Model-based Feedforward Control Research Articles

Hardware-in-the-loop dynamic load emulation of robotic systems actuated by fluidic artificial muscles

Hardware-in-the-loop (HIL) testing is a popular control system testing method because it bridges the gap between modeling/simulation and experiments. Instead of designing a full hardware-based experiment to validate the results of a simulation, the plant hardware can be replaced with an emulator device that responds to exogenous inputs and effectively emulates the dynamic behavior of a system. This approach can be more cost-effective and modular, since the emulated plant system can be modeled in a simulation environment, implemented on a simplified piece of hardware and changed quickly without having to fabricate new parts. This paper develops the hardware and control scheme for a certain type of HIL device called a dynamic load emulator that consists of a 1-DOF linear hydraulic dynamometer equipped with in-line sensing to measure both its own position and the force exerted on it by a device-under-test. This measured force is passed to a real-time model of the emulated dynamic system. The model outputs the emulated system position, and a closed-loop controller is used to emulate this position. The emulator controller incorporates both model-based feedforward and standard feedback PI control. This paper characterizes the dynamometer-based dynamic load emulator and its controller, determining its hardware limitations and validating its capabilities when experiencing a force input from a linear spring with known parameters. Additionally, this paper demonstrates the ability of the emulator to represent the dynamics of a 1-DOF robotic joint when actuated by a pair of fluidic artificial muscles (FAMs). The primary contribution of this work is to allow for more comprehensive testing of FAM configurations, topologies, and controllers for a wide range of parameters, because the same hardware can be used to emulate multiple systems. As a result, this work will lead to more cost-effective, time-efficient, and energy-efficient designs of robotic systems and the FAMs used to actuate them.

Optimal iterative feedforward parameter tuning for varying trajectory under actuator constraints

AbstractThis paper presents a feedforward control algorithm that combines the benefits of optimal iterative learning control (OILC) and model‐based feedforward control (MFC) using iterative feedforward tuning and input shaping filter (IFT‐ISF) for industrial motion systems. OILC effectively compensates for tracking errors in repeating tasks under actuator constraints. However, its performance deteriorates when the trajectory changes. In contrast, MFC can achieve high performance for varying trajectory tracking tasks, but its performance may degrade for constrained systems if the control force exceeds the actuator saturation boundary. The proposed algorithm aims to overcome these limitations to achieve optimal trajectory tracking performance for varying trajectories under actuator constraints. Simulation and experimental results demonstrate that the proposed algorithm achieves optimal tracking performance while complying with the actuator constraints. The algorithm provides a data‐driven approach without requiring the tedious process of model identification. By combining the benefits of OILC and IFT‐ISF, the proposed algorithm can achieve high‐performance trajectory tracking for both repeating and varying tasks under actuator constraints, making it suitable for industrial motion systems.

Model-based feedforward control for an optimized manipulation of acoustically levitated spheres

We present a simple dynamic model for predicting the manipulation behavior of an acoustically levitated sphere. The model allows for the calculation of the sphere position over time, which is demonstrated for two manipulation strategies: a straight motion with a constant manipulation velocity and a straight motion in which the sphere acceleration follows a cosine function. The dynamic model as well as the manipulation strategies is verified experimentally in an acoustic levitator system consisting of an array of 16 by 16 ultrasonic transducers emitting at 40 kHz and an opposing reflector. In this system, a glass sphere of a diameter of 2 mm is manipulated horizontally by controlling the phases of the transducers. The sphere motion is recorded using a high-speed camera, and a tracking algorithm is used for capturing the sphere position over time. Moreover, a model predictive control algorithm is applied on a path-following problem to move the sphere along a given reference trajectory by means of a model-based optimal feedforward control. The proposed dynamic model as well as the methodology presented in this paper enables faster manipulation speeds with reduced oscillations during object movement.

