Loop Shaping Method Research Articles

Impact of Weight Functions on Performance of Three-Input Integrated Dc-Dc Converter in H ∞ Control

Many power electronic systems applications namely locomotives, hybrid electric vehicles, and all renewable energy sourced systems are shifting towards Multi-Input Multi-Output (MIMO) integrated DC-DC converters due to their reliability and flexible nature. Designing controllers for MIMO integrated DC-DC converter is complicated due to its integrated structure, presence of common elements, and interactions between the input and output variables of the converter. In this work, a Three-Input Integrated DC-DC (TIID) converter is modeled using state-space analysis, and a Transfer Function Matrix (TFM) is acquired from the small signal continuous time model. A robust controller based on the loop shaping method is designed for the TIID converter. In this loop-shaping method, the desired robustness and the performance of the controller are represented with weight functions i.e., loop-shaping filters. These weight functions are designed using TFM and are frequency-dependent. The robustness of the controller depends on the weight function parameters. The effect of varying the parameters of the weight functions on system dynamics, robustness, and performance are studied and plotted. TIID converter of 288 W, 24V-30V-36V to 48 V is considered and the impact of weight function on closed-loop system dynamics and sensitivity characteristics under varying parameter conditions are analyzed in MATLAB Environment.

Performance investigation and control design of SSI grid-connected system for PV applications with maximum power extraction

Split-source inverter (SSI) has been recently developed as an alternative to the commonly used ZSI where it can serve an interface between the renewable energy sources and the common grid. This paper presents a mathematical model and control strategy for grid-connected SSI system with either constant voltage source or photovoltaic (PV) source. The control strategy is based on linear PI controllers which are fine-tuned by the frequency loop shaping method with the help of the derived mathematical model to ensure the stability of the system with robust dynamic behavior. The derived mathematical model provides a straightforward and efficient understanding of the dynamics resulting from the interaction between the PV and the SSI grid-connected system. The simulation results indicate that the system has a robust dynamic behavior when subjected to various transient conditions. Finally, a downscaled prototype of SSI grid-connected system is implemented to experimentally validate both the mathematical model and control strategy.

H∞ Loop Shaping Using Polytopic Weights and Pole Assignment to Missile Autopilot

Modern missiles must deal with stringent performance requirements and ensure robustness across a wide range of operating conditions during flight time. Classic gain-scheduling designs have been successful in practice, but do not provide theoretically ensured bounds on both performance and robustness. Controllers are interpolated at intermediate operating conditions and switching them may cause instability. On the other hand, polytopic linear parameter-varying (LPV) controllers avert this switching and use real-time information about the plant, in order to smooth out the gain scheduling. We hereby propose a novel procedure to yield an output feedback LPV controller that ensures robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}_{\infty} $ </tex-math></inline-formula> performance to a missile longitudinal autopilot. Our novel approach considers the four-block loop-shaping <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}_{\infty} $ </tex-math></inline-formula> control theory with polytopic LPV weights that use polytopic coordinates of the LPV plant. One is capable of adjusting the singular values of the open-loop plant individually at the polytope vertices, and benefits from a trade-off between linear matrix inequalities (LMI) based optimization tools and the designer experience. This can be construed as a natural extension of the traditional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}_{\infty} $ </tex-math></inline-formula> loop-shaping method that uses linear time-invariant (LTI) weights. Assuming the scheduling variables are frozen, we also include LMI conditions for assigning closed-loop poles and hence circumvent controller order reduction. Nonlinear simulations assess the proposed autopilot, and results show an improved robust stability margin, in addition to an improved response to the acceleration command, concerning the LTI-based approach.

