AVS design.

Implementation and Optimization of Two Degree of Freedom H∞ Loop Shaping Control for Average Current Mode Control Buck Converter using Genetic Algorithm

Implementation and Optimization of Two Degree of Freedom H∞ Loop Shaping Control for Average Current Mode Control Buck Converter using Genetic Algorithm

Turbojet Thrust Augmentation through a Variable Exhaust Nozzle with Active Disturbance Rejection Control

Turbojets require variable exhaust nozzles to fit high-demanding applications; however, few reports on nozzle control are available. The purpose of this paper is to investigate the possible advantages of an exhaust gas control through a variable exhaust nozzle. The control design method combines successful linear active disturbance rejection control (LADRC) capabilities with a loop shaping controller (LSC) to: (i) allow designing the closed-loop characteristics in terms of gain margin, phase margin and bandwidth, and (ii) increase the LSC disturbance rejection capabilities with an extended state observer. A representation of the nozzle dynamics is obtained from first principles and adapted to achieve a stream-velocity-based control loop. The results show that the resulting controller allows improving the expansion of the exhaust gas to the ambient pressure for the whole operating range of the turbojet, increasing the estimated thrust by 14.23% during the tests with experimental data.

Decoupled Multi-Loop Robust Control for a Walk-Assistance Robot Employing a Two-Wheeled Inverted Pendulum

This paper develops a decoupled multi-loop control for a two-wheeled inverted pendulum (TWIP) robot that can assist user’s with walking. The TWIP robot is equipped with two wheels driven by electrical motors. We derive the system’s transfer function and design a robust loop-shaping controller to balance the system. The simulation and experimental results show that the TWIP system can be balanced but might experience velocity drifts because its balancing point is affected by model variations and disturbances. Therefore, we propose a multi-loop control layout consisting of a velocity loop and a position loop for the TWIP robot. The velocity loop can adjust the balancing point in real-time and regulate the forward velocity, while the position loop can achieve position tracking. For walking assistance, we design a decoupled control structure that transfers the linear and rotational motions of the robot to the commands of two parallel motors. We implement the designed controllers for simulation and experiments and show that the TWIP system employing the proposed decoupled multi-loop control can provide satisfactory responses when assisting with walking.

Robust Control of Interlinking Converter Using PSO and ABC Algorithms

Objective: In this paper, an optimal control scheme for the Interlinking Converter (IC) system is achieved by the proper regulation of its gate switching functions through appropriate optimal feedback controller design. Methods: Proportional-Integral-Derivative (PID), Fractional Order Proportional-Integral-Derivative (FOPID) and H-infinity loop shaping controller have been designed for the two-fold control objective of simultaneous improvement in system robustness and reduced tracking error using parameter tuning via Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC) optimization algorithms. Results: The controller parameters are obtained by optimization algorithms. The comparative analysis of the controller performance is carried out through simulation in the MATLAB platform to validate the effectiveness of the controller design under various changing situations. Conclusion: The optimized controller parameters obtained through ABC algorithm are better than that obtained through PSO algorithm in terms of both objective function values and execution time. The resultant robust control strategy for IC system obtained through the H-infinity loop shaping controller provides reduced tracking error and improved stability as compared to PID and FOPID controller, as proved by the simulation results.

Active damping and robust loop shaping control for harmonic minimization

This paper presents an h-infinity robust loop shaping control and LCL filter to mitigate the effects of harmonic currents in the photovoltaic system integrated with the grid. To eliminate the negative effects of the LCL filter, this work applied notch filter active damping. Existing methods for the elimination of harmonic currents were reviewed. Proportional integral control, fuzzy logic control, h-infinity control, and robust loop shaping control are presented. The grid current was analyzed in the system with all controllers applied to control the voltage source inverter of the system to eliminate harmonics in the grid current caused by the inverter and nonlinear loads for two cases, one being constant loading of the linear and nonlinear load and another is the switching of the nonlinear load during the simulation. The results obtained from the proposed method for the two tests conducted were compared with those from other methods to prove the robustness of the proposed technique. The method manages to reduce the total harmonic distortion of the grid current from 7.85% to 0.79% for case 1 and from 11.67% to 1.14% for case 2.

