Third-order System Research Articles

Informative Order-Reduction of Underdamped Third-Order Systems

Model order reduction simplifies the understanding of a given system and minimizes the simulation studies computational burden. A new order reduction method that depends on a predetermined normalized error of the transient performance indices is introduced. Ten percent and five percent error criteria in modeling and analyzing the transient performance of the third-order system are considered to have an accurate study. All sufficient special conditions and general rules required to achieve precise order reduction are determined. This work focuses on underdamped third-order systems without zeros. Third-order systems with three real poles are also analyzed for the study completeness. The relationships between the characteristic equation parameters are identified and the range in which the reduction is accurately valid is clearly specified. Each approximation or order reduction is studied separately in terms of the transient response characteristics: rise time, settling time and percentage overshoot. The comparison shows the effectiveness of the proposed method.

Generating Infinitely Many Coexisting Attractors via a New 3D Cosine System and Its Application in Image Encryption

In this paper, a new third-order chaotic system which has extremely multistability is constructed by introducing the boosted control of cosine function. In comparison with other chaotic systems of extremely multistability, the proposed chaotic system can spontaneously generate the infinitely many coexisting attractors towards two directions of the phase plane. It indicates the proposed system can output more chaotic sequences of different amplitudes at the same time. This peculiar physical phenomena is very interesting and worth studying. Relative to original chaotic system, the chaos characteristic of the proposed system is obviously enhanced, the value of max Lyapunov exponent is increased significantly and the complexity value was higher. In particular, many periodic windows of the original chaotic system become chaos. It means the proposed chaotic system has better chaotic characteristics. If the new system is applied to the field of cryptography, it would be a better system model as a pseudo-random signal generator (PRSG). Then, the new image encryption algorithm is designed based on the proposed discrete system, and its safety performance is tested. The experimental results demonstrate the feasibility of its application in the field of cryptography.

A Light Space Manipulator with High Load-to-Weight Ratio: System Development and Compliance Control

In order to meet the requirements of the space environment for the lightweight and load capacity of the manipulator, this paper designs a lightweight space manipulator with a weight of 9.23 kg and a load of 2 kg. It adopts the EtherCAT communication protocol and has the characteristics of high load-to-weight ratio. In order to achieve constant force tracking under the condition of unknown environmental parameters, an integral adaptive admittance control method is proposed. The control law is expressed as a third-order linear system equation, the operating environment is equivalent to a spring model, and the control error transfer function is derived. The control performance under the step response is further analyzed. The simulation results show that the proposed integral adaptive admittance control method has better performance than the traditional method. It has no steady-state error, overcomes the problems caused by nonlinear discrete compensation, and can facilitate analysis in the frequency domain, realize parameter optimization, and improve calculation accuracy.

A consistently fast and accurate algorithm for estimating camera pose from point correspondences

This paper presents an accurate and simultaneously efficient algorithm for the Perspective-n-Point (PnP) problem that estimates the absolute pose of a fully-calibrated camera from given 3D-to-2D point correspondences. Previous works typically use the depth of each 3D point to formulate the PnP problem, which will bring extra variables. In contrast, the presented algorithm does not involve any depth factor. By introducing the Cayley–Gibbs–Rodriguez (CGR) parameterization, the modified formulation is first compressed to a nonlinear least-square cost function that only depends on three unknown rotation parameters and a known symmetric coefficient matrix. The Gröbner basis method is then adopted to find a set of solutions for the rotation parameters by solving a third-order polynomial system arising from the first-order optimality conditions of the cost function. Lastly, the rotation and translation are efficiently computed by back-substitution. Furthermore, a novel approach is developed for handling singularities of the CGR parameterization. It is improved by applying fixed pre-rotations, as opposed to randomly generated rotations in previous works, to 3D points. This improvement will facilitate the calculation of the coefficient matrix involved in a cost function when re-solving the PnP problem. Extensive experiments on both simulated and real data demonstrate that the presented algorithm can achieve the state-of-the-art accuracy with reduced computational requirements.

