Loop-shaping Technique Research Articles

Road profile estimation based on the second generation CRONE control

The objective of this paper is to present a new design method for an unknown input estimator with a closed-loop structure. A frequency domain approach is carried out using a model-based design method and a loop-shaping technique. The loop-shaping approach used to the estimator design is usually applied in the context of control system design. More precisely, it is the second generation CRONE system design methodology that is used. This method is applied to the estimation of a speed bump by using one of the sensors initially intended for suspension control. Note that the noise measurement used in the simulation is recorded from on-board sensors used to control the piloted suspension of a DS7 Crossback. The time responses of the estimator, obtained with a non-linear quarter-car simulator, illustrate the very good results obtained.

Control Scheme for a Quadratic-Based Step-Down On-Board DC/DC Converter to Be Used in Hybrid Electric Vehicles

This paper discusses a switching regulator with a quadratic-based step-down DC/DC converter designed using a reduced redundant power processing principle. This converter benefits from a non-complex topology, which aims to process energy more efficiently. The switching regulator can be used on-board in hybrid electric vehicles and has a non-pulsating input current, which is suitable to process energy from lithium-ion batteries. Design expressions and steady-state operating conditions are given for the converter. Models are obtained to design and implement a two-loop controller. The simplicity of this approach is of significant value in a method of design-oriented analysis, in which the analytic results can be used to make design choices. Loop-shaping techniques are used to design a robust controller to regulate the output voltage of the proposed converter under voltage variations on the lithium-ion batteries and the changes in load current requirements, as well as parameter uncertainties of the converter. The design conditions for the gains of the controller are derived. The models of the converter are verified through experimental results for a 300 W prototype and used to design a robust controller. Finally, closed-loop time and frequency domain tests are given to show the performance of the switching regulator.

Smart Structures Innovations Using Robust Control Methods

This study’s goal is to utilize robust control theory to effectively mitigate structural oscillations in smart structures. While modeling the structures, two-dimensional finite elements are used to account for system uncertainty. Advanced control methods are used to completely reduce vibration. Complete vibration suppression is achieved using advanced control techniques. In comparison to traditional control approaches, Hinfinity techniques offer the benefit of being easily adaptable to issues with multivariate systems. It is challenging to simultaneously optimize robust performance and robust stabilization. One technique that approaches the goal of achieving robust performance in mitigating structural oscillations in smart structures is H-infinity control. H-infinity control empowers control designers by enabling them to utilize traditional loop-shaping techniques on the multi-variable frequency response. This approach enhances the robustness of the control system, allowing it to better handle uncertainties and disturbances while achieving desired performance objectives. By leveraging H-infinity control, control designers can effectively shape the system’s frequency response to enhance stability, tracking performance, disturbance rejection, and overall robustness.

Vertical road profile reconstruction from vehicle embedded-sensors

This paper proposes a method for the reconstruction of the vertical road profile from embedded sensors in a car. The study details the specifications in the time domain to ensure a good tracking of the road variation. To meet these specifications, a frequency domain approach is carried out using a model-based design method with a closed-loop structure and a loop shaping technique. The frequency and time responses of the reconstructor obtained in simulation are presented to illustrate the performances. Note that the road profile used in simulation comes from a test bench recording. Similarly, the measurement of noises used in the simulation recorded from on-board sensors used to control the piloted suspension of a DS7 Crossback.

Settling Time Optimization in Wire Bonder Systems via Extremum-Seeking Control1

Adequate tuning of control laws is essential for high positioning accuracy, large system throughput, and reliability in high-end mechatronic and robotic systems. However, a population of such systems generally shows slight variations in dynamic responses due to, e.g., manufacturing tolerances, different disturbance situations, or position-dependent dynamics. Given the time-consuming nature of controller design, even by experienced control engineers, typically just one control law is designed for the whole system population based on worst-case bounds on variations in dynamic responses, resulting in a loss of individual system performance. The main contribution of this paper is the development of an automated controller tuning approach, based on extremum-seeking control, for settling time optimization via individual controller tuning. While other automated controller tuning methods exist, the developed approach allows inclusion of closed-loop stability and robustness constraints based solely on non-parametric frequency-response measurements of open-loop plant dynamics, and therewith directly optimizes transient system performance in a purely data-based manner. The proposed approach has been applied in simulation in an industrial case study for settling time optimization in point-to-point motions of a wire bonder system. In this case study, the effectiveness of the approach has been shown by achieving significant performance increases of 39.4% and 40.6% compared to controllers designed by experienced control engineers using manual loop-shaping techniques and a frequency-based auto-tuner, respectively, without needing manual tuning effort.

