Nonlinear Feedforward Control Research Articles

Nonlinear feedforward controller design of gasoline engine air-path system for reducing engine torque overshoot

In gasoline engines, the amount of fresh air in the cylinder becomes temporarily excessive owing to the slow response in exhaust gas recirculation (EGR) gas under a high EGR ratio. This phenomenon should be avoided, as it causes an engine torque overshoot because the amount of fuel also increases to follow the stoichiometric ratio, and can cause discomfort to the driver. In this study, we investigate reducing torque overshoot using a feedforward controller, which is a simple and effective method for improving the response of a control system. The feedforward controller is typically designed based on the inverse of the plant model. However, designing a feedforward controller for a high-order and nonlinear plant, such as an engine air-path system, can be challenging. Therefore, we exploit the fact that if a given nonlinear system satisfies the flatness property, a feedforward controller based on the inverse model can be easily obtained. The effectiveness of the proposed feedforward controller is evaluated through simulations.

Output Voltage Precise Tracking Control for Boost Converters Based on Noncausal and Nonlinear Feedforward Control

Output Voltage Precise Tracking Control for Boost Converters Based on Noncausal and Nonlinear Feedforward Control

Output Voltage Precise Tracking Control for Boost Converters based on Noncausal and Nonlinear Feedforward Control

Boost converters are key components of DC power conversion used for electric mobility and renewable energy applications. In addition to constant voltage control of the output, variable voltage control has been attracting attention in recent years for high-efficiency drive of loads. However, the dynamic characteristics of boost converters exhibit nonlinear and nonminimum phase characteristics. Therefore, the inverse model for feedforward control is unstable, making high-precision voltage trajectory tracking control challenging. This study aims to present a noncausal and nonlinear feedforward controller to compensate for the nonlinear and nonminimum phase characteristics of the boost converter and to achieve perfect tracking control with respect to the output voltage trajectory. This study also establishes a method for identifying circuit parameters and deriving the time length of noncausal control input for practical implementation. The effectiveness of this control method is demonstrated by experiments using a boost converter.

Comparison of Deep Learning and Deterministic Algorithms for Control Modeling.

Controlling nonlinear dynamics arises in various engineering fields. We present efforts to model the forced van der Pol system control using physics-informed neural networks (PINN) compared to benchmark methods, including idealized nonlinear feedforward (FF) control, linearized feedback control (FB), and feedforward-plus-feedback combined (C). The aim is to implement circular trajectories in the state space of the van der Pol system. A designed benchmark problem is used for testing the behavioral differences of the disparate controllers and then investigating controlled schemes and systems of various extents of nonlinearities. All methods exhibit a short initialization accompanying arbitrary initialization points. The feedforward control successfully converges to the desired trajectory, and PINN executes good controls with higher stochasticity observed for higher-order terms based on the phase portraits. In contrast, linearized feedback control and combined feed-forward plus feedback failed. Varying trajectory amplitudes revealed that feed-forward, linearized feedback control, and combined feed-forward plus feedback control all fail for unity nonlinear damping gain. Traditional control methods display a robust fluctuation for higher-order terms. For some various nonlinearities, PINN failed to implement the desired trajectory instead of becoming “trapped” in the phase of small radius, yet idealized nonlinear feedforward successfully implemented controls. PINN generally exhibits lower relative errors for varying targeted trajectories. However, PINN also shows evidently higher computational burden compared with traditional control theory methods, with at least more than 30 times longer control time compared with benchmark idealized nonlinear feed-forward control. This manuscript proposes a comprehensive comparative study for future controller employment considering deterministic and machine learning approaches.

Gaussian Processes for Advanced Motion Control

Machine learning techniques, including Gaussian processes (GPs), are expected to play a significant role in meeting speed, accuracy, and functionality requirements in future data-intensive mechatronic systems. This paper aims to reveal the potential of GPs for motion control applications. Successful applications of GPs for feedforward and learning control, including the identification and learning for noncausal feedforward, position-dependent snap feedforward, nonlinear feedforward, and GP-based spatial repetitive control, are outlined. Experimental results on various systems, including a desktop printer, wirebonder, and substrate carrier, confirmed that data-based learning using GPs can significantly improve the accuracy of mechatronic systems.

