Feedforward Torque Control Research Articles

An approach to nonlinear optimisation via set stabilisation of dynamical systems with an application to synchronous machines

An approach to constraint nonlinear optimisation is proposed, where the variables of the objective function and of the constraint function belong to the state of a nonlinear dynamical system. A nonlinear closed-loop feedback system is designed, whose solutions converge to a target set consisting of the optimal points of the underlying optimisation problem. The feedback law for the control input of the nonlinear dynamical system is designed by exact linearisation of a dynamical formulation of a first-order optimality condition. For the problem formulation and the stability analysis of the nonlinear closed-loop feedback system, the notion of V-detectability is considered. An application to energy-optimal feed-forward torque control for different types of synchronous machines is presented, which demonstrates the usefulness of the method. In this regard, anisotropic permanent magnet synchronous machines and electrically excited synchronous machines are covered.

Multiobjective Hyperparameter Optimization of Artificial Neural Networks for Optimal Feedforward Torque Control of Synchronous Machines

Multiobjective Hyperparameter Optimization of Artificial Neural Networks for Optimal Feedforward Torque Control of Synchronous Machines

High Precision Hybrid Torque Control for 4-DOF Redundant Parallel Robots under Variable Load

As regards the impact and chattering of 4-DOF redundant parallel robots that occur under high-speed variable load operating conditions, this study proposed a novel control algorithm based on torque feedforward and fuzzy computational torque feedback hybrid control, which considered both the joint friction torque and the disturbance torque caused by the variable load. First of all, a modified dynamic model under variable load was established as follows: converting terminal load change to terminal centroid coordinate change, then mapping to the calculation of terminal energy, and lastly, establishing a dynamic model for each branch chain under variable load based on the Lagrange equation. Subsequently, torque feedforward was used to compensate for the friction torque and the disturbance torque caused by the variable load. Feedforward torques include friction torque and nonlinear disturbance torque under variable load. The friction torque is obtained by parameter identification based on the Stribeck friction model, while the nonlinear disturbance torque is obtained by real-time calculation based on the modified dynamic model under variable load. Finally, dynamic control of the robot under variable load was realized in combination with the fuzzy computational torque feedback control. The experimental and simulation results show that the motion accuracy of the fuzzy calculation torque feedback and torque feedforward control of the three drive joints of the robot under variable loads is 49.87%, 70.48%, and 50.37% lower than that of the fuzzy calculation torque feedback. Compared with pure torque feedback control, the speed stability of the three driving joints under fuzzy calculation torque feedback and torque feedforward control is 23.35%, 17.66%, and 25.04% higher, respectively.

Nonlinear Modeling, Identification, and Optimal Feedforward Torque Control of Induction Machines Using Steady-State Machine Maps

A novel but simple machine map-based modeling, identification, and optimal feedforward torque control (OFTC) approach for induction machines (IMs) is presented. It is based on, first, a generic, nonlinear transformer-like machine model considering nonlinear flux linkages (with magnetic saturation and cross coupling) and iron losses in the stator laminations in a novel, arbitrarily rotating but unique, robust, and reproducible ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d,q$</tex-math></inline-formula> )-reference frame; second, a holistic machine identification procedure, which evaluates steady-state measurements over a grid of ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d,q$</tex-math></inline-formula> ) stator currents and produces temperature and frequency dependent machine maps, for example, flux linkages, torque, iron resistance, and efficiency; and third, a numerical offline optimization and extraction of different OFTC look-up tables (LUTs) for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">optimal</i> current reference generation depending on reference torque and electrical frequency (and temperature). During the identification, stator winding temperature and electrical stator frequency of the IM are kept constant by an intelligent temperature and the speed control system. The presented measurement results for a squirrel-cage IM confirm that compared to constant flux operation or scalar V/Hz control, efficiency can be increased particularly in part-load operation by up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{7} \,\%$</tex-math></inline-formula> by Maximum Torque Per Losses minimizing copper <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</i> iron losses.