A Novel Compliant Nanopositioning Stage Driven by a Normal-Stressed Electromagnetic Actuator

This article reports on the design, modeling, control, and testing of a novel compliant nanopositioning stage driven by a self-developed normal-stressed electromagnetic actuator. To facilitate the parameter selection for the stage to achieve the desired stroke and natural frequency, an analytical model of both the electromagnetic circuit and flexure mechanism is established, which is then systematically verified through finite element analysis. By combining a proportional—integral—differential (PID)-based main controller with a system dynamics inversion-based feedforward compensator, a closed-loop control system for the stage is constructed with the main controller being tuned through Bode’s ideal transfer function-based loop-shaping method. The experimental result shows that a stroke of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\pm } 95 ~\mu \text{m}$ </tex-math></inline-formula> and a first natural frequency of 743 Hz are achieved for the designed stage. Finally, taking advantage of the constructed control system, the nanopositioning capability is demonstrated by finely tracking the harmonic and nanostair commands. Note to Practitioners—Piezoelectric actuators (PEAs) and voice coil motors (VCMs) are commonly adopted for the actuation of nanopositioning stages. In general, constrained by the inherent small strain, PEA is more suitable for the generation of dynamic motions in dozens of micrometers. Meanwhile, VCM has a theoretically infinite motion range but a slow response due to its low force density nature. Taking advantage of a newly developed normal-stressed electromagnetic actuator (NSEA), we demonstrate the design, modeling, control, and testing of an NSEA-based nanopositioning stage with a relatively long motion range, high bandwidth, and compact size. Considering the high force density and relatively large motion range only constrained by the effective air gap, the NSEA-based stage is demonstrated herein to be very promising to achieve highly dynamic motions within hundreds of micrometers.

루프 형성기법을 이용한 필터보상형 LQ-PID 제어기 설계

System control requires high-speed response performance, stability, and robustness. However, tuning controller design parameters for high-speed response performance, stability, and robustness is a challenging task. The LQ-PID controller design parameter tuning method proposed in this paper satisfies the design condition since it ensures stability and robustness, which are the advantages of LQR control and the design weighting factors Q and R are selected using the loop shaping method. Since the proposed method achieves the characteristic of avoiding the high-and the low-frequency region through the setting of the filter coefficients included in the two zero points and the differential time term of the PID controller. it satisfies the performance in the frequency domain with improved features compared to the existing LQ-PID controller design parameter tuning method.

Design of Robust Decentralized Control Systems for Distillation Columns

This paper is devoted to the development of a decentralized control system design method with improved robustness, applicable to distillation columns control problem. The aim is attained by solving the following tasks: selection of representative models of columns; development of an effective transfer function identification algorithm; development of a decentralized controller design algorithm, which takes into account the cross-links impact; verification of the developed method for the selected models of columns. The most important result is the developed design method, which includes two algorithms. The first algorithm can be used to identify simplified models of the effective transfer functions. The second algorithm makes it possible to design a decentralized control system based on the ratio between the diagonals of the original model and effective transfer functions. Modified PI controller is used. The achievement of the distillation column control system robustness to the synchronous technologically conditioned deviation of the model parameters by up to three hundred percent of the nominal value is the paper significant result. The digital implementation of the designed controllers is simple. The analysis of the literature shows that none of the previously proposed methods for designing decentralized automatic control systems solved such a problem. The efficiency of the developed algorithms is illustrated using the known models of dynamics of distillation columns. The analysis of limitations of the method as well as its significant differences to the Biggest Log Tuning and H∞ loop shaping methods is presented.

Model-free repetitive control design and implementation for dynamical galvanometer-based raster scanning

Data-driven repetitive control (RC) is proposed in this work to track online, dynamical raster trajectories in galvanometer-based scanning. To remove the requirement of a plant model in conventional model-based RC, we use model-free iterative learning control (ILC) to synthesize the data-driven repetitive controllers. Specifically, the frequency-domain plant-inversion and loop-shaping methods are both converted into time-domain trajectory tracking problems. The ILC is then applied to solve the trajectory tracking problems and subsequently derive the repetitive controllers from data. The stability conditions of both methods are analyzed and used to guide the data-driven control design. Experimental results on a commercially available galvanometer scanner demonstrate that the proposed methods improve the tracking error of a predefined raster scan by more than 30 times, as the conventional ILC does. Moreover, after applying data-driven RC, users can online assign various center positions and magnitudes of the raster trajectory. Once assigning a new reference in this continuous mode, the tracking error rapidly converges to the steady-state within ten periods.

