Feedforward Part Research Articles

H∞ Tracking Control for Linear Discrete-Time Systems: Model-Free Q-Learning Designs

In this letter, a novel model-free Q-learning based approach is developed to solve the H ∞ tracking problem for linear discrete-time systems. A new exponential discounted value function is introduced that includes the cost of the whole control input and tracking error. The tracking Bellman equation and the game algebraic Riccati equation (GARE) are derived. The solution to the GARE leads to the feedback and feedforward parts of the control input. A Q-learning algorithm is then developed to learn the solution of the GARE online without requiring any knowledge of the system dynamics. Convergence of the algorithm is analyzed, and it is also proved that probing noises in maintaining the persistence of excitation (PE) condition do not result in any bias. An example of the F-16 aircraft short period dynamics is developed to validate the proposed algorithm.

GRU-Type LARC Strategy for Precision Motion Control With Accurate Tracking Error Prediction

To simultaneously achieve accurate tracking error prediction, rigorous motion accuracy, and certain robustness to parameter variations and unknown disturbances, this article proposes a data-based learning adaptive robust control (LARC) strategy based on gated recurrent unit (GRU) neural network. Firstly, parameter adaptive control and robust control are utilized to guarantee the robustness against parametric uncertainties and unknown disturbances. A GRU neural network is then constructed and capable of precisely predicting the tracking error after training with data collected from a linear-motor-driven stage. Essentially, the GRU network can be viewed as a data-based model, which captures the tracking error dynamic characteristics and provides a prediction even before implementing the real trajectory. Consequently, a reference modification and a feedforward compensation part can be formed, which is the significant part of the whole LARC control structure. Comparative experimental investigation not only validates the effectiveness of the tracking error prediction ability, but also demonstrates the practically satisfactory transient/steady-state tracking performance of the proposed control strategy.

A learning-based optimal tracking controller for continuous linear systems with unknown dynamics: Theory and case study

In this article, a novel continuous-time optimal tracking controller is proposed for the single-input-single-output linear system with completely unknown dynamics. Unlike those existing solutions to the optimal tracking control problem, the proposed controller introduces an integral compensation to reduce the steady-state error and regulates the feedforward part simultaneously with the feedback part. An augmented system composed of the integral compensation, error dynamics, and desired trajectory is established to formulate the optimal tracking control problem. The input energy and tracking error of the optimal controller are minimized according to the objective function in the infinite horizon. With the application of reinforcement learning techniques, the proposed controller does not require any prior knowledge of the system drift or input dynamics. The integral reinforcement learning method is employed to approximate the Q-function and update the critic network on-line. And the actor network is updated with the deterministic learning method. The Lyapunov stability is proved under the persistence of excitation condition. A case study on a hydraulic loading system has shown the effectiveness of the proposed controller by simulation and experiment.

Robust dynamic positioning of autonomous surface vessels with tube-based model predictive control

This paper proposes two robust dynamic positioning (DP) approaches for autonomous surface vessels when full states are measurable and when only partial states are available with measurement errors. High fidelity nonlinear hydrodynamics are considered which are approximated as linear models in the local area of DP setpoint. The linearization errors are seen as bounded unmodeled dynamics and are accommodated in the tube-based model predictive control (MPC) together with environmental disturbances. The tube-based MPC controller contains all the possible uncertain trajectories in a tube that is based on a precomputed robust positive invariant set and a nominal trajectory solved online. The total controller consists of a feedforward part compensating the predicted environmental forces, a nominal part guiding the vessel towards and stabilizing it at the origin, and an affine feedback part bounding the uncertain vessel trajectory within the tube. Furthermore, an output feedback robust DP controller is proposed by utilizing a simple Luenberger observer to estimate the system states when full states are not available. The resultant estimation and measurement errors are also incorporated in the tube-based MPC. Simulation results show that the proposed full state and output feedback robust DP controllers can achieve the DP goals within system constraints.