Modeling, heat dissipation design, and force tracking control for temperature-dependent hysteresis of magnetorheological damper

The temperature-dependence (T-dependence) characteristics of magnetorheological fluids (MRFs) cause the damping force of magnetorheological dampers (MRDs) to change with temperature. The rapid temperature rise can lead to performance degradation or even failure of MRFs, reduced damping force of MRDs, and decline in control performance. In this paper, numerical simulations and predictions of the temperature rise characteristics of the MRD are performed and heat sinks are designed and optimized. The experimental results verify the efficiency of the simulations and predictions, and the heat sinks can significantly reduce the rate of temperature increase and improve the ability of the damper to operate for long hours. In order to accurately compensate for T-dependence characteristics of the MRD, a T-dependence hysteresis model and a model-based feedforward force tracking control method with disturbance observation of the MRD are proposed and validated by experiments. The experimental results indicate that the proposed T-dependence model has better prediction accuracy than the general hysteresis model, and the feedforward control method achieves good force tracking performance even without expensive force sensors.

A Generalized and Efficient Control-Oriented Modeling Approach for Vibration-Prone Delta 3D Printers Using Receptance Coupling

Delta 3D printers can significantly increase throughput in additive manufacturing by enabling faster and more precise motion compared to conventional serial-axis 3D printers. Further improvements in motion speed and part quality can be realized through model-based feedforward vibration control, as demonstrated on serial-axis 3D printers. However, delta machines have not benefited from model-based controllers because of the difficulty in accurately modeling their position-dependent, coupled nonlinear dynamics. In this paper, we propose an efficient framework to obtain accurate linear parameter-varying models of delta 3D printers at any position within their workspace from a few frequency response measurements. We decompose the dynamics into two sub-models&#x2013;(1) an experimentally-identified sub-model containing decoupled vibration dynamics; and (2) an analytically-derived sub-model containing coupled dynamics&#x2013;which are combined into one using receptance coupling. We generalize the framework by extending the analytical model of (2) to account for differing mass profiles and dynamic models of the printer&#x2019;s end-effector. Experiments demonstrate reasonably accurate predictions of the position-dependent dynamics of a commercial delta printer, augmented with a direct drive extruder, at various positions in its workspace. <i>Note to Practitioners</i>&#x2014;This work aims to equip high-speed 3D printers, like delta machines, with model-based controllers to complement their speed with high-accuracy. Due to the coupled kinematic chains of the delta, complex control methodologies, some of which require real-time state measurements, are often used to achieve satisfactory control performance. Our modeling approach provides an efficient methodology for obtaining accurate linear models without the need for real-time measurements, thus enabling practitioners to design linear model-based feedforward controllers to achieve the high throughput and accuracy desired in additive manufacturing (AM). The models we develop in this paper are intended for use with feedforward vibration compensation methods, which can be beneficial for both industrial-scale AM machines that have high-powered servo motors and feedback controllers, as well as consumer-grade AM machines which use stepper motors in feedforward control.

Observer-Based Control for a Torque Converter Lock-Up Clutch Utilizing a Steady-State Torque Map

Torque converter (TC) slip control is one of the most important ways to improve vehicle fuel economy and ride comfort without changing hardware. Several model-based feed-forward controllers have been proposed to improve control performance. However, model-based controllers depend on a torque map (lookup table) measured in a steady state; thus, they have errors in transient situations. Therefore, this article proposes an observer-based feed-forward controller that utilizes a steady-state torque map. To overcome the limitation of the torque map and unknown road torque, a novel observer is proposed that makes it possible to use both the advantages of a torque map and a vehicle driveline model. The proposed observer can adjust dependency on the map in real time with the observer index. A fuzzy logic-based observer index can obtain near-optimal gain with minimal tuning and low computation. In addition, a real-time TC map-update algorithm using a recursive least square (RLS) method is proposed. As a result, the feed-forward controller is designed considering the error of torque maps. The effectiveness of the proposed observer and feed-forward controller was verified using a simulation based on experimental data from an actual vehicle.