RBF Neural Network Sliding Mode Control Method Based on Backstepping for an Electro-hydraulic Actuator

Aiming at the interference problem and the difficulty of model parameter determination caused by the nonlinearity of the valve-controlled hydraulic cylinder position servo system, this study proposes a radial basis function (RBF) neural network sliding mode control strategy based on a backstepping strategy for the electro-hydraulic actuator. First, the non-linear system model of the third-order position electro-hydraulic control servo system is established on the basis of the principle analysis. Second, the model function RBF adaptive law and backstepping control law are designed according to Lyapunov’s stability theorem to solve the problem of external load disturbance and modelling uncertainty, combined with sliding mode control strategy and virtual control law. Finally, simulation and experiment on MATLAB Simulink and semi-physical experimental platform are accomplished to show the effectiveness of the proposed method. Moreover, results show that the designed controller has high tracking accuracy to the given signal.

Harmonic tremor model during the 2011 Shinmoe-dake eruption, Japan

Summary The Shinmoe-dake volcano started with three sub-Plinian eruptions from 26 to 27 January 2011, followed by a magma effusive stage from 28 to 31 January 2011, and Vulcanian eruptions occurred frequently during 1 to 10 February 2011. During the magma effusive and Vulcanian stages, multiple episodes of harmonic tremors were observed at stations near the summit crater. Although harmonic tremors have been observed at various volcanoes worldwide, the source mechanism remains poorly understood. This paper proposes a source model for harmonic tremors, which is composed of a nonlinear viscous fluid flow in a flexible channel. A simple lumped parameter model is used to consider the process. The dynamics are described by a third-order system of ordinary differential equations using model variables for a cross-sectional area of the constricted segment and the fluid velocities in the upstream and downstream tubes. This model produces various kinds of trajectories for self-sustained oscillations that change the reservoir pressure connected on the upstream channel of the model. Linearization analysis around the stationary point and global analysis employing nullcline planes reveal the mechanism of self-sustained oscillations of the system qualitatively. To consider both the frequency peaks of the harmonic tremor and the characteristics of observed phase spectra, the qualitative characteristics of an observed phase portrait are compared to those of a simulated one. This tremor model simulates the frequency peaks and the phase portraits of typical harmonic tremors observed during the 2011 Shinmoe-dake eruption. Because this model involves several geometrical configuration parameters, it has the potential to reveal the source mechanism of various kinds of harmonic tremors.

Parametric Blending of Hole Patches Based on Shape Difference

A triangular mesh obtained by scanning 3D models typically contains holes. We present an effective technique for filling a hole in a triangular mesh in geometric modeling. Simple triangulation of a hole is refined and remeshed iteratively to generate an initial patch. The generated patch is then enhanced to become a target patch by minimizing the variation of principal curvatures. In discrete approximation, this produces a third-order Laplacian system of sparse symmetric positive definite matrix, and the symmetry can efficiently be used to find the robust solutions to the given Laplacian system. Laplacian smoothing of the target patch is defined as a source patch. The shape difference between two corresponding vertices of the source and the target patches is measured in terms of Euclidean distance and curvature variation. On the basis of the shape difference and a user-specified control parameter, different blending weights are determined for each vertex, and the final patch is generated by blending two patches. We demonstrate the effectiveness of our technique by discussing several examples. The experimental results show that our technique can effectively restore salient geometric features of the original shape.