Nonlinear Noncausal Optimal Control of Wave Energy Converters Via Approximate Dynamic Programming

This article proposes a novel nonlinear receding horizon optimal control algorithm for wave energy converter (WECs) with nonlinear dynamics. It is well accepted that the WEC control problem is essentially a noncausal constrained optimal control problem, where the energy output can be improved by incorporating the short-term wave prediction into the control synthesis. Inspired by this fact, we suggest a new nonlinear noncausal optimal control (NNOC) for WECs based on the principle of approximate dynamic programming, which can, first, explicitly use the wave prediction to improve the energy conversion efficiency; second, handle the state and control input constraints; third, reduce the computational burden. Different to the existing linear noncausal optimal control, the derived Hamilton-Jacobi-Bellman equation for NNOC does not have an analytic solution. To tackle this problem, a critic neural network (NN) is adopted to approximate its solution in a receding horizon manor. The weights of NN are determined via a policy iteration algorithm. The resulting NNOC consists of a causal state feedback part and a noncausal feedforward part to explicit incorporate wave prediction information. Numerical simulations are provided to verify the efficacy of the proposed NNOC method.

An optimal control strategy for a heat pump in an integrated solar thermal system

In this paper, an optimal control strategy is developed for managing a heat pump in an integrated solar thermal system. Solar thermal systems usually operate with both feedback and feedforward controllers. The focus of many existing studies in solar thermal system applications has been on the feedback part, while less effort has been made to improve the performance of the feedforward part. This paper introduces a novel robust feedforward controller as a sub-controller of an optimal controller for operating a heat pump integrated with the solar thermal system. In a simulation environment, the optimal control structure is implemented, and the performance of the robust feedforward controller is compared with a simple feedforward controller. Regarding the electrical power consumption, the simulation results demonstrate that the optimal control structure with the proposed robust feedforward controller outperforms the control structure with the simple feedforward controller.

From Manoeuvre Assistance to Manoeuvre Automation

One of the greatest challenges in shipping automation is the automatic manoeuvring in areas with high safety standards which are executed today exclusively by nautical officers with appropriate expertise. Precise manoeuvre plans and suitable control solutions are missing because the human operators act according their mental strategies. The presented approach for automated manoeuvring primarily bases on a complex dynamic motion model of a specific vessel. This model is adapted and used to plan a complete manoeuvre sequence considering the common nautical guidelines and the vessel characteristics. The resulting digital manoeuvre plan forms the basis for the assistance during manual manoeuvring as well as the automatic manoeuvring. Prognosticated weather conditions can be involved already during the planning. For automatic manoeuvring, the deduced manoeuvre trajectory is implemented into the feed-forward part of velocity control. The entire control structure is cascaded in outer trajectory controller and inner velocity controller. The described approach was successfully applied for large vessels in ship handling simulator for automatic collision avoidance and port manoeuvres.

Online speed optimization with feedforward of unmanned sailboat via extremum seeking without steady-state oscillation

Concentrated on the problem of steady-state oscillation of the traditional extremum seeking algorithm (ESA) that it is not beneficial to the speed optimization of unmanned sailboat, a novel speed optimization scheme with feedforward of unmanned sailboat via extremum seeking without steady-state oscillation (ESWSO) is proposed. This scheme consists of feedforward and feedback control: the feedforward part firstly presets the initial sail angle of attack according to an approximate piecewise constant function of the sailing speed polar diagram, its main function is avoid the large deviation of the longitudinal speed from the optimal value. Subsequently, the feedback part fine-tunes the speed to reach the optimal value through the extremum seeking (ES) control. In the process of continuously optimizing longitudinal speed, a functional relationship between the excitation signal amplitude and the extremum estimation error is constructed to eliminate the steady-state oscillation. Besides, the rigorous stability Proof of the scheme is given. Finally, taking a 12-m class unmanned sailboat as the simulation object, the results show that the optimization scheme can effectively eliminate steady-state oscillation and enable the sailing speed to reach the ideal optimal value, as well as has a high control accuracy and strong robustness.