Cascaded iterative learning motion control of precision maglev planar motor with experimental investigation

Cascaded iterative learning control (CILC) is explored for a magnetically levitated (maglev) planar motor to achieve excellent tracking motion performance in this paper. The CILC control method is based on traditional iterative learning control (ILC) with deeper iterations. CILC solves the difficulty of ILC in constructing perfect learning filter and low-pass filter to obtain excellent accuracy. Specifically, in CILC, the traditional ILC strategy is implemented several times by the operation of feedforward signal registering and clearing in a cascaded structure, which makes the motion error reach an accuracy level superior to traditional ILC even though the filters are imperfect. The fundamental principle, convergence and stability of CILC strategy are explicitly presented and analyzed. Through the structure of CILC, the repetitive component of the convergence error can be completely eliminated in theory, while the non-repetitive component is accumulated but the sum is bounded. Simulation investigation and comparative experimental investigation on maglev planar motor are both conducted. The results consistently show that the CILC strategy is not only superior to PID and model-based feedforward control, but also obviously outperforms traditional ILC. The CILC investigations on maglev planar motor also provide a clue that CILC has appreciable application prospect for precision/ultra-precision systems requiring extreme motion accuracy.

Characteristic Prediction and Temperature-Control Strategy under Constant Power Conditions for Lithium-Ion Batteries

Accurate characteristic prediction under constant power conditions can accurately evaluate the capacity of lithium-ion battery output. It can also ensure safe use for new-energy vehicles and electrochemical energy storage. As the battery voltage continues to drop under constant power conditions, the battery current output will accordingly increase, which brings a risk of thermal runaway in instances of weak heat dissipation. Therefore, knowing how to control the battery temperature is very critical for safe use. At present, the model-based method for characteristic prediction and temperature control has been used by most scholars, and that is also the key to this method. This work firstly extends a cell model to a pack-based electrochemical two-dimensional thermal coupling model, considering the heterogeneity of different cells inside the pack, and obtains the model parameters for a prismatic lithium-ion battery with a rated capacity of 42 Ah. Characteristic prediction under constant power conditions is then conducted based on an iterative solution method. Validations of characteristic prediction indicate the convenience of the developed models, with average absolute errors of voltage and temperature less than 36 mV and 0.4 K, respectively, and power error less than 0.005%. Finally, two model-based temperature feed-forward control strategies with lower cooling costs and shorter prediction times were developed based on the battery characteristic predictions, which leaves room for further controller development.

Formation tracking control design for uncertain artificial swarm systems under inequality constraints: Leakage and dead-zone type

The paper proposes a formation tracking control method for the uncertain artificial swarm systems under the inequality constraints. Not only can the agents perform swarm behaviors (e.g., convergence, formation and avoidance of collision), but they can also track the fixed targets in a constrained area (which is formulated as the inequality constraints, such as unilateral constraint and bilateral constraint.). The swarm behaviors are creatively considered as the servo constraints or the control objectives for the swarm agents. Based on the Udwadia–Kalaba (U–K) equation, those prescribed behaviors are realized by a model-based control design (that is the servo constraints force model-based feedforward control). To deal with the inequality constraints in the formation tracking process, a differential homeomorphism transformation is used to relieve the environmental constraints for the swarm agents. Moreover, the uncertainty of the swarm agents (i.e., the parameter uncertainty in modeling and the external disturbances) is considered, which is time-varying and unknown (but bounded). An uncertainty estimation method with dead-zone and leakage term is designed to calculate the possible upper bound of the uncertainty. In virtue of the estimated upper bound of the uncertainty, a robust control is designed for the uncertain swarm agents to obey the prescribed swarm behaviors in the formation tracking task. The system performances of the artificial swarm systems under the proposed control are theoretically guaranteed by a range of rigorous theorems and numerically verified by the simulations of three agents.