High Performance of an Adaptive Sliding Mode Controller under Varying Loads for Lifting-Type Autonomous Grounded Robot

To work in shared space with humans, autonomous systems must carry unknown loads in predefined missions. With the conventional control scheme, the grounded robot would suffer unstable motion and imprecise tracking performance. To overcome these challenges, in this paper, a novel controller using an adaptive sliding mode for autonomous grounded robots (AGR) is proposed. This control strategy takes into consideration uncertain characteristics, varying loads, and external disturbances. To analyze the tracking performance precisely, the overall error of motion system is decoupled into two subsystems where the second-order system is related to the angular tracking error and the third-order system is associated with the linear one. Initially, the dynamics model of the grounded robot is established containing different elements of nonlinear forces in order to address the technical problems. Then, the system state equation of the autonomous system is mentioned to indicate the theoretical characteristics. Based on the proposed controller, the stability of the system is validated by the Lyapunov theorem. From the results of numerical tests, three practical situations consisting of separately linear and circular trajectories with varying loads and an S-curve trajectory of a working map are suggested. The tracking performance validates that the proposed control scheme is, in various scenarios, robust, effective, and feasible. From these superior outcomes, it can be determined obviously the property of our works in accommodating the variations of cargo from applications in distribution centers, material transportation, or handling equipment.

Metode Tuning Operating Range Fuzzy PID Controller pada Sistem Orde Tiga

This research discusses the development of a model Fuzzy Proportional, Integral, Derivative (Fuzzy PID) controller models and self-tuning. This method has been implemented in the third-order system of Differential Equations, as a sample implementation of a PID controller. The methods self-tuning known are fuzzy rules, membership function (MF), and scaling factor. The focus of the discussion in this research is to introduce self-tuning to the operating range (OR) setting of MF. Previous research has succeeded in converting a PID controller to a Fuzzy Logic Controller (FLC) which is in accordance with the PID structure. The FLC has three inputs and one output as in the PID controller, hereinafter referred to as Fuzzy PID controller. Knowledgebase on the FLC structure of three inputs one output is expressed in the form of cubic fuzzy associative memory (FAM). The conversion was done by mapping errors, integrals error, derivative errors and outputs of PID controller into the OR of MF Fuzzy input/output. The size of the OR conversion value on the MF fuzzy input was set, so the response transient is set-to-point. While the OR value of the MF fuzzy output was fixed as a limitation. Improved settling time was reached up to 75.3% and percent overshoot was reduced by 57.7% in Fuzzy PID with PID controller. The output signal from the Fuzzy PID controller showed the smallest amplitude of 24.12, while the PID controller was 32.53. The amplitude unit depends on the Fuzzy PID controller parameters when it applied the real plant. The third-order Fuzzy PID controller has been successfully simulated in Simulink/Matlab.

Characteristic analysis of a simple fractional-order chaotic system with infinitely many coexisting attractors and Its DSP implementation

A new simple third-order chaotic system is proposed. The numerical solution of the proposed chaotic system is calculated by using the Adomian decomposition method. The phenomena of infinitely many coexisting attractors is found in this new chaotic system. This interesting physical phenomenon don’t disappear after fractional-order processing. Conversely, with the order of fractional-order system changes, it shows more complex dynamical characteristic than the original system. In particular, the dynamical behavior of the new fractional-order system is analyzed by using the methods of bifurcation diagram, complexity. Finally, the chaotic attractors are physically implemented by DSP experiment. An extremely simple chaotic system as the demonstration of the fractional-order characteristic, it is of great significance to the application of the special chaotic system in related fields.

A New Chaotic Jerk System with Double-Hump Nonlinearity

In this paper, we report a new third-order chaotic jerk system with double-hump (bimodal) nonlinearity. The bimodal nonlinearity is of basic interest in biology, physics, etc. The proposed jerk system is able to exhibit chaotic response with proper choice of parameters. Importantly, the chaotic response is also obtained from the system by tuning the nonlinearity preserving its bimodal form. We analytically obtain the symmetry, dissipativity and stability of the system and find the Hopf bifurcation condition for the emergence of oscillation. Numerical investigations are carried out and different dynamics emerging from the system are identified through the calculation of eigenvalue spectrum, two-parameter and single parameter bifurcation diagrams, Lyapunov exponent spectrum and Kaplan–Yorke dimension. We identify that the form of the nonlinearity may bring the system to chaotic regime. Effect of variation of parameters that controls the form of the nonlinearity is studied. Finally, we design the proposed system in an electronic hardware level experiment and study its behavior in the presence of noise, fluctuations, parameter mismatch, etc. The experimental results are in good analogy with that of the analytical and numerical ones.