Seamless mode shift control for a new Simpson planetary gearset based dual motor powertrain in electric vehicles

This paper proposes a seamless mode shift control strategy for a Simpson planetary gearset based dual motor powertrain (SPGDMP) which has 6 driving modes. The dynamic model of SPGDMP is built, where the rotational inertia of transmission components, the flexibility of shafts, dynamic response of motor torque and brake pressure, and stick-slipping friction phenomenon of brake are considered. A seamless mode shift control strategy is proposed to avoid power interruption and reduce the vehicle jerk. The mode shift is decoupled to the torque transition process and speed transition process, which lowers the control difficulty. The step function is used to produce the smooth transition trajectories of torque and speed, which eliminates the large vehicle jerk induced by the unsmooth driving torque. In the speed transition process, a combination of speed feedback and torque feedforward control strategy is proposed to track the designed motor speed trajectory and the driver's input torque simultaneously. The simulation results demonstrate that the proposed mode shift control strategy can reduce the peak-to-peak value of vehicle jerk to a value below 2 m/s3.

Dynamics Modeling of a Delta Robot with Telescopic Rod for Torque Feedforward Control

This paper presents dynamics modeling of a Delta robot with three revolute legs and a telescopic rod. Firstly, two generalized coordinate systems are established to describe the relationship between the movement of the telescopic rod and the position of the moving platform, and the telescopic rod system kinematics are established through singularity analysis. Secondly, taking the telescopic rod as the research object, the corresponding dynamics model is established using the Euler–Lagrange method. Moreover, this paper proposes a method to convert the force exerted by the telescopic rod motion on the moving platform into actuator torques. Thirdly, the dynamics model of the Delta robot with a telescopic rod is established, and numerical simulations are performed to demonstrate this approach. Finally, the influence of the telescopic rod on the actuator torques is verified using an experiment. A comparison is drawn between the two dynamics models used in torque feedforward control to validate the proposed dynamics model.

Artificial Neural Network Based Optimal Feedforward Torque Control of Interior Permanent Magnet Synchronous Machines: A Feasibility Study and Comparison with the State-of-the-Art

A novel Artificial Neural Network (ANN) Based Optimal Feedforward Torque Control (OFTC) strategy is proposed which, after proper ANN design, training and validation, allows to analytically compute the optimal reference currents (minimizing copper and iron losses) for Interior Permanent Magnet Synchronous Machines (IPMSMs) with highly operating point dependent nonlinear electric and magnetic characteristics. In contrast to conventional OFTC, which either utilizes large look-up tables (LUTs; with more than three input parameters) or computes the optimal reference currents numerically or analytically but iteratively (due to the necessary online linearization), the proposed ANN-based OFTC strategy does not require iterations nor a decision tree to find the optimal operation strategy such as e.g., Maximum Torque per Losses (MTPL), Maximum Current (MC) or Field Weakening (FW). Therefore, it is (much) faster and easier to implement while (i) still machine nonlinearities and nonidealities such as e.g., magnetic cross-coupling and saturation and speed-dependent iron losses can be considered and (ii) very accurate optimal reference currents are obtained. Comprehensive simulation results for a real and highly nonlinear IPMSM clearly show these benefits of the proposed ANN-based OFTC approach compared to conventional OFTC strategies using LUT-based, numerical or analytical computation of the reference currents.

Feed-forward control of elastic-joint industrial robot based on hybrid inverse dynamic model

A novel feedforward control method of elastic-joint robot based on hybrid inverse dynamic model is proposed in this paper. The hybrid inverse dynamic model consists of analytical model and data-driven model. Firstly, the inverse dynamic analytical model of elastic-joint robot is established based on Lie group and Lie algebra, which improves the efficiency of modeling and calculation. Then, by coupling the data-driven model with the analytical model, a feed-forward control method based on hybrid inverse dynamics model is proposed. This method can overcome the influence of the inaccuracy of the analytical inverse dynamic model on the control performance, and effectively improve the control accuracy of the robot. The data-driven model is used to compensate for the parameter uncertainties and non-parameter uncertainties of the analytical dynamic model. Finally, the proposed control method is proved to be stable and the multi-domain integrated system model of industrial robot is developed to verify the performance of the control scheme by simulation. The simulation results show that the proposed control method has higher control accuracy than the traditional torque feed-forward control method.

