Bifurcations Caused by Sampling Effects in Robotic Force Control

The article is dedicated to optimizing the digital current control loop of a thyristor converter-driven electric drive, essential for ensuring stable, precise, and reliable operation of electric drives in automated and industrial systems. The primary goal of this research is to develop and enhance the digital current regulator (DCR), which enables the drive system to achieve desired performance, including rapid and stable response to current changes without excessive overshoot or oscillations. Optimization of the current loop improves energy efficiency, enhances dynamic properties, and increases resistance to external disturbances, all of which are critical for modern electric drive systems. The introduction discusses key aspects of digital current loop optimization, specifically dynamic characteristics such as time delays, sampling rate, and bandwidth, which significantly impact the efficiency of digital controllers. Special attention is given to the tuning of proportional-integral (PI) controller parameters, allowing quick and stable response to current changes. The developed model allows preliminary simulation of the current loop’s performance, providing an opportunity to test different configurations before actual implementation. To improve the accuracy and stability of the system, filtering methods are proposed to reduce the impact of high-frequency noise, ensuring the system’s precision and robustness against external interference. Optimization criteria are introduced, including minimizing the integral square error (ISE) and reducing energy consumption, which significantly decreases system losses and increases the energy efficiency of electric drives. In developing the optimized control loop, the following assumptions are considered: 1) the thyristor converter (TC) operates in continuous current mode, 2) the current loop dynamics are studied within a narrow range of TC phase angle changes, and 3) a discrete dynamic TC model is used with averaging of electromotive force (EMF) over the conduction interval. Optimizing the digital current loop addresses several critical tasks, including enhancing control accuracy, reducing overshoot and oscillations, and improving the system’s dynamic response, allowing for reduced delays and a faster reaction to load changes. The optimization results of the digital current regulator (DCR) show reduced energy consumption and significant improvements in control accuracy. The high-speed performance of the digital current loop enables fast transient processes within a single sampling interval of the thyristor converter, which is crucial for systems requiring rapid regulation. Additionally, the digital control loop provides flexibility in control, as it allows for system adjustments to different operating conditions through a software-based approach. The study’s final results demonstrate the potential of digital current loops in modern electric drives. With advances in microprocessor technology, digital regulators enable more complex control algorithms, including adaptive and predictive strategies, which further enhance system efficiency. These approaches are especially relevant for industrial electric drives that require high precision and response speed, making digital current loops a promising solution for contemporary automated control systems.

This paper addresses modeling and control issues related to practical high-frequency digital PWM control of constant-frequency boost, buck-boost and flyback converters. Discrete-time models, including the effects of A/D sampling and delays in the digital control loop, are derived for two cases: output voltage A/D sampling during transistor off time in combination with trailing-edge (TE) DPWM, and A/D sampling during transistor on time in combination with leading-edge (LE) DPWM. We show that off-time sampling with TE-DPWM, which is a common approach in digital controller realizations, can result in desirable minimum-phase responses, thus simplifying compensator design in wide bandwidth closed-loop voltage regulators based on boost or flyback converters. The results are verified by simulation and experimental results on a boost converter prototype.

Mitigating collision is a fundamental issue in contact problems, and is required to ensure the safety of a robotic cell. Research into the contact problem between robots and their environment is divided into two parts: one uses the environmental contact model and parameter estimation, the other uses the robot force control method. There are two main problems with this research method. One is that the two research levels are not effectively combined to form a complete solution for force control in practice. The other problem is that research on excessive contact force in the collision phase has not been studied in depth for force control. In this paper, a sensing-executing bionic system is proposed that combines environmental detection and robotic force control based on the way an ant functions. The bionic system clearly explains the process from environment detection to robot control, which can provide guidance when designing a new robot control system. An adaptive switching control algorithm is proposed to mitigate the collision force in the collision phase. From the simulation results, the collision force is significantly reduced due to the implementation of adaptive switching control. Finally, a new self-sensing device is designed which can be integrated into the robot control device. However, as there are no additional sensors or computational complexity in the system, the effectiveness of the circuit and superiority of the adaptive parameter update must be verified by experimentation.

In order to make BEPC-II to run at a higher energy, the Institute of High Energy Physics undertook an upgrading project. One of the important factors limiting the energy boost is the power and performance of the dipole magnet power supplies; therefore, these four magnet power supplies are developed for the BEPC-II upgrading. The power supplies adopt topologies of thyristor rectifiers to realize a high-power output. In the control unit of each power supply, a digital current closed loop is adopted, and the key components in the feedback loop are thermostatically controlled. In order to improve the performances of the power supplies, analog voltage regulators are added to the inner control loops. These four power supplies have been tested and have already been officially used in BEPC-II, and their powers have reached the requirements of the upgrading. The test results of the current stability are described and shown in this paper, which testifies that the stabilities meet the design parameters. A digital control is applied to each SCR rectifier control. The performances of the power supplies are improved by the combination of digital current control loops and the analog voltage control loops, which makes the performances of the dipole magnet power supplies meet the requirements of the upgrading project.