A novel control solution for improved trajectory tracking and LVRT performance in DFIG-based wind turbines

This paper presents a new control strategy for the rotor side converter of Doubly-Fed Induction Generator based Wind Turbine systems, under severe voltage dips. The main goal is to fulfill the Low Voltage Ride Through performance, required by modern grid codes. In this respect, the key point is to limit oscillations (particularly on rotor currents) triggered by line faults, so that the system keeps operating with graceful behavior. To this aim, a suitable feedforward-feedback control solution is proposed for the DFIG rotor side. The feedforward part exploits oscillation-free reference trajectories, analytically derived for the system internal dynamics. State feedback, designed accounting for control voltage limits, endows the system with robustness and further tame oscillations during faults. Moreover, improved torque and stator reactive power tracking during faults is achieved, proposing an exact mapping between such quantities and rotor-side currents, which are conventionally used as controlled outputs. Numerical simulations are provided to validate the capability of the proposed approach to effectively cope with harsh faults.

Linear Optimal Noncausal Control of Wave Energy Converters

This paper addresses the fundamental theoretical development of a linear optimal noncausal control for wave energy converters (WECs) in a closed analytic form. It is well known that the WEC control is a noncausal control problem, i.e., the future wave information contributes to the present control action. This paper provides a reliable, efficient, and simple linear optimal controller with guaranteed stability for the WEC control problem. The proposed WEC linear optimal control consists of a causal linear state feedback part and an anticausal linear feedforward part to incorporate the influence of future incoming waves. The stability of the closed-loop WEC control system with the proposed linear optimal controller is proven. The contribution of the noncausal term using wave prediction information to the optimal control and the energy output is analyzed quantitatively. The proposed linear controller can be more preferred when constraint satisfaction becomes a less important issue for mild sea states and some well-designed WECs with an ample operation range. The proposed optimal control strategy can be extended for a generic class of energy maximization problems. Numerical simulations are presented to justify the efficacy of the proposed WEC optimal control.

Hybrid Feedback-Feedforward Fuzzy Control of PEM Fuel Cell Air Feed System with Electromagnetic Field Optimization

Optimal air feed control of PEM fuel cell system is a very important issue to prevent stack degradation and maximize the net power output of the fuel cell stack. The control objective is to adjust the oxygen excess ratio at the required reference value to avoid the oxygen starvation at sudden current demand preventing the fuel-cell stack damage. This paper proposes a new controller which combines fuzzy feedback and fuzzy feedforward to eliminate the effect of the disturbance. The feedback part comprises a fuzzy PID controller and the feedforward part comprises a single input single output fuzzy controller. Simultaneous optimization of the controller parameters is accomplished using a new optimization algorithm called electromagnetic field optimization (EFO). EFO is a new physics-inspired evolutionary algorithm with a high level of cooperation between population members. This paper is the first use of the EFO algorithm for control applications and fuzzy controller optimization with the application to PEMFC air feed system. Simulation results show the effectiveness of the proposed controller by improving the transient response and regulating the oxygen excess ratio at the required value.

Open-Closed-Loop Iterative Learning Control for Linear Systems With Iteratively Variable Trail Lengths

This paper addresses the open-closed-loop iterative learning control (ILC) issue for linear systems with iteratively variable trail lengths. Due to the varying trail lengths in iteration domain, some tracking information would be lost at the previous iterations. To compensate the absent information, an open-closed-loop ILC scheme composing of a feed-forward ILC part and a feedback control part is designed. The convergence of ILC tracking error in mathematical expectation sense is guaranteed by the feed-forward part. The tracking information of the current iteration is employed by feedback control part to compensate the missing tracking information at the previous iterations. To deal with the iteratively variable trail lengths, a modified tracking error at desired trail length is adopted in the designed ILC scheme. It is shown that the mathematical expectation of tracking error is convergent to zero. Two illustrative examples are carried out to show the effectiveness of the proposed ILC schemes.