Realization of Low-Voltage and High-Current Rectifier Module Control System Based on Nonlinear Feed-Forward PID Control

The low-voltage and high-current permanent magnet synchronous generator (PMSG), which has characteristics of high power density, small size, and excellent energy saving, is representative of the generators. As a key module of the integrated DC output system of PMSG, the low-voltage and high-current rectifier module is also a nonlinear time-varying system that is readily influenced by parametric changes and external disturbances. Aiming at the shortcomings of traditional control strategies, this paper proposes a novel low-voltage and high-power rectifier module control strategy based on nonlinear feed-forward PID control. The controller has a wide range of environmental applications because of its greater robustness. At the same time, the introduction of feed-forward control shortens regulation time of the system. Therefore, the combination of the two control methods can improve the dynamic performance of the system without influencing the steady-state performance. The simulation model of an integrated rectifier system based on SVPWM control was constructed by Simulink, which can achieve a rated output of 5 V/300 A. At the same time, the simulation model of the controller is constructed and applied to the rectifier output system of a 5 V/300 A synchronous generator to complete the nonlinear feed-forward PID control. Through the comparison between simulation and experiment, it has been proven that the control method can effectively resist the load disturbances and improve the response speed of the system.

Energy and flow effects of optimal automated driving in mixed traffic: Vehicle-in-the-loop experimental results

This paper experimentally demonstrates the effectiveness of an anticipative car-following algorithm in reducing energy use of gasoline engine and electric Connected and Automated Vehicles (CAV), without sacrificing safety and traffic flow. We implement a Vehicle-in-the-Loop (VIL) testing environment in which experimental CAVs driven on a track interact with surrounding virtual traffic in real-time. We explore the energy savings when following city and highway drive cycles, as well as in emergent highway traffic created from microsimulations. Model predictive control handles high level velocity planning and benefits from communicated intentions of a preceding CAV or estimated probable motion of a preceding human driven vehicle. A combination of classical feedback control and data-driven nonlinear feedforward control of pedals achieve acceleration tracking at the low level. The controllers are implemented in ROS and energy is measured via calibrated OBD-II readings. We report up to 30% improved energy economy compared to realistically calibrated human driver car-following without sacrificing following headway.

Automated nonlinear feedforward controller identification applied to engine air path output tracking

This paper introduces a feedforward control method for physical systems that can be described with linear parameter-varying (LPV) models. The proposed feedforward controller structure is consequently derived from a generic LPV representation and is shown to be identifiable directly from noisy measurement data. The identified structure is advantageous for feedforward control, as using a simple least squares algorithm allows to parameterize basis functions representing the required input trajectory to follow a given output trajectory. Also, with the proposed regularisation, the input trajectory remains bounded even when the physical system exhibits non-minimum phase behaviour. Additionally, the proposed controller structure does not possess states but only considers the inputs and outputs signals and their derivatives, leading to a unique physical interpretation of each controller's parameter. Multiple feedforward controllers identified at various operating points can therefore be directly merged to create a parameter-varying controller. A nonlinear and locally non-minimum phase system is considered in this study, i.e. an engine air path, to evaluate the performances of the proposed feedforward strategy. The controller parameters are first identified from noisy measurement data, and then the proposed feedforward controller is implemented with a feedback controller to track the exhaust pressure and concentration. Using a detailed physical simulation of the engine air path, the proposed feedforward strategy showed encouraging output tracking performances compared to state-of-the-art control methods. The presented feedforward method is shown to be straightforward to identify and calibrate while guaranteeing a contained computational complexity and being applicable to many physical systems thanks to its modularity.

Nonlinear feedforward controller design for air-path system with transport dynamics of external EGR system

Abstract Advanced combustion, such as homogenous charge compression ignition (HCCI), requires precise control of the in-cylinder gas condition. Such advanced combustion does not always result in stoichiometric combustion; therefore, the changes in the oxygen concentration of the burned gas must be considered in the controller design. Furthermore, the changes in the oxygen concentration in the exhaust manifold are transferred to the intake manifold with delay. In this research, the transport dynamics of the exhaust gas recirculation (EGR) path were modeled by a pure time-varying delay and a second-order filter, and the model was used to estimate the oxygen concentration through the EGR valve. The feedforward controller was obtained based on the inverse model, which calculates the throttle and EGR valve positions based on the target values of the intake manifold pressure, EGR ratio, and estimated oxygen concentration at the EGR valve. The control performance of the proposed feedforward controller was evaluated by conducting simulations using both the mean value model and the precise model constructed using 1D simulation software.

Verified Polynomial Controller Synthesis for Disturbed Nonlinear Systems

Abstract We introduce a new control synthesis approach to solve reach-avoid problems occurring in many fields, such as autonomous driving or robot motion planning. Our control approach steers a set of initial states as close as possible to a given target state while provably satisfying constraints on both inputs and states. We compute a control law consisting of a state-dependent, piecewise constant feedforward controller and a continuous feedback controller. The feedforward controller can be polynomial in the state and steers the initial set of states as close as possible to the target state for an undisturbed system, while the feedback controller minimizes the effect of disturbances and abstraction errors. Compared to other formal synthesis approaches, our approach can be verified in polynomial time and generates nonlinear feedforward control laws. The achievable control performance is demonstrated by two use cases.

