Inverse System Dynamics Research Articles

A MATLAB toolbox for training and implementing physics–guided neural network–based feedforward controllers

Physics-guided neural networks (PGNNs) enable accurate identification of inverse system dynamics by effectively embedding a known physical model within a neural network (NN), and thereby achieve high performance when implemented as feedforward controllers. However, training PGNNs using existing NN toolboxes is complicated. Therefore, this paper presents a MATLAB toolbox that systematically implements, trains, and validates PGNNs. Dedicated functions implement recent results that have been proposed in literature, i.e., we ensure that the PGNN converges to a value of the cost function that is strictly upperbounded by the value obtained when using only the physical model, while also imposing a form of graceful degradation when the trained PGNN is used on data that was not present in the training data. The toolbox is available at:https://github.com/mbolderman/PGNN-Toolbox/.

Control of biomass grate boilers using internal model control

A new model-based control strategy for biomass grate boilers is presented in this paper. Internal model control is used to control four outputs of the plant and to achieve a control structure with fewer control parameters needing to be experimentally tuned. A nonlinear state–space model describing the essential behaviour of the biomass grate boiler is used for controller design. The inverse system dynamics representing the main part of internal model control are designed with the help of this model. In doing so the properties of differentially flat systems are used. Due to a time delayed input, the inverse system is determined only for three input output channels. The stabilization of the inverse system dynamics, however, is a challenging task. A stabilization method with the help of the time delayed input is suggested and a stability analysis is given. The new control strategy has only three parameters to be tuned, representing a major reduction of complexity in comparison to existing model-based approaches. Finally, experimental results of the implemented control strategy on representative biomass grate boiler with a nominal capacity of 180 kW are presented and compared to an existing model-based control strategy based on input output linearization. The experimental evaluation proves that it is possible to operate the biomass boiler in all load ranges with high efficiency and low pollutant emissions.

Disturbance-Observer-Based Tracking Controller for Neural Network Driving Policy Transfer

The neural network policies are widely explored in the autonomous driving field, thanks to their capability of handling complicated driving tasks. However, the practical deployment of such policies is slowed down due to their lack of robustness against modeling gap and external disturbances. In our prior work, we proposed a planner-controller architecture and applied a disturbance-observer-based (DOB) robust tracking controller to reject the disturbances and achieved zero-shot policy transfer. In this paper, we present our latest progress on improving the policy transfer performance under this framework. Concretely, we applied adaptive DOB, so as to more accurately model the inverse system dynamics and increase the cut-off frequency of the Q-filter in the DOB. A closed-loop reference path smoothing algorithm is introduced to alleviate the step disturbance input imposed by the reference trajectory re-planning. On the neural network control policy side, we applied the parallel attribute networks, a hierarchical modular policy network to dynamically handle various driving tasks. We have carried out various simulations and experiments to validate the capability of our proposed method to achieve sim-to-sim and sim-to-real policy transfer. The proposed method achieves the most outstanding performance among a series of baseline control schemes.

An Inverse Neural Controller Based on the Applicability Domain of RBF Network Models.

This paper presents a novel methodology of generic nature for controlling nonlinear systems, using inverse radial basis function neural network models, which may combine diverse data originating from various sources. The algorithm starts by applying the particle swarm optimization-based non-symmetric variant of the fuzzy means (PSO-NSFM) algorithm so that an approximation of the inverse system dynamics is obtained. PSO-NSFM offers models of high accuracy combined with small network structures. Next, the applicability domain concept is suitably tailored and embedded into the proposed control structure in order to ensure that extrapolation is avoided in the controller predictions. Finally, an error correction term, estimating the error produced by the unmodeled dynamics and/or unmeasured external disturbances, is included to the control scheme to increase robustness. The resulting controller guarantees bounded input-bounded state (BIBS) stability for the closed loop system when the open loop system is BIBS stable. The proposed methodology is evaluated on two different control problems, namely, the control of an experimental armature-controlled direct current (DC) motor and the stabilization of a highly nonlinear simulated inverted pendulum. For each one of these problems, appropriate case studies are tested, in which a conventional neural controller employing inverse models and a PID controller are also applied. The results reveal the ability of the proposed control scheme to handle and manipulate diverse data through a data fusion approach and illustrate the superiority of the method in terms of faster and less oscillatory responses.

