Full Nonlinear Dynamic Model Research Articles

Dynamics of a large-diameter and multi-section pipeline inspection gauge when crossing obstacles

The dynamic behavior generated by the collision between multi-section Pipeline Inspection Gauge (PIG) and obstacles inside the pipeline is highly complex. A double section PIG is connected through a double universal joint and is divided into front section and rear section. The transmission patterns of vibration and their effects between the two sections are not yet fully known. This study investigates the vibration response and transmission law of a large-diameter and multi-section PIG when crossing obstacles. By constructing a high fidelity, full size, full factor nonlinear multi-system dynamic model of double section Φ1219mm PIGs, the changes in vibration acceleration of the PIG under different operating speeds are simulated. A full-size traction experimental setup has been built. The simulation results are compared with traction experiment and field experiment. The findings indicate that the sudden change in axial acceleration caused by collision is mainly concentrated in the frequency range of 0–50 Hz.

Component sizing and sensitivity analysis of design parameters of a hydraulic-pneumatic regenerative braking system for heavy duty vehicles

A regenerative hydraulic-pneumatic braking system for trucks or busses must allow recovery of braking energy in both high energy/low power situations, such as long downhill grades, and low energy/high power situations, such as those typical of urban traffic. Proper component sizing must get the best out of both situations. The main contribution of this work is the development of a component sizing strategy that will greatly accelerate the development of designs for a given target. Once components are defined, subsequent studies can be performed under dynamic conditions to refine the design, including improving local and higher-level controls. The design strategy presented is applied to a 12-ton commercial vehicle and its behavior is then simulated using a full nonlinear dynamic numerical model previously validated against a laboratory prototype. The efficiencies predicted by the design method deviate only by 3.1% and 6.7% from the results of the dynamic model for urban and highway traffic, respectively, which is reasonable for the design phase of a hybrid hydraulic-pneumatic powertrain. The component equations and computational strategy can also be used for sizing other hydraulic or pneumatic system architectures.

Cooperative Localization of 3D Vehicle Networks - The Dynamic Model

Cooperative localization (CL) algorithms have mainly focused on two-dimensional (2D) vehicle models and have almost uniformly employed only the kinematic model with velocities as inputs, making these algorithms unsuitable for force control problems. We have previously extended a CL algorithm to include a three-dimensional (3D) vehicle kinematic model with the use of quaternions to avoid singularities. In this paper, we extend the algorithm to a full 3D nonlinear dynamic vehicle model, again using quaternions. We evaluate the effectiveness of a CL algorithm and assess its benefits, when the full dynamic model is employed, by running a series of Monte Carlo type simulations with multiple relative pose measurements.

Nonparametric Method for Predicting the Trajectory of an Actively Maneuvering Vessel for Unmanned Aerial Vehicle Landing

The article is devoted to the development of algorithms for predicting the trajectory of maneuvering objects based on nonparametric systems theory. The analysis of uncertainties affecting the modeling of the movement maneuvering water objects is presented. An overview of parametric, nonparametric and combined methods for predicting maneuvering water objects trajectory is given. The problem of high-precision autonomous control of the landing unmanned aerial vehicles on the landing vessel in the conditions of its irregular movement caused by meteorological conditions and active maneuvering is being solved. The method for predicting the trajectory of a vessel’s movement based on solving direct problems of dynamics using nonparametric systems theory is proposed. The advantages of the proposed method are that it’s not affected by model errors, due to the fact that it is based only on a retrospective analysis of several consecutive values of the spatial vessel coordinates. The proposed method differs from similar nonparametric methods in that it does not require statistical calculations, own training, or time-consuming tuning. The method does not imply the solution of identification model parameters, state and control actions problems and can be applied with any unknown linearizable input control actions, including when the model of the vessel’s motion dynamics is not identifiable. The results of numerical modeling for solution the problem of predicting the trajectory of an actively maneuvering small-sized landing vessel using a full nonlinear dynamic model with six degrees of freedom are presented. The studies carried out confirm the efficiency, adequacy and very fast adjustment of the developed method under conditions of complete parametric and nonparametric uncertainty. The proposed method can be used to predict the trajectory of any vehicle under the condition of linearizability of its model and control signals over the observed time interval.

Multi-Rate Control Design Leveraging Control Barrier Functions and Model Predictive Control Policies

In this letter we present a multi-rate control architecture for safety critical systems. We consider a high level planner and a low level controller which operate at different frequencies. This multi-rate behavior is described by a piecewise nonlinear model which evolves on a continuous and a discrete level. First, we present sufficient conditions which guarantee recursive constraint satisfaction for the closed-loop system. Afterwards, we propose a control design methodology which leverages Control Barrier Functions (CBFs) for low level control and Model Predictive Control (MPC) policies for high level planning. The control barrier function is designed using the full nonlinear dynamical model and the MPC is based on a simplified planning model. When the nonlinear system is control affine and the high level planning model is linear, the control actions are computed by solving convex optimization problems at each level of the hierarchy. Finally, we show the effectiveness of the proposed strategy on a simulation example, where the low level control action is updated at a higher frequency than the high level command.