Data-Driven Feedforward Parameter Tuning Optimization Method Under Actuator Constraints

Feedforward control includes iterative force injection-based feedforward control and model-based feedforward control. Model-based feedforward control enables high performance for nonrepetitive motions in industrial motion systems. In particular, model-based feedforward control with a parameterized input shaping filter and a feedforward controller can effectively implement trajectory tracking tasks without relying on mathematical models of systems. However, the pre-existing model-based feedforward control does not consider the saturation boundary of the system actuator, which may lead to saturation of the feedforward force for actual systems with actuator constraints. Therefore, this article aims to develop a feedforward control method that obtains high tracking performance for nonrepetitive trajectory under actuator constraints. In particular, a parameterized input shaping and feedforward control method based on basis functions is pursued, which is combined with a data-driven iterative optimization approach to cope with nonrepetitive trajectory tracking tasks and actuator constraints. Simulations and experiments on a motion system confirm the optimal trajectory tracking performance under actuator constraints and robustness to nonrepetitive trajectory.

TOAST: Trajectory Optimization and Simultaneous Tracking Using Shared Neural Network Dynamics

Neural networks have been increasingly employed in Model Predictive Controller (MPC) to control nonlinear dynamic systems. However, MPC still poses a problem that an achievable update rate is insufficient to cope with model uncertainty and external disturbances. In this paper, we present a novel control scheme that can design an optimal tracking controller using the neural network dynamics of the MPC, making it possible to be applied as a plug-and-play extension for any existing model-based feedforward controller. We also describe how our method handles a neural network containing history information, which does not follow a general form of dynamics. The proposed method is evaluated by its performance in classical control benchmarks with external disturbances. We also extend our control framework to be applied in an aggressive autonomous driving task with unknown friction. In all experiments, our method outperformed the compared methods by a large margin. Our controller also showed low control chattering levels, demonstrating that our feedback controller does not interfere with the optimal command of MPC.

Application of Least-Squares Support-Vector Machine Based on Hysteresis Operators and Particle Swarm Optimization for Modeling and Control of Hysteresis in Piezoelectric Actuators

Nanopositioning systems driven by piezoelectric actuators are widely used in different fields. However, the hysteresis phenomenon is a major factor in reducing the positioning accuracy of piezoelectric actuators. This effect makes the task of accurate modeling and position control of piezoelectric actuators challenging. In this paper, the learning and generalization capabilities of the model are efficiently enhanced to describe and compensate for the rate-independent and rate-dependent hysteresis using a kernel-based learning method. The proposed model is inspired by the classical Preisach hysteresis model, in which a set of hysteresis operators is used to address the problem of mapping, and then least-squares support-vector machines (LSSVM) combined with a particle swarm optimization (PSO) algorithm are used for identification. Two control schemes are proposed for hysteresis compensation, and their performance is evaluated through real-time experiments on a nanopositioning platform. First, an inverse model-based feedforward controller is designed based on the LSSVM model, and then a combined feedback/feedforward control scheme is designed using a classical control strategy (PID) to further enhance the tracking performance. For performance evaluation, different datasets with a variety of hysteresis loops are used during the simulation and experimental procedures. The results show that the proposed method is successful in enhancing the generalization capabilities of LSSVM training and achieving the best tracking performance based on the combination of feedforward control and PID feedback control. The proposed control scheme outperformed the inverse Preisach model-based control scheme in terms of both positioning accuracy and execution time. The control scheme that uses the LSSVM based on nonlinear autoregressive exogenous (NARX) models has significantly less computational complexity compared to our control scheme but at the expense of accuracy.

Speed Fluctuation Suppression by Model-Based Feed-Forward Control in Gimbal System With Harmonic Drive

Harmonic drive is usually installed in the gimbal system of single gimbal magnetic suspended control moment gyroscope (SGMSCMG) not only to meet the requirements on the volume and weight but also output large torque. However, its nonlinear transmission characteristics are also introduced into the gimbal system and make the output speed fluctuate, which will seriously affect the output torque accuracy of SGMSCMG. Torque feedback control is an effective technique for achieving high-performance control for the above-mentioned problem. Nevertheless, it is difficult to add torque sensors in the gimbal system. In order to obtain nonlinear transmission torque without torque sensors, a novel online modeling method based on the Lagrange equation is put forward. Besides, to restrain the main torque disturbance, the gear-wave torque model is extracted. According to the above-mentioned models, a model-based feed-forward control method with phase advance is presented. Plentiful simulation and experiments on an SGMSCMG are performed, and the results show that the load speed fluctuation can be effectively suppressed.