Flatness Based Control of an Industrial Robot Joint Using Secondary Encoders

Due to their compliant structure, industrial robots without precision-enhancing measures are only to a limited extent suitable for machining applications. Apart from structural, thermal and bearing deformations, the main cause for compliant structure is backlash of transmission drives. This paper proposes a method to improve trajectory tracking accuracy by using secondary encoders and applying a feedback and a flatness based feed forward control strategy. For this purpose, a novel nonlinear, continuously differentiable dynamical model of a flexible robot joint is presented. The robot joint is modeled as a two-mass oscillator with pose-dependent inertia, nonlinear friction and nonlinear stiffness, including backlash. A flatness based feed forward control is designed to improve the guiding behaviour and a feedback controller, based on secondary encoders, is implemented for disturbance compensation. Using Automatic Differentiation, the nonlinear feed forward controller can be computed in a few microseconds online. Finally, the proposed algorithms are evaluated in simulations and experimentally on a real KUKA Quantec KR300 Ultra SE.

A Nonlinear Control Method for Bumpless Mode Transition in Noninverting Buck–Boost Converter

The noninverting buck-boost (NIBB) converter is a step-up and step-down dc-dc converter suitable for applications with a wide input voltage range. However, this circuit will face the problem of operating mode switching when the input voltage is close to the output voltage. Considering this problem, the principles of the NIBB converter are analyzed in this article. The duty cycle combinations of an NIBB converter are analyzed, and an analysis method for the mode transition problem from a geometric perspective is proposed. Using the two-edge pulsewidth modulation method, a novel bumpless mode transition control method is proposed. A nonlinear feedforward controller with hysteresis is designed according to the state equation of the circuit. Moreover, the inductor current reference value is compensated when the mode is switched so that the mode transition problem of the NIBB circuit is effectively solved. In addition, a small-signal analysis of the proposed method is performed. The analysis shows that the proposed method has good stability and dynamic performance in various typical conditions. A 10-kW NIBB prototype is built in this article, and the corresponding experimental scenarios are designed. The experimental results show that compared with the results of unified PI control during the mode transition, the transient oscillation of the output voltage is smaller, and the duration of the transient process is shorter.

Feedforward Compensation of Torque Harmonics in Permanent Magnet Synchronous Machines

This paper presents a method for compensation of torque ripples in electrical drives with permanent magnet synchronous machine. A standard field-oriented current control is complemented by a nonlinear feedforward control that influences the reference voltage. The compensation method has the advantage that it requires very little additional computing power and memory. Harmonic voltage components are provoked in a way that torque ripples are suppressed, while the instantaneous voltage vector magnitude of the nominal control is not changed. Additionally, an algorithm for time-saving identification of the operating point-dependent optimal compensation parameters is proposed.

Towards Safe Neural Network Supported Model Predictive Control

Model Predictive Control has proven to be a universal and flexible method to control complex nonlinear system with guaranteed constraint satisfaction. However, high dependency on model quality often renders it inappropriate for hard to model systems. On the other hand, machine learning methods show great performance when approximating functions based on data. This capability for learning with poor a priori knowledge, however, comes at the cost of low predictability and lack of safety guarantees. To overcome these drawbacks we illustrate how a neural network can be setup as a nonlinear feedforward control that augments the MPC control signal to approximate a desired control behaviour. For instance, it could aim to mimic the control behaviour of a human driver, while the underlying MPC exploits prior knowledge. Moreover, to preserve constraint satisfaction, we suggest to restrict the range of neural network outputs such that it intrinsically satisfies control input constraints. Subsequently, we represent the neural network control signal as a disturbance which enables the application of tube MPC to retain state constraints satisfaction at the cost of introducing some conservatism. We demonstrate these concepts via simulation, test and highlight both the advantages and the drawbacks of the proposed control structure.

Two-degree-of-freedom MIMO control for hydraulic servo-systems with switching properties

Today’s automotive industry is faced with the challenge of increasing the energy efficiency of passenger cars to meet ever tightening emissions regulations. An approach to overcome these challenges is the electrification of auxiliary units of the vehicle, such as the pump drive of a hydraulic servo-system for clutch actuation in automatic transmissions (AT) or dedicated hybrid transmissions (DHT). In this context, the model-based derivation of a nonlinear feedforward control law by application of input–output linearization to a non-flat system, is presented. The underlying model, which shows switching behaviour, is derived by simplification of a physical model of the investigated hydraulic servo-system with switching properties. The control objective consists in providing the required system pressure and volume flow for fast and accurate clutch actuation through operation of several servo-valves and an electric pump drive without using a hydraulic accumulator. In this context, planning of feasible trajectories is discussed for the investigated numerically and physically stiff multi-input multi-output system (MIMO). Additionally, a nonlinear two-degree-of-freedom control concept is designed by extension of the derived nonlinear feedforward controller with a PID feedback loop. The presented control schemes for trajectory tracking are examined in simulation and validated on testbed using real hydraulic hardware.

