Sixth-order Nonlinear Model Research Articles

Sustained oscillations and bifurcations in three‐phase voltage source converter tied to AC grid

Recently large-scale integration of power-electronic-based devices has made system-level oscillations occur frequently, which posed a big challenge for modern power grids. Previous studies mainly treated sustained oscillations under the framework of (linear) small-signal stability and/or by incorporating the impact of current saturation, but seldom considered system non-linearity like phase-locked-loop. In this study, the authors established a sixth-order non-linear model for a three-phase voltage-source converter tied to AC grid, and studied its dynamics completely from non-linear system theory and signal analysis technique, with all parameters including current controllers, phase-locked-loop, line inductance, and grid voltage. They found that the operation point usually becomes unstable by Hopf bifurcation, and the sustained oscillations are possible only for super-critical Hopf bifurcation. Based on these observations, sustained periodic oscillation should be treated as a limit cycle even without saturation. With saturation, some other phenomena have also been found, such as saturation-induced instability and saturation-restricted oscillation. In addition, they discovered that for sustained oscillations, the usual purely sinusoidal three-phase currents exhibit the form of sin ⁡ [ 2 π f 1 t + c sin ⁡ ( 2 π f d q t ) ] or cos ⁡ [ 2 π f 1 t + c sin ⁡ ( 2 π f d q t ) ] , where f 1 ( f d q ) denotes basic (modal oscillation) frequency with c a constant. This work could provide an improved understanding of sustained oscillations and associated system dynamics in an overall perspective manner.

Speed Observer and Reduced Nonlinear Model for Sensorless Control of Induction Motors

We consider field-oriented speed control of induction motors without mechanical sensors. We augment the traditional approach with a flux observer and derive a sixth-order nonlinear model that takes into consideration the error in flux estimation. A high-gain speed observer is included to estimate the speed from field-oriented currents and voltages. The observer design is independent of the feedback controller design. By high-gain-observer theory, we define a virtual speed output for the sixth-order nonlinear model, which can now be used to design a feedback controller whose performance is recovered by the speed observer when the observer gain is chosen high enough. We then focus on the traditional field oriented control (FOC) approach where the flux is regulated to a constant reference and high-gain current controllers are used. By designing a flux regulator to maintain the flux at a constant reference, and a current regulator to regulate the q-axis current to its command, we derive a third-order nonlinear model that captures the essence of the speed regulation problem. The model has the speed and two flux estimation errors as the state variables, the q -axis current as the control input, and the virtual speed as the measured output. It enables us to perform rigorous analysis of the closed-loop system under different controllers, and under uncertainties in the rotor and stator resistances and the load torque. In this paper, we emphasize the design of feedback controllers that include integral action. The analysis reveals an important role played by the steady-state product of the flux frequency and the q-axis current in determining the control properties of the system. The conclusions arrived at by using the reduced-order model are collaborated by simulation and experimental results.

Induced Master Motion in Force-Reflecting Teleoperation

Telerobotic systems have persistently struggled to provide users with realistic force feedback; high-frequency contact transients convey important information about the remote environment but are typically attenuated to avoid the contact instability they incite. This undesirable behavior can be traced to high-frequency induced master motion, movement of the master device that is caused by force feedback rather than user intention. Such motion is interpreted as a position command to the slave, closing an internal control loop that is unstable under high gain. This paper examines the phenomenon of induced master motion in position-force teleoperation, presenting a new approach for achieving stable, high-gain force reflection using model-based cancellation. Requirements for the model of the induced motion dynamics and methods for its characterization are described, focusing on successive isolation of inertial and connecting elements. The sixth-order nonlinear model obtained for a one-degree-of-freedom user-master system is validated and then tested in a cancellation controller. Canceling high-frequency induced master motion during teleoperation is shown to improve the stability of impacts, allowing significantly higher force reflection levels and a more authentic user experience.

Chaos in a Real System

Many studies of chaos involve using simplified equations with little relation to a real system. Lorenz proposed a real system that demonstrates chaotic behavior - the classic Lorenz water wheel. This wheel, a mechanical analog to fluid heating in a box, consists of a number of buckets on the outside of a spoked wheel which rotates in a vertical plane. A filling source at the top of the wheel fills buckets as they pass under it. The filled buckets cause rotational dynamics, which at times exhibit a chaotic behavior. The requisite equations for a four-bucket wheel (sixth-order nonlinear model) are developed and implementation considerations enumerated. Some typical responses are presented.

Roles of the elements of the triphasic control signal

In fast (time-optimal) movements about many joint systems, the triphasic EMG pattern has been observed. Although the first agonist burst obviously initiates the movement, the roles of the second and third bursts, appearing in the antagonist and agonist respectively, have been less clear. In this study, the timing of experimentally measured EMG signals led to construction of a three-pulse control signal that produced an accurate simulation of experimentally measured time-optimal head rotations using a sixth-order nonlinear model in conjunction with an optimization algorithm. By ablating pulses from the model control signal and observing the resulting dynamics, the roles of the three pulses can be assessed. As a result, the pulses can be designated PA, the action pulse (for the first agonist burst), PB, the braking pulse (for the antagonist burst), and PC, the clamping pulse (for the second agonist burst). Comparison of dynamic parameters from the simulated movements revealed strategies used to generate control signals for movements of various speeds.

Unequal saccades during vergence.

An examination of saccades during vergence eye movements (accommodative and disparity) reveals that binocular saccades have unequal magnitudes in each eye, the smaller saccade of each pair opposing the vergence movement. Furthermore, this inequality cannot be explained by linear summation of the saccadic amplitudes onto the ongoing vergence. Saccadic inequalities are usually greater at the start of the vergence; the amplitude of the smaller saccade may be reduced 70% from that of the larger. Using a sixth-order nonlinear model of the eye movement plant and linear summation of saccadic (pulse-step) and vergence (step) control signals to drive the plant, we have produced a reduction in saccadic amplitudes between the two eyes during vergence that is similar to those found in our subjects. These results suggest that the reduction of saccadic amplitudes is due to an interaction in the muscular system moving the eye, not to a nonlinear neuronal interaction more centrally located.

Tracked Air Cushion Vehicle Suspension Models: Analysis and Comparison

ABSTRACT In this paper several dynamical models of fluid suspensions for tracked air cushion vehicles are analyzed and compared. Specifically, the models considered conform to: a fifth-order linear suspension, a nonlinear configuration with a constant supply pressure, a nonlinear model with compressor characteristics, and a sixth-order nonlinear model with a supply duct connecting the compressor to the cushion chamber. Nonlinearities included in the analysis are the flexible-skirted cushion capacitance, cushion entrance and exit orifice restrictions, feeding system duct fluid capacitance, and compressor pressure-flow characteristics. Temporal responses are obtained for guideway and external force inputs. Back flow conditions under which the supply compressor can stall are examined. It is shown that the general behavior resulting from linear analysis is in many respects similar to that obtained from the nonlinear analysis. Thus, a linear model could provide a good initial basis for a preliminary design and...