Interactive digital control using PMBus protocol can significantly improve performance, efficiency and reliability in high frequency low voltage DC (LVDC) microgrid applications using online optimization through shared clock and data. Modeling and analysis of digitally controlled standalone DC-DC converters, considering finite sampling delays, have been well reported in the past; however, modeling and analysis of fast scale stability and performance limits, under finite sampling delay and clock shift, have not been investigated so far in digitally controlled LVDC microgrids. This paper considers an intermediate bus architecture (IBA), consisting of an intermediate bus converter (IBC) followed by a point-of-load (PoL) converter, under clock-synchronized digital current mode control (DCMC). Considering the IBA dynamics, a discrete-time (DT) framework is proposed, and DT small-signal models are derived for stability and performance analysis. It is shown that the clock shift between individual converters and the sampling delays of their corresponding digital controllers have significant impacts on the fast-scale stability of the overall IBA system, which may lead to severe fast-scale instability with complex nonlinear phenomena and resulting in much higher (inductor) current ripple and RMS quantities. Simulation case studies are presented, and the stability boundaries are found to be consistent with the analytical predictions. The proposed framework will be helpful to design stable digital control in DC microgrids.

Application of Digital Control Techniques for Satellite Medium Power DC-DC ConvertersThe objective of this paper is to present a work concerning a digital control loop system for satellite medium power DC-DC converters that is done in Space Research Centre. The whole control process of a described power converter is based on a high speed digital signal processing. The paper presents a development of a FPGA digital controller for voltage and current mode stabilization that was implemented using VHDL. The described controllers are based on a classical digital PID controller. The converter used for testing is a 200 kHz, 750W buck converter with 50V/15A output. A high resolution digital PWM approach is presented. Additionally a simple and effective solution of filtering of an analog-to-digital converter output is presented.

Robotic force control is a core research direction in robotics technology. For tasks such as polishing and assembly, it requires not only precise motion control but also compliant force control by adjusting output force and torque. Traditional impedance control can ensure accuracy in a single environment, but it is limited by the difficulty in accurately acquiring parameters in complex environments; although variable impedance control can adapt to the environment, it faces challenges in control law design. This paper integrates the extended Twin Delayed Deep Deterministic Policy Gradient (ex-TD3) algorithm with impedance control, proposing an ex-TD3-based intelligent impedance control optimization algorithm. A Python-MATLAB/SimMechanics co-simulation platform is established to verify its effectiveness. The experiment adopts a scenario where the robot moves linearly along the z-axis, with fixed environmental stiffness and the desired tracking force changing in stages over time. The model training is iterated for 300 episodes, after which the reward tends to stabilize and the control strategy converges. Experimental results show that, compared with the traditional adaptive impedance control algorithm, the proposed algorithm in this paper exhibits faster force response, smaller force fluctuations during force step changes, smoother force output throughout the process: the maximum overshoot of force control decreases from 6.21N to 1.33N (a reduction rate of 77.63%), and the maximum position tracking error is reduced by 69.5%. With the above optimized design, this study significantly improves the energy efficiency and long-term operational sustainability of mechatronic systems; its precise control of force overshoot and position tracking error effectively reduces mechanical losses and unnecessary energy consumption during the system’s dynamic interaction with the environment.

The present work aims at vibration control of a structure/rotor using a one-sided magnetic actuator. For such an actuator, the actuator force is a nonlinear function of current through the coil of the actuator and the gap between the actuator and the structure/rotor. Though the actuator introduces sufficient nonlinearity to the system, it has the advantage that, for applying force in a direction, this actuator needs to be placed in only one side of the structure/rotor. For vibration control of the structure/rotor, a simple digital proportional derivative (PD) control technique is suggested here. It is considered that the displacement signal from the sensor is sampled at specific instants of time and a series of discrete values of displacement is made available to the digital controller. The controller processes the above values of displacement to compute the values of control current that produces the values of appropriate control force at the corresponding instants. The input current to the actuator is kept constant between two consecutive sampling instants. The response of the controlled system (the structure/rotor along with the digital controller) is computed using standard time-marching algorithms (with time steps much smaller than the sampling interval). The effect of the sampling interval in the response pattern is observed for a single-degree-of-freedom (SDOF) system, a finite element model of a beam and a four degree-of-freedom model of a rotor.