Combined Optimal Torque Feedforward and Modal Current Feedback Control for Low Inductance PM Motors

Small sized electric motors providing high specific torque and power are required for many mobile applications. Air gap windings technology allows to create innovative lightweight and high-power electric motors that show low phase inductances. Low inductance leads to a small motor time constant, which enables fast current and torque control, but requires a high switching frequency and short sampling time to keep current ripples and losses in an acceptable range. This paper proposes an optimal torque feedforward control method, minimizing either torque ripples or motor losses, combined with a very robust and computation-efficient modal current feedback control. Compared to well-known control methods based on the Clarke-Park Transformations, the proposed strategy reduces torque ripples and motor losses significantly and offers a very fast implementation on standard microcontrollers with high robustness, e.g., against measurement errors of rotor angle. To verify the accuracy of the proposed control method, an experimental setup was used including a wheel hub motor built with a slotless air gap winding of low inductance, a standard microcontroller and GaN (Gallium Nitride) Power Devices allowing for high PWM switching frequencies. The proposed control method was validated first by correlation of simulation and experimental results and second by comparison to conventional field-oriented control.

Gantry type Lapping Manipulator toward Unmanned Lapping Process for a Large Work Surface

This paper presents a developed manipulator and control method for automatic lapping process applied to a large work surface. A lapping machine consists of a newly designed parallelogram-type 5-axis manipulator and a conventional 3-axis gantry machine. The gantry machine is utilized to precision positioning over a large work area, and the manipulator is controlled by a separate controller for lapping operation in the local surface area which is provided by the CNC controller of gantry machine. The lapping process is, as a first step, needed to remove milling tool marks without injuring original shape, and then to correct the shape error. Wheel compliance becomes different in accordance with the special purpose such as tool mark removal and shape correction. Both processes require high stiffness of the manipulator. In this study, newly designed joints are adopted to secure the stiffness of the joints in both normal and lateral directions. Deadweight of manipulator including wheel motor as well as feed-forward torque control are adopted to suppress the vibration caused by abruptly dynamic cutting force. It was confirmed that the lapping operation was successful in wiping the curved contour without the structural vibration, and that the feed-forward torque control produces twice higher machining efficiency as well as 30% higher surface quality in comparison with the existing compliance control method. The experiment investigated the effects of the abrasive wheel compliance and the dynamic cutting force. In results, the smooth surface was achieved within a satisfied quality level of less than Rz 0.5 μm. It is considered that the proposed manipulator has great potential to be applied in unmanned lapping systems for a large work surface.

Torque Control of a Series Elastic Tendon-Sheath Actuation Mechanism

Tendon-sheath actuation mechanisms can provide compact and lightweight tendon routing. However, torque control of a tendon-sheath actuation system is challenging because of variable friction with respect to the sheath configuration. Model-based feedforward friction compensation algorithms have been developed to accurately deliver desired torque, but it is difficult to apply such algorithms to multi-degrees of freedom (DOFs) systems because of changes in sheath configurations that in turn alter the base tension and friction parameters. In this article, we develop a series elastic tendon-sheath actuation mechanism that allows feedforward torque control in multi-DOFs systems. The mechanism features series elastic elements on the motor side to reduce base tension changes and enable accurate input torque control. Friction is compensated by a feedforward controller with a modeled friction parameter to transmit desired torque to the distal joint under varying sheath configurations. The performance of the proposed series elastic tendon-sheath actuation mechanism is demonstrated in experiments using a control interface for a tele-operation system.

Research on Integrated Control Method for Helicopter/Turboshaft Engine with Variable Rotor Speed Based on the Error Between Engine Required and Real Output Torque

In order to achieve more rapid response control for integrated helicopter/turboshaft engine system with variable rotor speed, an integrated control method based on the error feedforward between engine required and real output torque is proposed. Firstly, based on the principle of incremental nonlinear dynamic inversion, an online acceleration estimation method of gas turbine speed (Ngdot) is proposed to realize the cascade control for turboshaft engine based on Ngdot. Then, a rotor demanded torque predicted model is developed through min-batch gradient descent-neural network. Meanwhile, a feedforward compensation method based on the error between engine required and real output torque is proposed according to the rotor dynamics characteristics of engine output shaft with variable rotor speed to suppress the interference of the rotor demanded power during variable rotor speed. The simulation results show that under different flight conditions, compared with the collective pitch feedforward and the rotor predicted torque feedforward control, the feedforward control method based on the error between engine required and real output torque can effectively reduce the overshoot of the relative speed of power turbine by about 14%. In addition, the settling time of power turbine speed is shorter, and the dynamic performance is superior, which can realize the rapid response control of turboshaft engine better.