Design, analysis, and validation of an orderly recruitment valve for bio-inspired fluidic artificial muscles

Biological musculature employs variable recruitment of muscle fibers from smaller to larger units as the load increases. This orderly recruitment strategy has certain physiological advantages like minimizing fatigue and providing finer motor control. Recently fluidic artificial muscles (FAM) are gaining popularity as actuators due to their increased efficiency by employing bio-inspired recruitment strategies such as active variable recruitment (AVR). AVR systems use a multi-valve system (MVS) configuration to selectively recruit individual FAMs depending on the load. However, when using an MVS configuration, an increase in the number of motor units in a bundle corresponds to an increase in the number of valves in the system. This introduces greater complexity and weight. The objective of this paper is to propose, analyze, and demonstrate an orderly recruitment valve (ORV) concept that enables orderly recruitment of multiple FAMs in the system using a single valve. A mathematical model of an ORV-controlled FAM bundle is presented and validated by experiments performed on a proof-of-concept ORV experiment. The modeling is extended to explore a case study of a 1-DOF robot arm system consisting of an electrohydraulic pressurization system, ORV, and a FAM-actuated rotating arm plant and its dynamics are simulated to further demonstrate the capabilities of an ORV-controlled closed-loop system. An orderly recruitment strategy was implemented through a model-based feed forward controller. To benchmark the performance of the ORV, a conventional MVS with equivalent dynamics and controller was also implemented. Trajectory tracking simulations on both the systems revealed lower tracking error for the ORV controlled system compared to the MVS controlled system due to the unique cross-flow effects present in the ORV. However, the MVS, due to its independent and multiple valve setup, proved to be more adaptable for performance. For example, modifications to the recruitment thresholds of the MVS demonstrated improvement in tracking error, albeit with a sacrifice in efficiency. In the ORV, tracking performance remained insensitive to any variation in recruitment threshold. The results show that compared to the MVS, the ORV offers a simpler and more compact valving architecture at the expense of moderate losses in control flexibility and performance.

Adaptive disturbance observer-based control of hydraulic systems with asymptotic stability

As control precision is the most important indices of control precision, this study concerns with high accuracy tracking control of hydraulic systems. We suggest an adaptive disturbance-observer-based asymptotic tracking control strategy to hydraulic systems for achieving our motivation. It is of note that parameter uncertainty and disturbance are challenges in the area of hydraulic system control. In this study, the time-varying disturbance is compensated by model-based feed-forward control terms which are designed by a sign of error-function-based disturbance observer. To avoid the high learning burden of the disturbance, which is resulted from the parameter uncertainty, online adaptive control is integrated with the mentioned disturbance observer. To guarantee the theoretical feasibility of the proposed controller, the stability analysis Xis accomplished by introducing the Lyapunov stability theory. Compared with previous works reported in the literature, the proposed adaptive disturbance observer-based a controller can achieve global asymptotic stability when the considered systems are subjected to mismatched or match disturbance. The comparative experimental results reveal that the proposed method can obtain state-of-the-art tracking performance for hydraulic systems under the influence of parameter uncertainty and time-varying disturbance.

Model-Based Feedforward Control of an Intra- and Interspecific Competitive Population System

Intra-and interspecific competitive population systems are relevant for a variety of applications, such as bioreactors or wastewater treatment plants. These systems are described by coupled hyperbolic semilinear integro partial differential equations with non-local integral boundary conditions. This type of population system has not been considered in the context of control theory in the literature to date. It is assumed that it is possible to measure both species separately, but only one control input is available, namely the dilution rate. A system analysis allows for the determination of infinitely many, but uniquely determined steady-states that are used to derive nonlinear input-output dynamics via the relation of hyperbolic partial differential equations to integral delay equations. A model inversion yields a feedforward control to control the two different outputs, which are a weighted integral over the population density. This results in a restriction in the choice of reference trajectories due to the undercount of inputs. Simulations show the great potential that can be achieved with model-based feedforward control in the context of population systems.