Extension of the divide-and-conquer algorithm for the efficient inverse dynamics analysis of multibody systems

This paper presents a new mathematical framework to extend the Generalized Divide-and-Conquer Algorithm (GDCA) for the inverse dynamics analysis of fully actuated constrained multibody systems. Inverse-GDCA (iGDCA) is a highly parallelizable method which does not create the mass and Jacobian matrices of the entire system. In this technique, generalized driving forces and constraint loads due to kinematic pairs are clearly and separately differentiated from each other in the equations of motion. As such, it can be easily used for control scheme purposes. iGDCA works based on a series of recursive assembly and disassembly passes to form and solve the equations governing the inverse dynamics of the system. Herein, the mathematical formulations to efficiently combine the dynamics of consecutive bodies in the assembly pass for the purpose of inverse dynamics analysis are presented. This is followed by generating the disassembly pass algorithm to efficiently compute generalized actuating forces. Furthermore, this paper presents necessary mathematical formulations to efficiently treat the inverse dynamics of multibody systems involving kinematic loops with various active and passive boundary conditions. This is followed by the design of a new strategy to efficiently perform the assembly–disassembly pass in these complex systems while avoiding unnecessary computations. Finally, the presented method is applied to selected open-chain and closed-chain multibody systems.

A larger family of nonlinear systems for the repetitive learning control

A generalization of the PIDρ−1 control has been recently presented in Marino et al. (2012), which guarantees the output tracking of smooth periodic reference signals (with known period) for uncertain minimum phase nonlinear systems in output feedback form with any relative degree ρ≥1. In this note, we show that the repetitive learning control proposed in Marino et al. (2012) also solves the same output tracking problem for a larger class of uncertain nonlinear systems in normal form, provided that the inverse system dynamics satisfy the Demidovich condition on suitable compact sets.

Multiple Fault Isolation to a Servo-Valve Controlled Motor Transmission System

Model based quantitative fault diagnosis procedure is based on generation of fault indicators, structural analysis and finally estimation of parameters. In this article, bond graph modelling is used to describe the system model and generate fault indicators by evaluating a set of Analytical Redundancy Relations (ARR), which are obtained from differentially causalled bond graph model to satisfy inverse system dynamics. Multiple fault case is realised by changing the parameters simultaneously. Thereafter the parameters related only to unstructured part of the fault subspace are estimated by optimising an objective function containing ARRs. Sometimes the derivative form of ARRs creates problem of singularity in estimation, and to avoid such a singularity problem we have estimated the corresponding parameters directly from constraint relations and thereafter those values are called in the main objective function to estimate rest of the parameters. The algorithm provides quicker fault isolation because it does not need several model simulations; thereby making it suitable for real-time process supervision.

Dual‐mode control with neural network based inverse model for a steel pickling process

AbstractThis article describes a novel implementation of the dual‐mode (DM) control utilizing a neural network inverse model on a multivariable process (a steel pickling process). This process is highly nonlinear with variable‐interaction, and is multivariable in nature, hence an accurately nonlinear model is required to provide acceptable control. The requirement of a true analytical inverse can be avoided when neural network models are used; they have the ability to approximate both the forward and the inverse system dynamics. Various changes in the open‐loop dynamics are performed before implementation of the inverse neural network modeling technique. DM control based on neural network inverse model strategy is used to design the controllers to control concentration and pH of the process, which is guaranteed to remove steady‐state offset in the controlled variables to obtain the maximum reaction rate and to comply with limits imposed by legislation. The robustness of the proposed DM control is investigated with respect to changes in disturbances and model mismatch. Comparisons are also made with the conventional inverse neural network controller (NNDIC) and other conventional controller proportional‐integral (PI). Simulation results show the superiority of the DM controller in the cases involving disturbance and model mismatch, while the conventional controller gives better results in the nominal case. Copyright © 2007 Curtin University of Technology and John Wiley & Sons, Ltd.