Modelling and Control Development of a Cascaded NPC-Based MVDC Converter for Harmonic Analysis Studies in Power Distribution Networks

Today’s power distribution networks are predicted to incorporate more Power Electronics (PE)-based power conversion systems, widely acknowledged as harmonic sources. Concerns about power harmonic severity in the distribution networks can arise, especially with the growing numbers of Medium Voltage Direct Current (MVDC) systems, which are also facilitated by such power converters. Yet, an accurate harmonic model of the MVDC converter is required to investigate its harmonic emissions, propagations, effects, and solutions in today’s distribution networks. This article is devoted to the development of a detailed model of a cascaded Neutral Point-Clamped (NPC)-based MVDC converter for accurate harmonic analysis studies. An appropriate control system with a simple Proportional Integral (PI) controller tuned using the loop-shaping technique is developed. An interleaved Sinusoidal Pulse-Width Modulation (SPWM) scheme aiming to improve the harmonic performance of such an application is introduced. The detailed model of the MVDC system was developed using the Simulink/MATLAB simulation environment, for which the concept of operation was validated, control system performance was investigated, and the effectiveness of the harmonic reduction method was analysed. The key finding is that the interleaved SPWM technique has significantly reduced the Total Harmonic Distortion (THD) to 2% with no significant even-order harmonic components in comparison to the reported models.

Optimizing the Control System of Clinker Cooling: Process Modeling and Controller Tuning

This paper aims to present efficient efforts to optimize the proportional-integral-differential (PID) controller of clinker cooling in grate coolers, which have a fixed grate and at least two moving ones. The process model contains three transfer functions between the speed of the moving grate and the pressures of the static and moving grates. The developed software achieves the identification of the model parameters using industrial data and by implementing non-linear regression methods. The design of the PID controller follows a loop-shaping technique, imposing as a constraint the maximum sensitivity, Ms, of the open-loop transfer function and providing a set of PIDs that satisfy a range of Ms. A simulator determines the optimal PID sets among those calculated at the design step using the integral of absolute error (IAE) as a performance criterion. The combination of a robustness constraint with a performance criterion, Ms and IAE respectively, leads to an area of controllers with Ms belonging to the range of 1.2 to 1.35. The IAE is between 4.2% and 4.8%, depending on the set-point value. PID sets located near the middle of this area can be chosen and implemented in the cooler’s routine operation.

Real-Time Implementation of Robust Loop-Shaping Controller for a VSC HVDC System

Voltage source converter (VSC) based HVDC systems are one of the most promising technologies for high voltage bulk power transmission. The reliability and stability of a VSC-based HVDC system greatly depends on the design of a proper controller for the inner decoupled d-q current loop. One of the major causes of instability in a properly tuned controller is due to system parameter variation. This paper presents the design of a fixed parameter robust controller for the inner decoupled d-q current loop for a VSC-based HVDC system to deal with the uncertainties due to system parameter variations. The method of multiplicative uncertainty is employed in the robust design to model the variations in the system parameters. The robust control design was realized through a graphical procedure known as the loop-shaping technique. The graphical loop shaping technique is a much simpler and more straightforward method compared to the traditional H∞-based algorithms for robust controller design. The designed robust controller was experimentally verified using a real-time hardware in loop (HIL) system and was tested on a VSC HVDC system. The performance of the designed robust controller is compared to that of a traditional PI controller. It has been observed that a classical PI controller is effective for a given operating point, and its performance deteriorates when the operating point changes or when the system parameters change. The studies conducted using real-time hardware in the loop (HIL) system prove that the designed loop-shaping-based robust controller provides very good performance and stability for a wide range of system parameter variations, such as changes in resistance and the inductance of the VSC HVDC system compared to the PI controller tuned using conventional methods.