Obtaining Robust Performance of a Current fed Voltage Source Inverter for Virtual Inertia Response in a Low Short Circuit Ratio Condition

Low inertia levels are typical in island power systems due to the relatively small rotational generation. Displacing rotational generation units with static inertia-less PV power results in a significant increase in the frequency volatility. Virtual inertia provided by inverter-storage systems can resolve this issue. However, a low short circuit ratio (SCR) at the point of common coupling together with a fast phase locked loop (PLL) will compromise the response performance of the system. To address this issue, a robust PI controller (RPI) for the inner current-loop of a current fed grid-connected inverter is proposed. The PLL disturbance and grid impedance are incorporated into a single model and recast to a generalized representation of the system, thereby allowing easy tuning of the RPI by the mixed sensitivity H∞ method. The performance of the RPI is compared with that of a PI controller (PI) tuned by the regular loop-shaping method. The results show that when the SCR is above 10, the performance of both controllers is equivalent. However, lowering of the SCR compromises the performance of the system with PI and it becomes underdamped at SCR &lt; 2. On the contrary, the system with the RPI is capable of maintaining the nominal performance throughout the same SCR decrease.

Disturbance rejection and control system design based on a high-order equivalent-input-disturbance estimator

This paper presents an improved equivalent-input-disturbance (EID) approach to deal with exogenous disturbances. A high-order filter is newly used to construct an improved EID estimator. The parameters of the filter are selected to improve the disturbance-rejection performance without changing the bandwidth of an EID-based control system. The stability and disturbance-rejection mechanism of the system are analyzed using the transfer function from the EID to the output. The high-order filter is designed using the loop-shaping method. Simulation results of a rotational control system demonstrate the validity of the approach and superiority over other methods.

Robust Stability Control for Electric Vehicles Connected to DC Distribution Systems

DC power distribution systems will play an important role in the future urban power distribution system, while the charging and discharging requirements of electric vehicles have a great impact on the voltage stability of the DC power distribution systems. A robust control method based on H∞ loop shaping method is proposed to suppress the effect of uncertain integration on voltage stability of DC distribution system. The results of frequency domain analysis and time domain simulation show that the proposed robust controller can effectively suppress the DC bus voltage oscillation caused by the uncertain integration of electric vehicle, and the robustness is strong.

Combined system identification and robust control of a gimbal platform

Gimbaled imaging systems require very high performance inertial stabilization loops to achieve clear image acquisition, precise pointing, and tracking performance. Therefore, higher bandwidths become essential to meet recent increased performance demands. However, such systems often posses flexible dynamics around target bandwidth and time delay of gyroscope sensors which put certain limit to achievable bandwidths. For inertial stabilization loops, widely used design techniques have difficulty in achieving large bandwidth and satisfying required robustness simultaneously. Clearly, high performance control design hinges on accurate control-relevant model set. For that reason, combined system identification and robust control method is preferred. In the system identification step, accurate nominal model is obtained, which is suitable for subsequent robust control synthesis. Model validation based uncertainty modeling procedure constructs the robust-control-relevant uncertain model set, which facilitates the high performance controller design. Later, with skewed- µ synthesis, controller is designed which satisfies large bandwidth and robustness requirements. Finally, the experimental results show that significant performance improvement is achieved compared to common manual loop shaping methods. In addition, increased performance demands for new imaging systems are fulfilled.

Employing Finite Element Analysis and Robust Control Concepts in Mechatronic System Design-Flexible Manipulator Case Study

The paper deals with development of a methodology for mechatronic system design using state-of-the-art model-based system engineering methods. A simple flexible robotic arm is considered as a benchmark problem for the evaluation of various techniques used in the phases of modelling, analysis, control system design, validation, and implementation. The flexible nature of the mechanical structure introduces inherently oscillatory dynamics in the target bandwidth range, which complicates all the above-mentioned design steps. This paper demonstrates the process of deriving a complex nonlinear model of the flexible arm setup. An initial idea about the plant dynamics is acquired from analytical modelling using the Euler–Bernoulli beam theory. A more thorough understanding is subsequently acquired from finite element analysis. Linearisation and order reduction are the next steps necessary for the derivation of a simplified control-relevant model. A time-dependent variable parameter of load mass position is considered and a robust controller is subsequently designed in order to fulfil certain performance criteria for all the admissible plant configurations. This is performed using a recent H-infinity loop shaping method for fixed structure controller design. The results are validated by means of a physical plant, comparing the experimental data with the model predictions.