6-DOF formation keeping control for an invariant three-craft triangular electromagnetic formation

Spacecraft relative motion with inter-craft electromagnetic force has distinct advantages, and its invariant shapes that are convenient for formation keeping ensure some potential significant applications. However, the electromagnetic actuators affect both the relative trajectory and attitude motion, complicating related researches on issues of invariant shape design and formation control. In this paper, the formation keeping problem for an invariant three-craft triangular electromagnetic formation is investigated on the basis of a 6-DOF full nonlinear dynamic model. Moreover, a combined control scheme consisting of feed-forward and feed-back control components is proposed to handle the high nonlinearity, strong coupling, model uncertainties and external disturbances. The feed-forward component is obtained through desired invariant shape design which is complicated by the coupling and superposition effects of any two distinct magnetic dipoles, and the feed-back component is developed with a combination of linear feed-back controller by the LQR method and active disturbance rejection by the extended state observer. Finally, the numerical simulation is presented to verify the feasibility and validity of the proposed 6-DOF combined control scheme.

Adaptive Path-Following Control for an Unmanned Surface Vessel Using an Identified Dynamic Model

This paper proposes a path-following control method for an unmanned surface vessel (USV) based on an identified dynamic model. To handle the USV dynamic model effectively, a three degree-of-freedom model is employed instead of a full nonlinear dynamic model and linearized at specific equilibrium condition. The linearized model is identified with real data from several experiments by utilizing a particle swarm optimization method. Then, based on the identified model, an adaptive control algorithm is proposed to follow several waypoints and velocity command. The proposed control method utilizes virtual control input, dynamic surface control method, and adaptive terms to handle matched and unmatched uncertainties simultaneously. The overall closed-loop stability is analyzed by introducing deadzone errors composed of tracking error and saturation function. Finally, some experiment with a remodeled commercial fishing boat are conducted and analyzed to validate the performance of the proposed methods.

Continuous nonlinear asymptotic tracking control of an air-breathing hypersonic vehicle with flexible structural dynamics and external disturbances

In this paper, the tracking control problem of an air-breathing hypersonic vehicle with structural flexibility is addressed. Due to the harsh high Mach flight condition, the influence associated with the dynamic flexible modes of the hypersonic vehicle cannot be neglected. These flexible dynamic modes, which are affected by the vehicle’s states and control surface deflections, can be viewed as an internal dynamics associated with the system outputs. A new nonlinear robust continuous tracking controller is developed to drive the vehicle’s outputs, which include the vehicle’s velocity, altitude, and attack angle, to track the desired time-varying trajectories in the presence of flexible structural dynamics, parametric uncertainties, and external nonvanishing disturbances. A Lyapunov-based stability analysis is employed to prove that the proposed control design can achieve asymptotic tracking while keeping the internal dynamics to be bounded-input/bounded-output stable. Numerical simulations are performed on the full nonlinear dynamic model to demonstrate the tracking performance of the controller, and highlight the robustness with respect to parametric uncertainties and external disturbances.

Nonlinear dynamic model identification methodology for real robotic surface vessels

This paper presents a methodology for identifying the nonlinear dynamic model of underactuated surface vessels for the purpose of model-based controller design. The methodology outlines the required tests that need to be performed and the formulations that need to be used for sequentially identifying the model parameters one by one. The identification methodology is performed on a robotic vessel by testing in outdoor environments and the accuracy of the dynamic model is verified. The physical control inputs to the vessel are a propeller rotational speed and a rudder angle. 3 degrees of freedom are assumed for the nonlinear dynamic model of the surface vessel. Finally, an approach is proposed that discusses how the identified full nonlinear dynamic model can be used for control design. Results of typical closed-loop control tests are presented.