Theory of the perceived motion direction of equal-spatial-frequency plaid stimuli.

At an early stage, 3 different systems independently extract visual motion information from visual inputs. At later stages, these systems combine their outputs. Here, we consider a much studied (>650 publications) class of visual stimuli, plaids, which are combinations of 2 sine waves. Currently, there is no quantitative theory that can account for the perceived motion of plaids. We consider only perceived plaid direction, not speed, and obtain a large set of data exploring the various dimensions in which same-spatial-frequency plaids differ. We find that only 2 of the 3 motion systems are active in plaid processing, and that plaids with temporal frequencies 10 Hz or greater typically stimulate only the first-order motion system, which combines the plaid components by vector summation: Each plaid component is represented by a contrast-strength vector whose length is contrast-squared times a factor representing the relative effectiveness of that component's temporal frequency. The third-order system, which becomes primary at low temporal frequencies, also represents a plaid as 2 vectors that sum according to their contrast strength: a pure plaid in which both components have equal contrast and a residual sine wave. Second-order motion is irrelevant for these plaids. These principles enable a contrast-strength-vector summation theory for the responses of the first-order and third-order motion systems. With zero parameters estimated from the data, the theory captures the essence of the full range of the plaid data and supports the counterintuitive hypothesis that motion direction is processed independently of speed at early stages of visual processing. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Binary memory with orthogonal eigenspaces: from stable states to chaotic oscillations

This short paper demonstrates numerically and experimentally observed transitions between the stable states, regular and chaotic oscillations in the case of state representations of binary memory transformed into the Jordan form. Math model of original memory describes simple anti-series connection of two resonant tunneling diodes (RTDs). Derived third-order dynamical system is analyzed with respect to global behavior and, consequently, implemented as lumped analog circuit with piecewise linear (PWL) vector field. Oscilloscope screenshots prove that chaotic motion of binary memory is robust.

Multi-robot formation control based on high-order bilateral consensus

A high-order bilateral consensus robot formation control protocol for multi-agent systems is proposed in this paper. Considering the relationship between the state of the information exchange topology and derivatives, a third-order bilateral consistency protocol is presented and is extended it to a higher order bilateral consensus protocol. First, sufficient conditions for the third-order multi-agent system are given to achieve the bilateral consensus control protocol, and the system’s asymptotical stability is also achieved by adjusting the feedback system gain parameters. Then, by further studying the cohesive relationship between each state variable of the third-order protocol and the gauge transformation, the sufficient conditions of the higher order system are also provided. Finally, by applying the third-order control protocol to the control of multi-robot formation, the general control scheme of robot formation is given and the control of robot formation is successfully achieved.

Coexisting modes and bifurcation structure in a pair of coupled detuned third order oscillators

The bifurcation structure of a system of two non-linear coupled oscillators is considered here. This system is motivated by coupled micro-oscillators proposed for microelectromechanical systems (MEMS) applications. The model starts from previous work in which the authors considered the bifurcation structure in a pair of identical coupled, oscillators, each of which is modelled by a third-order nonlinear system. In the present paper, the case is considered where the two oscillators are non-identical i.e. detuned from each other. The series of bifurcations obtained is described in detail. It is seen that the symmetry of the bifurcation structure present in the identical oscillators is lost in the detuned oscillators. A very surprising homoclinic bifurcation is seen in one region of the parameter space, and this is examined in more detail through consideration of a simplified system.

Exact Traveling Wave Solutions of (3+1)-dimensional Kadomtsev-Petviashvili Equation

By transforming the (3+1)-dimensional nonlinear Kadomtsev-Petviashvili equation into an elementary integral form, the exact traveling wave solutions of (3+1)-dimensional nonlinear KP equation are obtained by using the third-order polynomial complete discriminant system method.