Min-Max Differential Dynamic Programming: Continuous and Discrete Time Formulations

In this work, the first min-max Game-Theoretic Differential Dynamic Programming (GT-DDP) algorithm in continuous time is derived. A set of backward differential equations for the value function is provided, along with its first- and second-order derivatives without assuming proximity of the initial nominal controls to the optimal controls. The corresponding update laws for both the minimizing and maximizing controls are also derived. For comparison, the derivation of the GT-DDP algorithm in discrete time is presented in order to better elucidate the differences between the continuous and discrete time formulations. The effect of the game-theoretic formulation in the feed-forward and feedback parts of the optimal control policies is analyzed, and the discrete and continuous time GT-DDP algorithms are compared through numerical examples. Experimental results using a quadrotor demonstrate the superiority of GT-DDP in handling model uncertainties and external disturbances over the standard DDP algorithm.

Conditional neural sequence learners for generating drums’ rhythms

Machine learning has shown a successful component of methods for automatic music composition. Considering music as a sequence of events with multiple complex dependencies on various levels of a composition, the long short-term memory-based (LSTM) architectures have been proven to be very efficient in learning and reproducing musical styles. The “rampant force” of these architectures, however, makes them hardly useful for tasks that incorporate human input or generally constraints. Such an example is the generation of drums’ rhythms under a given metric structure (potentially combining different time signatures), with a given instrumentation (e.g. bass and guitar notes). This paper presents a solution that harnesses the LSTM sequence learner with a feed-forward (FF) part which is called the “Conditional Layer”. The LSTM and the FF layers influence (are merged into) a single layer making the final decision about the next drums’ event, given previous events (LSTM layer) and current constraints (FF layer). The resulting architecture is called the conditional neural sequence learner (CNSL). Results on drums’ rhythm sequences are presented indicating that the CNSL architecture is effective in producing drums’ sequences that resemble a learnt style, while at the same time conform to given constraints; impressively, the CNSL is able to compose drums’ rhythms in time signatures it has not encountered during training (e.g. 17/16), which resemble the characteristics of the rhythms in the original data.

Gaussian Process Regression Feedforward Controller for Diesel Engine Airpath

Gaussian Process Regression (GPR) provides emerging modeling opportunities for diesel engine control. Recent serial production hardwares increase online calculation capabilities of the engine control units. This paper presents a GPR modeling for feedforward part of the diesel engine airpath controller. A variable geotmetry turbine (VGT) and an exhaust gas recirculation (EGR) valve outer loop controllers are developed. The GPR feedforward models are trained with a series of mapping data with physically related inputs instead of speed and torque utilized in conventional control schemes. A physical model-free and calibratable controller structure is proposed for hardware flexibility. Furthermore, a discrete time sliding mode controller (SMC) is utilized as a feedback controller. Feedforward modeling and the subsequent airpath controller (SMC+GPR) are implemented on the physical diesel engine model and the performance of the proposed controller is compared with a conventional PID controller with table based feedforward.

Adaptive Proportional-Derivative Sliding Mode Control Law With Improved Transient Performance for Underactuated Overhead Crane Systems

In this paper, an adaptive proportional-derivative sliding mode control U+0028 APD-SMC U+0029 law, is proposed for 2D underactuated overhead crane systems. The proposed controller has the advantages of simple structure, easy to implement of PD control, strong robustness of SMC with respect to external disturbances and uncertain system parameters, and adaptation for unknown system dynamics associated with the feedforward parts. In the proposed APD-SMC law, the PD control part is used to stabilize the controlled system, the SMC part is used to compensate the external disturbances and system uncertainties, and the adaptive control part is utilized to estimate the unknown system parameters. The coupling behavior between the trolley movement and the payload swing is enhanced and, therefore, the transient performance of the proposed controller is improved. The Lyapunov techniques and the LaSalle U+02BC s invariance theorem are employed in to support the theoretical derivations. Experimental results are provided to validate the superior performance of the proposed control law.

Evaluation of an advanced model reference sliding mode control method for cardiac assist device using a numerical model.