RTDS Implementation of Lyapunov Controller in Feedback Linearized Induction Motor Drive

Most of the stability study of induction motor is based on conventional steady state torque-speed characteristics. Stability study during transient conditions and rigorous stability analysis based on full nonlinear dynamical model are rather rare in literature. Global asymptotic stability of induction motor in the sense of Lyapunov is analyzed in this paper considering the full nonlinear dynamical model in stationary α-β reference frame. Controller is designed based on Lyapunov theorem. Stability of the closed loop system is investigated. Lyapunov controller is implemented in Real Time Digital Simulator (RTDS). Simulation and experimental results with Lyapunov controller are compared with those obtained using P-I controller

A DYNAMIC PROGRAMMING BASED PATH-FOLLOWING CONTROLLER FOR AUTONOMOUS VEHICLES

The problem of path following for autonomous vehicles under adversarial behaviour is considered. The objective is to keep the cross-track error to the reference path inside a given tolerance interval. The adversarial behaviour models system uncertainty and unknown or poorly estimated bounded disturbances to ensure that the concept of weakly invariant set is used, i.e., the set of states that the vehicle may enter while ensuring that the cross-track error will never exceed the tolerance interval. Two modes of operation are then considered: when the vehicle is inside the invariant set, the objective is to stay inside it while minimizing a combination of the actuation effort and cross-track error; otherwise, the objective becomes to reach the invariant set in minimum time. Each mode corresponds to a different optimal control problem which is dealt independently; thus, there is one different control law for each mode. The control laws are synthesized using a dynamic programming approach. Simulation results with a full nonlinear dynamical model illustrate the performance and robustness of the control strategy.

A Study of the Lyapunov Stability of an Open-Loop Induction Machine

The induction motor is widely utilized in industry and exists in a plethora of applications. Until the last 20 years or so, it was primarily used in an open-loop fashion (i.e., balanced sinusoidal voltages, constant load torque and viscous friction) with its inherent stability counted on to allow operation over a wide range of operating conditions. Unlike classical arguments based on the steady-state torque-slip curve, a rigorous analytical stability argument using the full nonlinear dynamical model is presented. In particular, conditions for global asymptotic stability of the induction motor in the sense of Lyapunov are given in terms of the motor parameters, operating slip, and synchronous frequency.

A new strategy for minimum usage of external yaw moment in vehicle dynamic control system

Due to the loss of vehicle directional stability in emergency maneuvers, a new complete desired model for vehicle handling based on the linear two-degrees-of-freedom (2DOF) model and tire/road conditions is presented to be tracked by the direct yaw moment control (DYC) system. In order to maintain the vehicle actual motions, yaw rate and side-slip angle, close to the proposed desired responses without excessively large external yaw moment, a complete linear quadratic (LQ) optimal problem is formulated and its analytical solution is obtained. Here, the derived control law is evaluated and its different versions are discussed. It is shown that the side-slip tracking by DYC is more effective than the yaw rate control to stabilize vehicle motions in nonlinear regimes. Also, optimal property of the control law provides the possibility of reducing the external yaw moment as low as possible, at the cost of some admissible tracking errors. Simulation studies of vehicle handling, with and without control, have been conducted using a full nonlinear vehicle dynamic model. The results, obtained during various maneuvers, indicate that when the proposed optimal controller is engaged with the model, improvements in the handling performance through a reduced external yaw moment can be acquired.

A response spectral decomposition approach for the control of nonlinear mechanical systems

This study investigates a control methodology for dynamic systems based on representing all possible system responses under all possible values of the control variables. The underlying idea is to extend the system along the 'control dimension' and explicitly account for the dependence of the system state on control variables. A spectral discretisation along the 'control dimension' is employed. The optimal control values are chosen to obtain the desired parameterised system response. This approach has the advantage of allowing an inexpensive search for the optimal control values at each time increment without having to run the full nonlinear dynamic model. Numerical studies for the control of linear and nonlinear quarter-car models riding on various terrain profiles show promising results.

Floating Time Algorithm for Time Optimal Control of Multi-Body Dynamic Systems

Moving a dynamic system in minimum time from a given initial state to a desired final state on a prescribed path is one of the oldest and most enduring technological dreams of the scientific and industrial communities. In this research, the problem of bounded-input time optimal control for applied multi-body dynamic systems subject to a full nonlinear dynamical model is solved. To solve the problem, an innovative method, called the ‘floating-time’ method is introduced and utilized. Compared to traditional methods, the floating-time method is an applied method not based on variational calculus. It can be applied to the full nonlinear model of the dynamical system and can handle static and dynamic constraints defined by differential or algebraic equations. The problem of time optimal control is as follows. Find the control law of bounded inputs that drive a given multi-body dynamic system (such as the gripper of a manipulator) along a pre-specified trajectory (in either configuration space or generalized coordinate space) from a given initial position to a given final position, minimizing the time of the motion as a performance index. Using variable time increments, the equations of motion of the system will be reduced to a set of algebraic equations. Searching for a set of time increments (floating-times) that make the equations to exert the maximum available effort produces the minimum possible floating-times, and minimizes the total time of motion. The applicability of the method will be shown by using three examples: a point mass sliding on a rough surface, a 2R robotic manipulator, and the well-known Brachistochrone.