Design and Comparison of Plasma H∞ Loop Shaping and RGA-H∞ Double Decoupling Multivariable Cascade Magnetic Control Systems for a Spherical Tokamak

The article aims to present an approach to design and compare cascade Hinf loop shaping and essentially new cascade RGA-Hinf double decoupling magnetic control systems for a multivariable dynamical plant, specifically plasma in a vertically elongated tokamak. Identification of the present control closed-loops containing a plasma linear model of a relatively high order for the spherical Globus-M tokamak (Ioffe Institute, St Petersburg, Russia) to derive a low order linear model (without the application of reduction algorithms) as a plant under control is undertaken. A robust H¥ loop shaping method was applied to the identified model to design a plasma position, current, and shape (6 gaps between the first wall and plasma separatrix) multivariable controller. A structural analysis was done to get the most effective structure of the square plant with the 3rd gap eliminated in the feedback and a separate loop for the plasma current control. The methodology of the relative gain array (RGA) was applied to this structure to choose the proper correspondences between inputs and outputs (pairing), which brought the plant model closer to a decoupling plant (first decoupling in the open plant model). Further, the Hinf adjustment of the control system with the pairing plant and an additional feedback decoupling matrix (second decoupling of the plant model in the feedback) and PI controllers in the feedback gave increased control system accuracy while tracking references. Comparison of the two control systems designed has shown that double decoupling gives higher performance accuracy and a less robust stability margin, while the robust loop shaping method allows the stability margin to be increased but gave less accurate control of the gaps.

Power-Synchronized Grid-Following Inverter Without a Phase-Locked Loop

This paper proposes a power-synchronized control strategy for grid-following inverters (GFLIs) to regulate their power exchange with the grid without any need for sensing/regulating the point of connection voltage. Contrary to conventional GFLIs, which rely on phase-locked loops for grid synchronization and have difficulties in weak grid conditions, the proposed strategy is power synchronized and utilizes the inverter terminal voltage for power control leading to its seamless performance in ultra-weak grids. Additionally, since the proposed approach does not require any voltage regulation at the point of connection to the grid, contrary to grid-forming inverters, it can reliably operate in stiff and/or series-compensated grids as well. The proposed approach benefits from a decoupling control structure that is tuned using a loop-shaping method. Compared to conventional GFLIs, this approach does not need any extra hardware; hence, it can easily be retrofitted into the existing large fleet of GFLIs. The performance of the proposed controller is evaluated in Matlab/PLECS for both weak and stiff grids, and the findings are experimentally validated in a scaled-down setup.

Multi-Objective Intelligent Optimization of Superheated Steam Temperature Control Based on Cascaded Disturbance Observer

Superheated steam temperature (SST) is one of the most critical parameters for the process safety, overall efficiency and pollution reduction of coal-fired power plants. However, SST control is challenging due to various disturbances and model uncertainties, especially in the face of the growing penetration of intermittent renewable energy into the power grid. To this end, a cascaded Disturbance Observer-PI (DOB-PI) control strategy is proposed to enhance control performance. The observer design and parameter tuning are carried out through mechanism analysis on the proposed structure. Furthermore, a robust loop shaping method is introduced as a hard constraint to balance the control performance and robustness. The controller parameters are optimized based on the multi-objective artificial bee colony optimization (MOABC) algorithm. Simulation results show that the proposed cascaded DOB-PI control strategy can significantly improve the disturbance rejection performance of both the inner- and outer-loops of the SST control system. This paper indicates promising prospects for the proposed method in future applications.

Design of Stable Controller for Flexible Solar Panel by H∞ Loop-Shaping Method

Flexible solar panels play an essential role in the field of aerospace. However, many difficulties appear in the control design due to the existence of a weakly damped resonance module. The design for flexible systems often causes an unstable controller so that the systems after design still have trouble in putting into practice. We adopt H∞ loop-shaping design and put forward a directive method for selecting the weighting function. The simulation results indicate that system bandwidth is optimized based on the stable controller. In this way, the control precision and response speed of the system are improved. In the meantime, the system is easy to put into use.