Flatness-based feedforward control for parabolic distributed parameter systems with distributed control

This paper deals with distributed parameter systems being described by inhomogeneous parabolic partial differential equations in one space dimension with a distributed control. The distributed control is presented by the right part of an equation, i.e. the source function. The source function can depend on the time as well as spatial variable. The approach for design of a feedforward control for the purpose of exact output tracking is presented. The design of the feedforward control is based on the examination of inverse system dynamics. The proposed technique utilizes the method of the variables separation and the representation of a solution by the power series in the time domain. Some examples and numerical simulations are included and demonstrate the efficiency of the proposed approach for developing the feedforward control.

Actuation and Control Strategies for Miniature Robotic Surgical Systems

During the past 20years, tremendous advancements have been made in the fields of minimally invasive surgery (MIS) and minimally invasive, robotically assisted (MIRA) cardiac surgery. Benefits from MIS include reduced pain and trauma, reduced risks of post-operative complications, shorter recovery times, and more aesthetically pleasing results. MIRA approaches have extended the capabilities of MIS by introducing three-dimensional vision, eliminating hand tremors, and enabling the precise articulation of smaller instruments. These advancements come with their own drawbacks, however. Robotic systems used in MIRA cardiac procedures are large, costly, and do not offer the miniaturized articulation necessary to facilitate tremendous advancements in MIS. This paper demonstrates that miniature actuation can overcome some of the limitations of current robotic systems by providing accurate, repeatable control of a small end effector. A 10× model of a two link surgical manipulator is developed, using antagonistic shape memory alloy wires as actuators, to simulate motions of a surgical end-effector. Artificial neural networks are used in conjunction with real-time visual feedback to “learn” the inverse system dynamics and control the manipulator endpoint trajectory. Experimental results are presented for indirect, on-line learning and control. Manipulator tip trajectories are shown to be accurate and repeatable to within 0.5mm. These results confirm that SMAs can be effective actuators for miniature surgical robotic systems, and that intelligent control can be used to accurately control the trajectory of these systems.

Structural Identification of Mir Using Inverse System Dynamics and Mir/Shuttle Docking Data

The objective of this work was to investigate the use of inverse system identification techniques on Mir/Shuttle docking data to identify Mir vibrational characteristics for ultimate application to damage detection. A time-domain technique called a Remote Sensing System was proposed as an approach. The method uses inverse structural dynamics to identify vibrational characteristics of a structure. The Remote Sensing System method was demonstrated with a numerical simulation of Mir/Shuttle docking assuming that sensors were collocated with the Mir docking location. The method was then applied to the combined set of docking data from Mir/Shuttle missions STS-81, STS-89, and STS-91. Overall, the results produced by this work appear to indicate that Mir was in an undamaged state, at least with respect to docking excitation, at the time of STS-91. The significance of the contribution of the Remote Sensing System approach is that it is not affected by the nonstationarity and nonlinearity associated with the Mir/Shuttle docking interface, and docking forces at the interface do not have to be measured.

Implementation of an Inverse-Model-Based Control Strategy Using Neural Networks on a Partially Simulated Exothermic Reactor

Recently, the use of control strategies based upon inverse process models for non-linear systems has been found promising. The requirement of a true analytical inverse can be avoided when neural network models are used; they have the ability to approximate both the forward and the inverse system dynamics. Although many simulation studies have illustrated the use of neural network inverse models for control, very few on-line applications have been reported. This paper describes a novel implementation of a neural network inverse-model based control method on a experimental system—a partially simulated reactor, designed to test the use of such non-linear algorithms. The implementation involved the control of the reactor temperature in the face of set point changes and load disturbances despite the existence of significant plant/model mismatch. Comparison was also made with conventional PID cascade control in several cases. The results obtained show the capability of these neural-network-based controllers and, incidentally, point out the differences between simulation studies and on-line experimental tests. Since the system in this study was only mildly non-linear, in some cases, the performance was comparable to that achieved by classical controllers while in other cases an improved control was achieved.