Realizations of fractional-order PID loop-shaping controller for mechatronic applications

A novel procedure for the realization of a fractional-order PID loop-shaping controller, suitable for precision control of mechatronic systems, is introduced in this work. Exploiting appropriate tools, the controller function is approximated as a whole, leading to a simple form of integer-order approximation, when compared to the case where each intermediate part of the PID transfer function is approximated. This leads to a direct implementation, composed of conventional active and passive elements. Simulation and experimental results, derived from the OrCAD PSpice simulator and a Field-Programmable Analog Array respectively, verify the efficient functionality of the proposed implementation procedure.

Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

Lateral Parameter-Varying Modelling and Control of a UAV on-Ground

Abstract Lateral modelling and control of a UAV on-ground is one of the critical phases of its flight. In this paper, a linear parameter-varying (LPV) mathematical model is proposed for the taxi phase. First, a complete non-linear taxi model has been derived, which includes the forces generated by both the aerodynamics and the interaction of the tyres and runway. The model is explicitly dependent on forward velocity of the UAV which continuously varies during take-off and landing both. Since, a single H∞ loop shaping controller designed at a particular velocity point does not suffice the design requirements of all other velocity points, so parameter-varying H∞ loop shaping controllers are developed. It utilizes the observer plus state feedback structure of H∞ loop shaping controller. A comprehensive control law in the parametric form in which the controller and observer gain matrices are explicitly dependent on the forward velocity has been derived. This control law is successfully evaluated on a real world example of a test UAV and actual results are in good comparison with the simulation.

Stability assessment and robust controller design of grid interactive offshore wind farm and marine current farm with STATCOM and BFCL

ABSTRACT In the context of larger renewable energy harnessing, combining offshore wind farm (OWF) and marine current farm (MCF) at the same location is often found suitable in terms of geographical conditions and economic reasons. However, stochastic nature of wind speed and marine current speed with increased penetration level significantly affects the system stability, grid voltage and raises some control and stability problem; furthermore, the parametric uncertainty of generators brings additional challenges under grid voltage distortion. Therefore, in this article, we present a consolidated application of STATCOM and BFCL in the context of stability assessment of integrated system. Consequently, a robust H∞ loop-shaping controller has been proposed in the presence of parametric uncertainties. In this context, optimizing controller performance with respect to the undesired parametric uncertainties and external disturbances has been proposed. The control effort is initiated by formulating the robust H∞ loop-shaping controller in the context of evaluating the controller parameters and gain with respect to desired robust stability margin. The efficacy of the proposed control scheme is measured through different case studies in real time digital simulation (RTDS) environment. The comparative analysis of simulation results demonstrates the effectiveness of the proposed control strategy in the context of integrated system stability and reliability.

Unified Smith predictor‐based loop‐shaping H ∞ damping controller for mitigating inter‐area oscillations in power system

Low-frequency inter-area oscillation is one of the major problems to transfer the bulk power from one area to another area in an interconnected large power system. A wide-area signal-based controller is more effective to improve the damping of the inter-area oscillation than a local area signal-based controller. A wide-area measurement system makes it easier to transmit the wide-area signal through the communication system from the remote location to the controller site. However, the involvement of the unavoidable time delay in the wide-area signal transmission from a remote area to a controller site is to possess a great deal of challenge to design a damping controller. In this study, a unified Smith predictor (USP)-based loop shaping controller is designed to handle the negative effect of the delay using the wide-area signal. The robust stabilization normalised co-prime factor problem is converted into a generalised H ∞ optimisation problem for additional pole placement constraints. The performances of the USP-based loop-shaping H ∞ controller are compared with the USP-based H ∞ controller. From the obtained results, it is verified that the proposed controller gives an excellent damping performance and handles the effect of time delay.

Position control of ball and beam system using robust h∞ loop shaping controller

&lt;p&gt;Laboratory Ball and Beam prototype (B&amp;amp;B) is a system designed to implement the controlling of space application studies such as aircraft flight and land. In this paper, to control the position of the rolling ball on the beam, MATLAB program will be used to design and implement PID and robust H&lt;sub&gt;∞ &lt;/sub&gt;Loop Shaping controllers. The open loop response of the system is unstable, because the ball continuously rolling on the beam when a constant input applied. To stabilize the system, a PID controller used first to achieve the desired position. Then, robust H&lt;sub&gt;∞ &lt;/sub&gt;Loop Shaping controller was used to achieve performance requirement for system with uncertainties. Results for the step response shows that robust H&lt;sub&gt;∞ &lt;/sub&gt;Loop Shaping controller response have no over shoot, faster about 80 times when compared to step response of PID controller, it's more effective and had better performance compared to other controllers in the control of B&amp;amp;B system.&lt;/p&gt;