In this study, the physiological control algorithm using sliding mode control method is implemented to track the reference input signal. The controller is developed using feed‐forward part, reference model, and steady‐state flow estimator. The proposed control method is evaluated using a dynamic heart‐pump interaction model incorporating descriptions of the cardiovascular system – rotary blood pump. The immediate response of the controller to preload as well as afterload was studied. Stability and feasibility of the control system were demonstrated through the tests. The results showed that the present controller, which allows the left ventricular to automatically adjust to the right ventricular output, reduces the risk of suction.

Feedforward-feedback control of a solid oxide fuel cell power system

One of the main challenges for wide-spread utilization of the solid oxide fuel cell (SOFC) power systems is how to achieve high electrical efficiency without increasing the degradation rate of the fuel cells. To run the SOFC power system at high efficiency over a long period of time, properly designed controllers are indispensable.Although a number of various approaches to control SOFC have been proposed so far, it seems that the design of control system, along with simple tuning procedure, has not been treated in a consistent manner. This issue is addressed in the present paper resulting in a feedforward-feedback control structure. The feedforward part is based on the stoichiometry of electro-oxidation, reforming and combustion reactions, which allow immediate response to variable current demand. The feedback part performs additional fine adjustment of fuel and air supply in order to minimize the undesired system temperatures variations. The selection of pairings of manipulated and controlled variables for control is based on physical knowledge of the system. Input/output pairing for single-loop feedback control is assessed by the relative gain analysis. An efficient procedure for tuning the parameters of the feedback controllers is suggested, relying on simple open-loop step responses of the system.The proposed low-level control is assessed on a detailed physical model of a 2.5 kW SOFC power system by simulating two nonstationary load regimes. Simulations show that the control provides a robust operation under large load variations while meeting the operating constraints. Due to its simplicity, the control is feasible for implementation on a real SOFC system.

A New Hybrid Active Noise Control System with Convex Combination of Time and Frequency Domain Filtered-X LMS Algorithms

A conventional single-channel feedforward active noise control (ANC) system encounters noise from multiple sources. In many cases, there is a reference signal that is independently available which is correlated with the ambient noise. However, in some situations, a portion of the noise generated is uncorrelated with the reference signal. In this paper, a new hybrid ANC (HANC) system is proposed using a convex combination of time and frequency domain Filtered-X LMS (FXLMS) algorithms. The feedforward part uses a time domain FXLMS (TDFXLMS) algorithm to control disturbances that are correlated with the reference noise and the feedback part uses a multiresolution analysis-based frequency domain wavelet packet FXLMS (WPFXLMS) algorithm to control the uncorrelated disturbances encountered during the operation of an ANC system. An extra adaptive filter is used to smoothen the error signal in the HANC system. An effort is made to exploit the benefits of the structural design and time–frequency domain signal processing techniques for active control of disturbances that are both correlated and uncorrelated with the reference noise. As a result of the convex combination of the TDFXLMS and WPFXLMS algorithms in a HANC system, the proposed method is successful in canceling the disturbances encountered by the ANC system from multiple noise sources.

Two Low Complexity MRC and EGC Based Receivers for SC-FDE Modulations with Massive MIMO Schemes

Massive multiple-input and multiple-output (MIMO) schemes involving several tens or even hundreds of antenna elements are pointed as one of the key technologies for 5G systems. However the huge capacity gains attainable by these schemes, are only possible with receivers able to cope with the frequency selective fading that may affect the signals. These systems can be combined with single-carrier with frequency domain equalization (SC-FDE) schemes to improve the power efficiency in uplink due to the low envelope fluctuations. However, when more antennas are involved in the communication link, channel matrix size grows and the complexity involved in equalization process can be an obstacle to power consumption and low latency. In this paper we will focus on the equalization applied in massive MIMO schemes, more specifically in two new low complexity receivers based on an iterative block decision feedback equalizer (IB-DFE) that avoid matrix inversion operation by replacing in the equalizer the feedforward part by an equal gain combiner (EGC) or a maximum ratio combiner (MRC) module.