유전알고리즘을 이용한 로봇 매니퓰레이터의 동적제어기 설계

Robot manipulators are highly nonlinear system with multi-inputs multi-outputs, and various control methods for the robot manipulators have been developed to acquire good trajectory tracking performance and improve the system stability lately. The computed torque controller has nonlinear feedforward control elements and so it is very effective to control robot manipulators. If the control gains of the computed torque controller is adjusted according the payload, then more precise control performance is attained. This paper extends the conventional computed torque controller in the joint space to the Cartesian space, and optimize the control gains for some specified payloads in both joint and Cartesian spaces using genetic algorithms. Also a neural network is employed to have proper control gains for arbitrary payloads using generalization properties of the neural network. Computer simulation results show that the proposed control system for robot manipulators has excellent performance in various conditions.

Control of nonlinear systems exhibiting chaos to desired periodic or quasi-periodic motions

A novel method in the design of controllers to drive general nonlinear systems to desired periodic or quasi-periodic motions is presented in this paper. The viability of the approach is demonstrated by controlling chaotic systems to desired motions. The proposed control system consists of a combination of a nonlinear feedforward controller and a linear feedback controller. The control gains for the feedback controller are determined by performing the stability analysis of the closed-loop systems that contain periodic or quasi-periodic coefficients. For the case of periodic coefficients, stability is determined using the well-known Floquet theory. Since there is no rigorous mathematical theory for the analysis of quasi-periodic systems, an approximate technique has been applied to determine the stability where the coefficients turned out to be quasi-periodic. In this approach, a quasi-periodic system is replaced by an approximate periodic system with an appropriate large principal period such that Floquet theory can be applied. State transition matrices for these closed-loop systems are computed symbolically in terms of the unknown control gains using shifted Chebyshev polynomials and Picard iterations. Stability diagrams obtained from the symbolic approach are used to select control gains to guarantee asymptotic stability of the feedback systems. Three examples of chaotic systems are studied in order to show applicability to a diverse class of problems. In the first case, the chaotic motion of a forced Duffing oscillator is driven to a two-frequency quasi-periodic square wave and a fixed point. In the control to a fixed point, the system is constrained to follow a logarithmic spiral trajectory. The second case involves the control of the chaotic attractor of a parametrically forced Lorenz system to a periodic orbit whose frequency is irrationally related to the parametric excitation frequency. In the last case, the chaotic behavior of a Mathieu–Duffing oscillator is successfully driven to a two-frequency quasi-periodic motion.

A Nonlinear Feedforward Controller Design Taking Account of Dynamics of Turbocharger and Manifolds for Diesel Engine Air-Path System

Abstract In this study, we propose a design method of a model-based nonlinear feedforward controller for a diesel engine air-path system. First, a physical air-path model of the diesel engine was developed. Then, a feedforward controller was developed based on the inverse characteristics of the developed physical model. To improve the transient responses of the boost pressure and EGR ratio, the response delay of the turbocharger and manifolds dynamics were considered while designing the feedforward controller. The effectiveness of the proposed method was evaluated by conducting experiments using a real diesel engine. The experimental results indicated a good tracking performance for both the boost pressure and EGR ratio.

Optimized Control Based on Nonlinear Modelling and Parameter Estimation of the Electro-Hydraulic Servo System

In this paper, a nonlinear physical model of the electro-hydraulic system is built and described in Bond Graph in order to show its physical structure and flow of energy. The nonlinear model is simplified based on response bandwidth of different parts of system and nonlinear degree. A series of typical parameters of the model are chosen based on the effect on nonlinear response of system and estimated with the experiment response. A simple and useful model based nonlinear feedforward PID control methods is proposed based on the steady state response of system and dynamic stribeck friction force. The simulation and experiment results of parameter estimation and feedforward control are presented, which shows that the model response with estimated parameters can fit the experimental data very well, and the simulation and experiment response of the optimized control can eliminate the nonlinear response very well. Therefore, the nonlinear model and control method used in this paper have a guiding significance and application value, and have theory value for the further research of hydraulic servo system with the similar structure.

Linear Time-Variant Vehicle Trajectory Guidance with Nonlinear Inversion-Based Feedforward Control

Abstract This work presents a two-degree-of-freedom (2DOF) control concept for vehicle trajectory guidance for automated driving on highways consisting of a nonlinear feedforward control and a linear time-variant feedback controller. To obtain a linear time-variant system of the error dynamics the nonlinear vehicle model is linearized along a given trajectory. To relieve the feedback controller future knowledge of the vehicle movement contained in the trajectory is used to create a nonlinear inversion-based feedforward control. Finally, the control concept is applied in a sophisticated simulation environment and compared to a nonlinear benchmark controller. In addition, model states are chosen in a way that all required signals can be obtained by state-of-the-art hardware of production vehicles.