An adaptive model-based feedforward temperature control of a 100 kW PEM electrolyzer

Polymer Electrolyte Membrane (PEM) electrolyzers will play a central role in future power-to-gas plants. Increasing the performance and scaling of PEM electrolyzers to the MW scale represents significant challenges for existing system components, as well as for optimal operational management. In relation to existing control loops, temperature control turns out to be critical. Due to scaling into higher performance classes and highly dynamic load profiles of green energy sources such as wind power and photovoltaics, the disturbance variable current density has an increasing influence on temperature control. The temperature is an essential operating parameter, especially for PEM electrolyzers, to be able to provide optimum efficiency, safety and prevent premature aging or destruction. In this article, we present an adaptive temperature control with a model-based feedforward control based on a model that considers the dependency of the operating parameters current density and stack temperature. In order to demonstrate the reliability and robustness of the control performance, an experimental validation of the adaptive temperature control with feedforward control is carried out on a 100 kW PEM electrolyzer. In this context, a comparison and an evaluation of the control concept to the existing proportional–integral–derivative (PID) control under highly dynamic load changes from wind power and photovoltaics is performed. Finally, the obtained results are discussed with respect to the aspects of optimal operational management.

Integrated Chassis Control and Control Allocation for All Wheel Drive Electric Cars with Rear Wheel Steering

This study investigates a control strategy for torque vectoring (TV) and active rear wheel steering (RWS) using feedforward and feedback control schemes for different circumstances. A comprehensive vehicle and combined slip tire model are used to determine the secondary effect and to generate desired yaw acceleration and side slip angle rate. A model-based feedforward controller is designed to improve handling but not to track an ideal response. A feedback controller based on close loop observation is used to ensure its cornering stability. The fusion of two controllers is used to stabilize a vehicle’s lateral motion. To increase lateral performance, an optimization-based control allocation distributes the wheel torques according to the remaining tire force potential. The simulation results show that a vehicle with the proposed controller exhibits more responsive lateral dynamic behavior and greater maximum lateral acceleration. The cornering safety is also demonstrated using a standard stability test. The driving performance and stability are improved simultaneously by the proposed control strategy and the optimal control allocation scheme.

Model-based feedforward control for suppressing torque oscillation of electric power steering system

Oscillation suppression is essential for the stability design of electric power steering (EPS) systems. The stability controller module in EPS controller is the key to solve the stability control problem of EPS system. This paper proposes a new method of stability analysis and stability controller module design for EPS systems. Furthermore, the dynamic characteristics of the EPS system are analyzed, and two critical factors on the resulting EPS stability, that is, large assist and variable assist gain are investigated experimentally. The transfer function from steering torque to sensor torque is redefined. A new transfer function is proposed for measuring the effect of variable assist gain on system performance. Based on the above factors and transfer functions, constraints on the stability controller design are proposed. Then the optimal parameters in the controller are obtained by maximizing an objective function including phase margin, gain margin, and crossover frequency. It is concluded from simulations and bench tests that the proposed stability controller can significantly reduce the torque oscillation of the EPS system.

Attaining Ultraprecision Machining by Feed Drive System Stability Control with Piezoelectric Preloading Actuators

In this paper, a variable preload force control structure utilizing piezoelectric actuators (PEAs) is proposed for the stability control of the feed drive system. Three PEAs are installed between the two nuts to exert preload force on the ball screw, leading to an elimination or substantial reduction of the backlash, which is the main cause of instability of feed drives. This results in better machining precision throughout the operation process. In addition, the force analysis of the whole preload feed drive system is established. Moreover, the hysteresis of the PEAs is determined with reference to the Prandtl–Ishlinskii (P-I) model. Lastly, the P-I model-based feedforward controller is applied to the feed drive system to improve the resultant machining precision. Based on the modeling and experiments, to demonstrate the efficacy and high-performance of the proposed P-I model-based control algorithm against conventional PID control system, comparative experiments are conducted, showing satisfactory results.