A simplified hybrid force/position controller method for the walking robots

Force and position sensors have been widely used in robots to realize compliance and precise control. Traditional force/position control methods were studied and developed by the inverse dynamics for decades. Generally speaking, the controller contains two parts: One is the error-driven part that guarantees system stability; another is the identification model of inverse dynamics that can compensate for system influence. In practical control engineering, a system inverse dynamics or its identification model is not easy to obtain, even when using nonlinear estimation methods. Moreover, the complicated control algorithm cannot be implemented in on-board microprocessors because of the limited speed and memory. Thus, a simplified control method using a forward system model is introduced in this paper. Since the direct dynamics of the system can be more easily obtained than the inverse dynamics, this, in turn, simplifies the control structure and increases control speed. Therefore, the proposed control policy has a wider practical application.

LOCALLY ACTIVATED NEURAL NETWORKS AND STABLE NEURAL CONTROLLER DESIGN FOR NONLINEAR DYNAMIC SYSTEMS

A stable neural control scheme using a locally activated neural network has been proposed for a class of nonlinear dynamic systems. The locally activated neural network, for a given input, essentially selects a small subset of the network hidden nodes for output computation using the CMAC-like content addressing mechanism. This network aims to maintain local representations of the system dynamics. Thus, the global control performance in the concerned state space is achieved by the cooperation of many local control efforts and furthermore, real-time control can be facilitated because only a small sized network is involved to control and learn at any given time. The proposed control scheme is composed of two stages: (1) prediction error based learning in which the network attempts to learn the nonlinear basis functions of the plant inverse dynamics by a modified backpropagation learning rule; and (2) tracking error based learning in which the network weights are further fine-tuned using the basis set obtained in (1). This basis set spans the locally partitioned vector space of the system inverse dynamics when the prediction error based learning is achieved within a prescribed error tolerance. For uniform stability, the sliding mode control is introduced as a safety mechanism when the network has not sufficiently learned the plant dynamics yet. With suitable assumptions on the controlled plant, global stability and tracking error convergence proof has been given. Finally, the proposed control scheme is verified with computer simulation.

Optimal Active Control of Nonlinear Vehicle Suspensions Using Neural Networks

This paper analyzes, theoretically and by computer simulation, the capabilities and limitations of neural networks to be used for the identification and optimal control of nonlinear dynamical systems. It is shown how neural networks can be efficiently trained to identify the forward and inverse dynamics of systems and also to work as optimal controllers which minimize some peformance measures of the system to be controlled. The performance of neural networks when applied to the optimal control of nonlinear vehicle suspensions is analyzed and compared with the performance of passive suspensions and that of active suspensions with linear (LQ) controllers designed by linearizing the nonlinear characteristics of the suspensions around the equilibrium point. It is found that nonlinear vehicle suspensions with neuro-control show better performance than suspensions controlled with conventional LQ regulators. Some issues about the implementation of neural networks to improve its convergence and generalization properties are analyzed.

Application of feedforward neural networks to dynamical system identification and control

Methods for identification and control of dynamical systems by adalines, two-layer, and three-layer feedforward neural networks (FNNs) using generalized weight adaptation algorithms are discussed. The FNNs considered contain odd nonlinear operators in both the neurons and the weight adaptation algorithms. Two application examples, each involving a nonlinear dynamical system, are considered. The first is identification of the system's forward and inverse dynamics. The second is control of the system using coordination of feedforward and feedback control combined with inverse system dynamics identification. Simulation results are used to verify the method's feasibility and to examine the effect of ENN parameter changes. Specifically the effect that the type of nonlinear activation functions present in the neurons and the type of nonlinear functions present in the weight adaptation algorithms have on FNN system dynamics identification performance is investigated. >