Sliding-mode control in dq-frame for a three-phase grid-connected inverter with LCL-filter

The three-phase LCL-filter-based grid-connected inverter (LCL-GCI) is a third-order and multi-variable system, and claiming a higher demand to the control system design. Aiming at this, an improved current sliding mode control (SMC) strategy combing with capacitor current feed-forward control is proposed to eliminate the distortion of the grid current for a three-phase LCL-GCI control system. Meanwhile, the modified exponential reaching law is presented to effectively alleviate the shaking shock effect caused by the traditional SMC strategy. The detailed theoretical analysis and design method of the proposed SMC strategy are presented. A simulation model and hardware-in-the-loop experimental platform on a 50 kW three-phase LCL-type grid inverter is built with Matlab/Simulink and RT-LAB, which are compared with the traditional control strategy for verifying the accuracy of the proposed SMC strategy. The simulation and experimental results show that with the proposed SMC strategy, the steady and transient performances of the grid current are effectively improved.

A Method for Improving Light Intensity Stability of a Total Reflection Prism Laser Gyro Based on Series Correction and Feedforward Compensation

The instability of scale factor and null shift are closely related to the change of the light intensity of a total reflection prism laser gyro (TRPLG). To improve the light intensity stability, the light intensity stabilization principle of TRPLG was analyzed, and a mathematical model of light intensity stabilization system was established. Aiming at the problem that original system has a long adjustment time, a series correction method of adding a proportional integral differential (PID) link in the forward channel was adopted. According to the third-order optimal design, the original I-type third-order overdamped system was optimized to the new II-type third-order underdamped system, which ultimately improved the system's dynamic and steady-state performance. Feedforward compensation was used to introduce the light intensity disturbance during the longitudinal mode hopping into the closed-loop system, which realized the full compensation of the light intensity error and improved the light intensity characteristics during the longitudinal mode hopping. Combined with the above two methods, experimental results showed that the new system with feedforward compensation improved the light intensity stability by 32% at constant temperature and by 40% at variable temperature, with the TRPLG's bias stability improved by more than 16% at constant temperature and by 22% at variable temperature.

On strongly unimodal third-order SISO linear systems with applications to pharmacokinetics

This paper addresses the problem of characterizing external positivity (equivalently, non-negative impulse response) of third-order single-input, single-output (SISO) linear systems. We show how an exact, geometric solution to this problem follows by first identifying an equivalence between the impulse response of an externally positive system on the one hand, and the probability density function of a non-negative random variable on the other, then drawing on the characterization of matrix exponential distributions, defined as probability distributions for which the Laplace transform is a rational function. The results are then extended to the characterization of strongly unimodal systems, defined as systems in which input signals with a time-derivative that has at most one sign variation (namely, are pulse-like) are mapped to output signals with the same property. The results are applied to a third-order compartmental system arising in pharmacokinetics, in which the properties of non-negativity of the impulse response and the preservation of unimodality from drug adminstration (input) to compartmental drug concentration (output) are of clinical relevance.

Theoretical Dynamic Modeling and Validation of Braided Pneumatic Artificial Muscles

Abstract The high force-to-weight ratios of braided fluidic artificial muscles (AMs) are ideal for human scale and mobile robot applications. Prior modeling efforts focus on the theoretical static characteristics or empirical dynamic models of these actuators when pressurized. This paper develops a comprehensive high fidelity theoretical dynamic model based on first principles for braided pneumatic AMs and presents experimental validation. A novel theoretical model for the nonlinear stiffness is derived to describe the pressure–displacement behavior. The stiffness model, together with friction, damping, and inertia models, forms an equation of motion (EOM) for braided pneumatic AMs. The EOM is coupled with first-order servopneumatic pressure dynamics, resulting in a third-order system model. System model simulations are compared to experimental results of prototypes with nine different geometries. On average, the system model is able to predict the quasi-static displacement within 7% and the dynamic response within 11%. The theoretical model is also benchmarked against a high fidelity curve fit method, with the empirical method showing a 2% improvement in only quasi-static scenarios. The model promises to be useful for mechanical system and model-based control designs.