Loop-shaping for reset control systems: A higher-order sinusoidal-input describing functions approach

The ever-growing demands on speed and precision from the precision motion industry have pushed control requirements to reach the limitations of linear control theory. Nonlinear controllers like reset provide a viable alternative since they can be easily integrated into the existing linear controller structure and designed using industry-preferred loop-shaping techniques. However, currently, loop-shaping is achieved using the describing function (DF) and performance analysed using linear control sensitivity functions not applicable for reset control systems, resulting in a significant deviation between expected and practical results. This major bottleneck to the wider adaptation of reset control is overcome in this paper with two important contributions. First, an extension of frequency-domain tools for reset controllers in the form of higher-order sinusoidal-input describing functions (HOSIDFs) is presented, providing greater insight into their behaviour. Second, a novel method that uses the DF and HOSIDFs of the open-loop reset control system for the estimation of the closed-loop sensitivity functions is proposed, establishing for the first time — the relation between open-loop and closed-loop behaviour of reset control systems in the frequency domain. The accuracy of the proposed solution is verified in both simulation and practice on a precision positioning stage and these results are further analysed to obtain insights into the tuning considerations for reset controllers.

Robust Stabilization of Interval Plants with Uncertain Time-Delay Using the Value Set Concept

This paper considers the robust stabilization problem for interval plants with parametric uncertainty and uncertain time-delay based on the value set characterization of closed-loop control systems and the zero exclusion principle. Using Kharitonov’s polynomials, it is possible to establish a sufficient condition to guarantee the robust stability property. This condition allows us to solve the control synthesis problem using conditions similar to those established in the loopshaping technique and to parameterize the controllers using stable polynomials constructed from classical orthogonal polynomials.

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.

Parameter Estimation, Robust Controller Design and Performance Analysis for an Electric Power Steering System

This paper presents a parameter estimation, robust controller design and performance analysis for an electric power steering (EPS) system. The parametrical analysis includes the EPS parameters and disturbances, such as the assist motor parameters, sensor-measurement noise, and random road factors, allowing the EPS stability to be extensively investigated. Based on the loop-shaping technique, the system controller is designed to increase the EPS stability and performance. The loop-shaping procedure is proposed to minimize the influence of system disturbances on the system outputs. The simplified refined instrumental variable (SRIV) algorithm, least squares state variable filter (LSSVF) algorithm and instrumental variable state variable filter (IVSVF) algorithm are applied to reduce the model mismatching between the theoretical EPS models and the real EPS model, as the EPS parameters can be accurately identified based on the experimental EPS data. The performance of the proposed method is thus compared to that of the proportional-integral-derivative (PID) test bench results for the EPS system. The experimental results demonstrated that the proposed loop-shaping controller provides good tracking performance while ensuring the stability of the EPS system.

Micro-lens fabrication by a long-stroke precision stage with switching control based on model response prediction

This paper develops an automatic control switching mechanism for a long-stroke precision stage intended to improve micro-lens fabrication. The stage consists of a piezoelectric transducer (PZT) stage and a motor stage that achieves centimeter-length travel distances with nanometer precision. We obtained the PZT stage model by experiments and then applied robust loop-shaping techniques to design two controllers: one gave fast responses and the other gave smooth responses. The two controllers were further simplified as robust proportional-integral-derivative (PID) controllers for hardware implementation. We then developed a control switching mechanism, based on model response prediction, to combine the merits of these two controllers. For the motor stage, we derived the stage model by experiments and designed a gain-scheduling controller that regulated the stage to move at the fastest speed for long travel distances until it was within the stroke of the PZT stage. The two stages were then combined with a double-loop control structure to provide a travel range of 10 cm with a precision of 1.23 nm. We implemented the designed control mechanisms and structures for experimental verification. The combined stage was also integrated with a two-photon polymerization (TPP) system to fabricate micro-lenses. The optical properties of the micro-lenses were evaluated to demonstrate the effectiveness of the proposed control in precision positioning for long travel distances.

Robust H∞ loop-shaping controller design for temperature and air flows control of a passive nonlinear air conditioning unit

This paper designs a controller of a passive nonlinear air-conditioning unit based on a loop-shaping approach, with respect of the environmental conditions for micro-climate in growth chambers and greenhouses. The control problem consists in mixing two prescribed air flows and tracking the mixed output set point temperature. Simulations were carried out on the closed-loop formed by connecting the controller to the nonlinear original system. The synthesized controller based on the H∞ loop-shaping technique provides robust stability and performance. Using the v-gap metric, the controller was shown to stabilize a large class of systems with uncertainties in power heating coefficients.

Development of dynamic phasor based higher index model for performance enhancement of dual active bridge

Renewable energy integration and control in microgrid demands computationaly efficient model along with effective control methodology for switched converters. The dual active bridge (DAB) being an integral part of the microgrid suffers from the stability issues. This research proposes dynamic phasor (DP) based higher index model of DAB and demonstrates the effect of appropriate selection of model on performance. To evaluate the system stability for performance objectives of voltage regulation, suppression of measurement noise, sinusoidal disturbances and robustness, a robust control strategy based on loop shaping technique for DP model of DAB is proposed. Comparison of the responses of the higher index model with existing DP model with dc and index 1 terms makes apparent the benefits of the proposed model. The Hardware-in-Loop (HIL) simulation using Opal-RT and dSPACE simulators is carried out for validation of the proposed control scheme.