Real Time Analysis of Microprocessor Control System

With the development of digital signal processing technologies, control and monitoring of power electronics conversion systems have been evolving to become fully digital. As the basic element in the design and analysis phases of digital controllers or filters, a number of unit delays (z−1) have been employed, e.g., in a cascaded structure. Practically, the number of unit delays is designed as an integer, which is related to the sampling frequency as well as the ac signal fundamental frequency (e.g., 50 Hz). More common, the sampling frequency is fixed during operation for simplicity and design. Hence, any disturbance in the ac signal will violate this design rule and it can become a major challenge for digital controllers. To deal with the above issue, this paper first exploits a virtual unit delay (z v -1) to emulate the variable sampling behavior in practical digital signal processors with a fixed sampling rate. This exploitation is demonstrated on a T/4 Delay Phase Locked Loop (PLL) system for a single-phase grid-connected inverter. The T/4 Delay PLL requires to cascade 50 unit delays when implemented (for a 50-Hz system with 10 kHz sampling frequency). Furthermore, digital frequency adaptive comb filters are adopted to enhance the performance of the T/4 Delay PLL when the grid suffers from harmonics. Experimental results have confirmed the effectiveness of the digital filters for advanced control systems.

In this paper we present an analysis of the stability of a two-degree-of-freedom system, modeling a robotic arm connected to the actuator through an elastic joint and subject to digital position control. The system consists of two lumped masses connected to each other through a spring and a damper. In the model there is only one actuator, so the system is underactuated in a certain sense; two cases are considered, referring to a collocated and a noncollocated configuration. Stability analysis is presented using both a continuous and a discrete time approach. The discrete time approach is related to the case of a digital controller, typical in real applications. This samples the position and the velocity signals at discrete time intervals and, therefore, it generates a piecewise constant control force, introducing a delay in the control system as well. The stability charts are presented in the parameter space of the sampling time and the control gains. Their differences highlight the role played by the resonances between the finite sampling frequency and the natural frequency of the system in achieving robust stability with respect to parameter variations.

Abstract. Switched-mode power supplies (SMPS) convert an input DC-voltage into a higher or lower output voltage. In automotive, analog control is mostly used in order to keep the required output voltages constant and resistant to disturbances. The design of robust analog control for SMPS faces parameter variations of integrated and external passive components. Using digital control, parameter variations can be eliminated and the required area for the integrated circuit can be reduced at the same time. Digital control design bears challenges like the prevention of limit cycle oscillations and controller-wind-up. This paper reviews how to prevent these effects. Digital control loops introduce new sources for dead times in the control loop, for example the latency of the analog-to-digital-converter (ADC). Dead times have negative influence on the stability of the control loop, because they lead to phase delays. Consequently, low latency is one of the key requirements for analog-to-digital-converters in digitally controlled SMPS. Exploiting the example of a 500 kHz-buck converter with a crossover frequency of 70 kHz, this paper shows that the 5 µs-latency of a ΔΣ-analog-to-digital-converter leads to a reduction in phase margin of 126°. The latency is less critical for boost converters because of their inherent lower crossover frequencies. Finally, the paper shows a comparison between analog and digital control of SMPS with regard to chip area and test costs.

In general, the contact force, which is used in controller design for robotic compliant motion, can be either explicitly calculated through complicated computation or measured by expensive force sensors. A force control strategy using the estimated contact force is proposed. The estimation of the contact force and states is primarily based on their previous observer design. It is shown that the controller achieves asymptotic stability.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

For successful object manipulation, the central nervous system must appropriately coordinate digit placement and force distribution. It is known that digit force planning is significantly influenced by previous manipulations even when object properties cannot be predicted on a trial-to-trial basis. We sought to determine whether this effect extends beyond force control to the coordination of digit placement and force. Subjects grasped and lifted an object whose center of mass (CM) was changed unpredictably across trials. Grasp planning was quantified by measuring the torque generated on the object at lift onset. We found that both digit placement and force were systematically affected by the CM experienced on the previous trial. Additionally, the negative covariation between digit forces and positions typically found for predictable CM presentations was also found for unpredictable CM trials. A follow-up experiment revealed that these effects were not dependent on visual feedback of object roll during object lift on the previous trial. We conclude that somatosensory feedback from previous grasp experience alone can affect high-level grasp planning by constraining the relation between digit force and position even when the task behavioral consequences cannot be reliably predicted. As learning of manipulations often involves interactions with objects in novel environments, the present findings are an important step to understanding the control strategies associated with the integration of sensorimotor memories and motor planning.

A digital pulsewidth control loop (PWCL) with a fixed-delay rising edge and digital stability control is proposed for multiphase clock applications. In the duty-cycle tracking mode, the linear range of the input duty cycle was measured to be 28%-70%, with a maximum linearity deviation of 0.5%. In the duty-cycle correction mode, the correction range of the input duty cycle was measured to be 25%-75%, with the output duty cycle within 50 plusmn 0.4%. The chip was fabricated by using a 0.25-mum CMOS process with a 2.5-V supply. The chip area and the power consumption were 200 mumtimes250 mum and 18 mW at an input clock frequency of 1.0 GHz, respectively