Robust controller design: Recent emerging concepts for control of mechatronic systems

The recent industrial revolution puts competitive requirements on most manufacturing and mechatronic processes. Some of these are economic driven, but most of them have an intrinsic projection on the loop performance achieved in most of closed loops across the various process layers. It turns out that successful operation in a globalization context can only be ensured by robust tuning of controller parameter as an effective way to deal with continuously changing end-user specs and raw product properties. Still, ease of communication in non-specialised process engineering vocabulary must be ensured at all times and ease of implementation on already existing platforms is preferred. Specifications as settling time, overshoot and robustness have a direct meaning in terms of process output and remain most popular amongst process engineers. An intuitive tuning procedure for robustness is based on linear system tools such as frequency response and bandlimited specifications thereof. Loop shaping remains a mature and easy to use methodology, although its tools such as Hinf remain in the shadow of classical PID control for industrial applications. Recently, next to these popular loop shaping methods, new tools have emerged, i.e. fractional order controller tuning rules. The key feature of the latter group is an intrinsic robustness to variations in the gain, time delay and time constant values, hence ideally suited for loop shaping purpose. In this paper, both methods are sketched and discussed in terms of their advantages and disadvantages. A real life control application used in mechatronic applications illustrates the proposed claims. The results support the claim that fractional order controllers outperform in terms of versatility the Hinf control, without losing the generality of conclusions. The paper pleads towards the use of the emerging tools as they are now ready for broader use, while providing the reader with a good perspective of their potential.

A Generic WebLab Control Tuning Experience Using the Ball and Beam Process and Multiobjective Optimization Approach

In control engineering education, the possibility of using a real control system in the learning process motivates professors to improve both students’ knowledge and skills, thus avoiding an approach only based on control theory. While considering that control engineering laboratories are expensive, mainly because educational plants should reproduce classical problems that are found in the industry, the use of virtual laboratories appears as an interesting strategy for reducing costs and improving the diversity of experiments. In this research, remote experimentation was assumed regarding the ball and beam process as an alternative didactic methodology. While assuming a nonlinear and unstable open-loop process, this study presents how students should proceed to control the plant focusing on the topic that is associated with multiobjective optimization. Proportional-Integral-Derivative (PID) controller was tuned considering the Non-dominated Sorting Genetic Algorithm (NSGA-II) to illustrate the WebLab learning procedures described in this research. The proposed strategy was compared to the Åström’s robust loop shaping method to emphasize the performance of the multiobjective optimization technique. Analyzing the feedback provided by the students, remote experimentation can be seen as an interesting approach for the future of engineering learning, once it can be directly associated with industry demand of connected machines and real-time information analysis.

A Model-Free Loop-Shaping Method based on Iterative Learning Control

Many techniques have been developed for the loop-shaping method in control design. While most loop-shaping methods apply a model of the open-loop controlled plant, the resulting performance depends on the accuracy of the dynamical model. This paper aims to develop a model-free loop-shaping technique. The core idea is to convert the model matching problem to a trajectory tracking problem. To achieve the desired loop gain, we need to determine the control input such that the system output tracks the impulse response of the loop gain function. In this paper, a model-free iterative learning control (ILC) algorithm is applied to solve this tracking problem. Once the ILC converges, the feedback controller that meets the desired loop gain can then be constructed. This method does not require the model of the controlled plant, hence it provides better performance of loop-shaping control design. The proposed method is validated through numerical simulation on a 3-rd order plant.

Control System Loop-Shaping as a Mathematical Optimization Problem: An Ensemble of Models

This paper proposes an extension to the established loop-shaping method, where the loop-shaping method is modeled mathematically and solved as a mathematical optimization program. In this process, a novel cost function is proposed and employed as the objective of optimization in the controller tuning problem. This cost function evaluates different characteristics of the system in the frequency domain, such as the stability margins and the operability bandwidth. These characteristics reflect the quality of load disturbance rejection, set-point tracking, and operability bandwidth of the control system. Consequently, the proposed technique circumvents running a time-domain simulation completely. More importantly, the proposed technique can be used with any controller structure. The generic cost function can be customized to fit any control objective and application. This is conducted in the second half of this paper, with the aim of obtaining a system with near-optimum time-domain performance with respect to the integral of time times absolute error (ITAE) criterion. At the same time, the control system obtained with the customized cost function has better operability bandwidth than that of a system optimized in the time-domain for the ITAE criterion. The proposed optimization model is analyzed for two plant models: first order and second order plus dead-time (FOPDT), (SOPDT), respectively.