Mixture ratio control of liquid propellant engines

PurposeDevelopment and application of a new systematic approach for design of a control system in order to control the mixture ratio of liquid propellant engines.Design/methodology/approachThe design approach is based on a full nonlinear dynamic model of the engine, and the controller design method is based on describing function models of the engine coupled with the factorization theory. The presented systematic design procedure is comprised of five primary steps. The developed software for the design approach is in the MATLAB environment.FindingsIt is found that the presented design approach may successfully be used to control the mixture ratio of a class of liquid propellant engines whose control loops are decoupled. The performance and robustness of the designed controller is found to be satisfactory.Research limitations/implicationsAt present, the research is limited to liquid propellant engines whose control loops are decoupled.Practical implicationsThe major outcome of this research is that complicated hydromechanical control valves that are used to control the mixture ratio may be replaced by simple microprocessor based servomechanisms that drive simple valves. This will allow for the engine to accept various set point values for mixture ratio as is required in multi‐regime engines.Originality/valueThis is the first paper in the area of mixture ratio control of a liquid propellant engine that is based on the application of describing function approach coupled with the factorization theory.

A HAPTIC EXCAVATOR SYSTEM WITH ACTIVE MASSES UNDER SLIDING MODE PD FORCE/FORCE-POSITION CONTROL

We present a haptic interface-based excavator training system. This system is based on the full nonlinear excavator dynamic model which mimics an industrial excavator, and six degrees of freedom haptic interface. The interface is characterized of been conformed by two controlled prismatic joints that compensate the gravitational effects leaving the full power of the actuators to kinesthetic sensations transmission. The control of gravity compensation is based in the gravitational force vector of the dynamic model. On the other hand the excavator control is carry out through a robust, model free second order sliding mode force-position controller. We present and discuss simulation results of the whole excavator training system.

Efficient synthesis model for bowed strings using a nonlinear bow–string interaction model

A digital simulation method for bowed strings was developed which combines features of preexisting ‘‘digital waveguide’’ and ‘‘commuted synthesis’’ methods. In both methods, sampled acoustic traveling waves are explicitly modeled in the string, and string losses are lumped at one or two points along the string for computational efficiency. In the digital waveguide case, the bow–string interaction model is based on the theory of McIntyre, Schmacher, and Woodhouse [J. Acoust. Soc. Am. 74 (1983)]. The commuted synthesis model [J. Smith, Int. Computer Music Conf., pp. 64–71 (1993)] interchanges the order of the string and body (assumed linear and time invariant), and therefore cannot support a nonlinear bow–string interaction model. However, according to theory and measurement of bow–string interaction, disturbances sent out by the stick–slip process along the string are fundamentally impulsive in nature. The proposed method consists of a full nonlinear dynamic model for the bow and string, without body, followed by an ‘‘impulse prioritizer,’’ which detects the most important impulsive events reaching the bridge, followed by a commuted synthesis model which drives a second string model with body impulse-responses initiated at the time and amplitude of each high-priority pulse.

Nonlinear Model Predictive Control with State and Parameter Estimation

Abstract Among nonlinear predictive control techniques, nonlinear quadratic dynamic matrix control is one of the most attractive mainly for the small additional computational demand with respect to its linear counterpart. However, in order to use a full first principle nonlinear dynamic model in the computation of the control actions, the addition of a state estimator to the algorithm is required. In this paper it is proposed to include parameter estimation in the estimator in order to avoid the problems connected with parametric uncertainty. The main issues connected with the choice of the parameters to be estimated for systems with a large number of uncertain parameters are addressed with reference to a terpolymerization reactor. Applications to this case study show that the modified technique offers a major improvement in performance with a minimal increase in computational complexity.

Adaptive explicit force control of position-controlled manipulators

This article presents a new adaptive outer-loop approach for explicit force regulation of position-controlled robot manipulators. The strategy is computationally simple and does not require knowledge of the manipulator dynamic model, the inner-loop position controller parameters, or the environment. It is shown that the control strategy guarantees global uniform boundedness of all signals and convergence of the position/force regulation errors to zero when applied to the full nonlinear robot dynamic model. If bounded external disturbances are present, a slight modification to the control scheme ensures that global uniform boundedness of all signals is retained and that arbitrarily accurate stabilization of the regulation errors can be achieved. Additionally, it is shown that the adaptive controller is also applicable to robotic systems with PID inner-loop position controllers. Computer simulation results are given for a Robotics Research Corporation (RRC) Model K-1207 redundant arm and demonstrate that accurate and robust force control is achievable with the proposed controller. Experimental results are presented for the RRC Model K-1207 robot and confirm that the control scheme provides a simple and effective means of obtaining high-performance force control. © 1996 John Wiley & Sons, Inc.