ANYexo: A Versatile and Dynamic Upper-Limb Rehabilitation Robot

This letter presents a versatile upper-limb exoskeleton based on low-impedance torque controllable series elastic actuators. This experimental platform is designed to validate novel algorithms and hardware concepts for more autonomous therapy of moderately and severely affected patients with a neural impairment. The design is optimized to achieve a large range of motion (ROM) and robust interaction force control to best mimic the compliant and accurate haptic interaction of therapists. The presented robot covers the relevant ROM required for activities of daily life (ADL) particularly, including poses close to the torso, head, and behind the back. The kinematics are optimized for high manipulability during ADL and low inertia. We use modified modular series elastic actuators that provide the required power and torque control performance. We demonstrate highly transparent behavior up to speeds of 11 rad/s with a feed-forward torque controller based on an accurate dynamic model. The presented robot unites a large ROM with optimized manipulability, high nominal power to weight ratio (111 W/kg), accurate torque control at speeds sufficient for unconstrained recovery of patients, and versatility for a broad variety of experiments in one device. To our knowledge, no other device is tailored to such an extent for this application.

Control of power-augmenting lower extremity exoskeleton while walking with heavy payload

This article presents a design and control framework for a prototype of lower extremity exoskeleton to enhance the human strength during locomotion. The hybrid control strategy is practically applied according to the two gait phases, that is, stance and swing. The weight shift method based on human’s weight shift information was proposed and implemented to acquire the detection of gait phase. In the stance phase, a stiff virtual wall method is applied to support the entire weight of the exoskeleton while carrying a heavy payload. Direct feedback and feed-forward torque control are used to reduce mechanical impedance in the swing phase. In experiments, to verify the performance of the proposed control strategy, a human subject wearing the prototype of power-augmenting lower extremity exoskeleton was able to walk with a 50-kg (110-lb) payload at a maximum speed of 1.67 m/s (6 km/h). Satisfactory results were obtained with regard to walking experiments with the heavy payload.

Power Perturbation Based MTPA With an Online Tuning Speed Controller for an IPMSM Drive System

A novel maximum torque per ampere (MTPA) method based on power perturbation for a field-oriented control interior permanent magnet synchronous motor (IPMSM) drive system is proposed in this study. The proposed MTPA method, which is parameter independent and can improve the motor operation at both start-up and low speed, is designed based on the power perturbation by using the signal injection in the current angle. Moreover, the influence of current and voltage harmonics to the MTPA control can be eliminated effectively. Furthermore, to enhance the robustness of the control system, an online tuning scheme for an integral-proportional controller using a new wavelet fuzzy neural network with disturbance torque feedforward control is developed where the disturbance torque is obtained from an improved disturbance torque observer. Finally, some experimental results using an IPMSM drive system based on a low-price digital signal processor are presented. From the experimental results, the proposed control approach can guarantee the control performance of the speed loop, even under a cyclic fluctuating load.

A power perturbation-based MTPA control with disturbance torque observer for IPMSM drive system

A novel maximum torque per ampere (MTPA) method based on power perturbation for a field-oriented control (FOC) interior permanent magnet synchronous motor (IPMSM) drive system is proposed in this study. The proposed MTPA method is designed based on the power perturbation resulting from the signal injection in the current angle. Moreover, the influence of current and voltage harmonics to the MTPA control can be effectively eliminated. Furthermore, to enhance the robustness of the control system, a real-time design scheme for the integral–proportional (IP) speed controller using a recursive least square (RLS) estimator with disturbance torque feedforward control is developed. The disturbance torque is obtained from an improved disturbance torque observer with online parameters updated. Finally, some experimental results using an IPMSM drive system based on a low-price digital signal processor (DSP) are presented. From the experimental results, the proposed control approach can guarantee the control performance of a speed loop even under a cyclic fluctuating load.