Feedforward Compensation for Suppression of Seam Boundary Error Propagation in Robotic Welding Systems

In this paper, a novel filling control algorithm for suppression of seam boundary error propagation is proposed for robotic multipass welding systems. First, the multipass welding process is formulated as a closed-loop control design problem with a low-gain feedback controller in the baseline loop. Next, a noncausal feedforward controller is designed for compensating the error from previous welding passes. The noncausal feedforward controller is optimized using the $H_\infty$ loop-shaping technique such that the error caused by nonrepetitive disturbances in one pass is gradually eliminated, while the error caused by repetitive disturbance in every pass is suppressed. Our experimental results on an industrial robotic welding system show that the proposed control algorithms eliminate seam boundary errors caused by nonrepetitive disturbances within five passes, and a reduction of 12.8% in root mean-square-error of seam boundary error when subjected to repetitive disturbances in every filling pass.

Scheduled Controller Design for Systems With Varying Sensor Configurations: A Frequency-Domain Approach

A novel parameter-dependent scheduled controller design is proposed for systems which exhibit switched dynamics. Switching is a result of varying sensor configurations available in the measurement system. The control architecture is based on a priori designed local linear time-invariant controllers, which are designed using frequency-domain loop-shaping techniques. Moreover, conditions on measured frequency response function data of the plant are provided under which the closed-loop system is input-to-state stable for arbitrarily fast parameter variations based on a generalized version of the circle criterion. By presenting a design and analysis framework for scheduled control systems that is easily implementable in existing control software, and does not require parametric plant models, this paper connects well to the industrial control practice. The effectiveness of the proposed scheduling technique, as a way to improve both transient and steady-state performance, is demonstrated by means of a case study which includes measurement results obtained from an industrial wafer stage system.

Reduced-order modeling and feedback control of a flexible wing at low Reynolds numbers

A state-space reduced-order model for the lift generated by the unsteady deflection of a two-dimensional flexible wing is presented. The wing’s deflection is decomposed using a truncated Fourier series in the contribution of single deflection modes; the global lift is then obtained using superposition. The presented model is an extension of the model introduced in Brunton et al. (2013) for rigid pitching and plunging. A realization of the model is obtained using lift pulse responses from Direct Numerical Simulation (DNS) at a Reynolds number of 100. The performance of the deflection modes are discussed from a feedback control point of view and controllers for mode 1, mode 2 and pitching are designed using loop-shaping techniques and tested, comparing the results with DNS. The performance limitations of mode 1 and mode 2 are overcome by using a multi-input controller that uses both deflection modes together. Finally, the controllers are tested in an off-design condition at a higher Reynolds number of 1000.

FLOreS - Fractional order loop shaping MATLAB toolbox

A novel toolbox named FLOreS is presented for intuitive design of fractional order controllers (FOC) using industry standard loop shaping technique. This will allow control engineers to use frequency response data (FRD) of the plant to design FOCs by shaping the open loop to meet the necessary specifications of stability, robustness, tracking, precision and bandwidth. FLOreS provides a graphical approach using closed-loop sensitivity functions for overall insight into system performance. The main advantage over existing optimization toolboxes for FOC is that the engineer can use prior knowledge and expertise of plant during design of FOC. Different approximation methods for fractional order filters are also included for greater freedom of final implementation. This combined with the included example plants enables additionally to be used as an educational tool. FLOreS has been used for design and implementation of both integer and fractional order controllers on a precision stage to prove industry readiness.

Iterative feedback tuning of wind turbine controllers

Abstract. Traditionally, wind turbine controllers are designed using first principles or linearized or identified models. The aim of this paper is to show that with an automated, online, and model-free tuning strategy, wind turbine control performance can be significantly increased. For this purpose, iterative feedback tuning (IFT) is applied to two different turbine controllers: drivetrain damping and collective pitch control. The results, obtained by high-fidelity simulations using the NREL 5MW wind turbine, indicate significant performance improvements over baseline controllers, which were designed using classical loop-shaping techniques. It is concluded that iterative feedback tuning of turbine controllers has the potential to become a valuable tool to improve wind turbine performance.