Rate of Torque Development and Feedforward Control of the Hip and Knee Extensors: Gender Differences

ABSTRACTThe purpose of this study was to determine whether women demonstrate decreased rate of torque development (RTD) of the hip and knee extensors and altered onset timing of the vastus lateralis and gluteus maximus during a drop-jump task when compared with men. On average, women demonstrated significantly lower normalized RTD of the hip extensors (women: 11.6 ± 1.3 MVT.s−1, men: 13.1 ± 0.9 MVT.s−1; p ≤ .01); however, there was no significant difference in knee extensor RTD. Women also demonstrated significantly earlier activation of their vastus lateralis (women: 206.0 ± 130.6 ms, men: 80.9 ± 69.6 ms; p ≤ .01) and gluteus maximus (women: 85.7 ± 58.6 ms, men: 54.5 ± 35.4 ms; p = .02). In both men and women, there was a significant negative correlation between the hip extensor RTD and the vastus lateralis electromyographic onset time (men: r = –.386, p = .046; women: r = –.531, p = .008). The study findings suggest that women may utilize a feedforward control strategy in which they activate their knee extensors earlier than men to compensate for deficits in hip extensor RTD. The impaired capacity to rapidly stabilize the hip and knee joints during dynamic maneuvers may contribute to the increased risk of anterior cruciate ligament injury observed in women.

A unified theory for optimal feedforward torque control of anisotropic synchronous machines

ABSTRACTA unified theory for optimal feedforward torque control of anisotropic synchronous machines with non-negligible stator resistance and mutual inductance is presented which allows to analytically compute (1) the optimal direct and quadrature reference currents for all operating strategies, such as maximum torque per current (MTPC), maximum current, field weakening, maximum torque per voltage (MTPV) or maximum torque per flux (MTPF), and (2) the transition points indicating when to switch between the operating strategies due to speed, voltage or current constraints. The analytical solutions allow for an (almost) instantaneous selection and computation of actual operation strategy and corresponding reference currents. Numerical methods (approximating these solutions only) are no longer required. The unified theory is based on one simple idea: all optimisation problems, their respective constraints and the computation of the intersection point(s) of voltage ellipse, current circle or torque, MTPC, MTPV, MTPF hyperbolas are reformulated implicitly as quadrics which allows to invoke the Lagrangian formalism and to find the roots of fourth-order polynomials analytically. The proposed theory is suitable for any anisotropic synchronous machine. Implementation and measurement results illustrate effectiveness and applicability of the theoretical findings in real world.

Development of ankle-less active lower-limb exoskeleton controlled using finite leg function state machine

An electric-powered lower-limb exoskeleton (HLEX-v2) was developed to provide walking assistance to the elderly. It was semianthropomorphically designed with two passive hip roll/yaw joints and two active hip/knee flexion/extension joints with an ankle-less foot. The gait phases of a pilot were estimated through a shoe insole embedded with two force sensing resistors–one to detect the pilot’s toe-contact and another to sense the heel-contact–to generate assistive torques at each active joint. The estimated gait phase indicated that the proposed controller commanded torques at hip and knee joints to achieve control tasks assigned from a developed finite leg function state machine (FLFSM). In the FLFSM, the controlled leg’s task was determined based on estimated gait phases of the leg itself and the contralateral leg. The impedance control and feed forward torque control were low-level control actions for handling force-interaction with the ground. The currents applied to each actuator were regulated with a PI controller based on current feedback sensing to increase the torque exertion bandwidth of the actuators. The proposed walking assistive torque generation control was implemented on the HLEX-v2. Experimental walking data for the robot were collected to verify the effectiveness of the exoskeleton with the walking assistance scheme.

Active torque ripple reduction based on an analytical model of torque

The vibration caused by torque ripple may degrade the performance of drivetrain, thus the reduction of torque ripple are necessary for hybrid electrical vehicle/electrical vehicle application, while an analytical description of torque will be the basis. In this study, two-dimensional Fourier series supplemented by polynomial fitting is introduced to reconstruct the numerical solution of magnetic coenergy (MCE) from finite element analysis. An analytical torque model, which can describe torque ripple precisely at all working points, is derived from the reconstructed MCE. On the basis of the torque model, the expressions of harmonic currents used to reduce torque ripple are obtained. The proposed expression also satisfies the principle of maximum torque per ampere. Then, a feedforward torque controller based on the expression of harmonic currents is introduced. Meanwhile, a feedback torque controller based on a torque observer is developed as a comparison. The results of simulation and experiments show that both two controllers can reduce the torque ripple in steady state, but the feedforward torque controller has obviously better effects when motor speed increases. Furthermore, the feedforward torque controller is also beneficial to decline torque ripple during transient process of torque response.