Hyperstability Theory Research Articles

DC Drive Adaptive Speed Controller Based on Hyperstability Theory

The scope of this research is to develop a hyperstable adaptive control system of a direct current (DC) drive speed for effective load torque attenuation. The proposed speed controller is based on the model reference adaptive control framework and integrated into the conventional DC drive cascade control system. Its main features are as follows: (1) the boundedness of the control action signal, as well as the armature current control loop non-stationarities, are taken into consideration with the help of the reference model hedging technique; (2) its inputs include only measurable signals, thus there is no need to use any kind of state estimators; (3) it attenuates the disturbances, which are matched with its control action signal, particularly, the inertia moment non-stationarity and load torque. The asymptotic hyperstability of the obtained DC drive control system is proven with the help of Lyapunov’s theorems and Popov’s criterion. The numerical experiments corroborate the obtained results. They include the demonstration of disadvantages of the conventional cascade control system under conditions of the drive parameters’ non-stationarity and advantages of the proposed solution for different disturbance types and amplitudes.

A High Torque Estimation Accuracy Direct Torque Control of Permanent Magnet Synchronous Motor Based on a Novel Iron Loss Resistance Observer

This paper proposes a direct torque control (DTC) of permanent magnet synchronous motor (PMSM) with high torque estimation accuracy. Based on the PMSM mathematical model considering iron loss resistance, this paper analyzes that when using stator current to estimate torque, the accuracy will be affected by iron loss resistance. Using stator magnetizing current can solve the current deviation caused by iron loss resistance and improve torque estimation accuracy. Since the stator magnetizing current cannot be obtained directly, a novel iron loss resistance observer based on the model reference adaptive system (MRAS) is designed to estimate iron loss resistance and stator magnetizing current simultaneously. Popov’s hyperstability theory guarantees the stability of the designed observer. Finally, a 1kW PMSM experimental platform is constructed to verify the proposed method. Both the simulation and experimental results show that the designed observer is stable, and using stator magnetizing current to estimate torque has better accuracy than stator current.

A novel resonant frequency tracking control for linear compressor based on MRAS method

To optimize the efficiency of the linear compressor, its operating frequency must be controlled equal to the system resonant frequency. The traditional resonant frequency tracking control algorithm relies on the steady state characteristics of the system, which suffers from slow convergence speed, low accuracy and slow system response. In order to solve these problems, a novel resonant frequency tracking control for linear compressor based on model reference adaptive system (MRAS) is proposed in this paper, and the parameter adaptive rate is derived by the Popov's hyperstability theory, so that the system resonant frequency can be directly calculated through the parameter adaptive rate. Furthermore, the traditional algorithm needs to calculate the piston stroke signal by integrating the back-EMF, which has the problem of integral drift. The algorithm proposed in this paper only needs the velocity signal, and the accuracy of the velocity calculation can be ensured by utilizing the self-adaptive band-pass filter (SABPF), thereby greatly improving the accuracy of the resonance frequency calculation. Simulation results verify the effectiveness of the proposed algorithm.

Model Reference Adaptive Control of Vehicle Slip Ratio Based on Speed Tracking

This paper investigates a slip ratio control problem of a vehicle braking system in which real-time road conditions are unavailable. To overcome the nonlinearity and uncertainties, the slip ratio control problem is converted to a speed tracking control problem. By introducing a road-condition observer, a model reference adaptive control (MRAC) method is proposed to overcome modeling errors and system uncertainties. The road condition observer based on the Lyapunov theory is designed and a sliding mode observer is also constructed to estimate the unknown vehicle velocity. The asymptotic and robustness property of the adaptive controller is derived by the Popov hyperstability theory. Simulations under different conditions including different road adhesion coefficient, system uncertainties and modeling errors are provided to illustrate the effectiveness and robustness of the proposed method.

Адаптивне керування процесами підготовки шихти для виготовлення залізорудних котунів на базі методів теорії гіперстійкості

Адаптивне керування процесами підготовки шихти для виготовлення залізорудних котунів на базі методів теорії гіперстійкості

Speed Sensorless Vector Control Based on Full-order Adaptive Observer for Induction Motor Drives at Low Speed

This paper presented a speed sensorless vector control method based on adaptive full-order state observer for induction motor. The rotor speed estimated by an adaptive full-order observer is fed back to the vector control system as a feedback signal to form a closed-loop control of speed. In addition, the stator resistance is also recognized and updated in real time, so the effect of change of stator resistance on accuracy of speed estimation can be eliminated. The parameter identification system is achieved according to the Popov’s hyperstability theory, therefore the system is stable enough even at very low speed. The simulation and experimental results illustrated the correctness and effectiveness of the presented control algorithm.

Adaptive Control Design and Stability Analysis of Robotic Manipulators

In this paper, the author presents the adaptive control design and stability analysis of robotic manipulators based on two main approaches, i.e., Lyapunov stability theory and hyperstability theory. For the Lyapunov approach, the author presents the adaptive control of a 2-DOF (degrees of freedom) robotic manipulator. Furthermore, the adaptive control technique and Lyapunov theory are subsequently applied to the end-effector motion control and force control, as in most cases, one only considers the motion control (e.g., position control, trajectory tracking). To make the robot interact with humans or the environment, force control must be considered as well to achieve a safe working environment. For the hyperstability approach, a control system is developed through integrating a PID (proportional–integral–derivative) control system and a model reference adaptive control (MRAC) system, and also the convergent behavior and characteristics under the situation of the PID system, model reference adaptive control system, and PID+MRAC control system are compared.

Second-Order Sliding-Mode MRAS Observer-Based Sensorless Vector Control of Linear Induction Motor Drives for Medium-Low Speed Maglev Applications

This paper presents a speed estimation scheme by combining a second-order sliding-mode observer (SMO) with the model reference adaptive system (MRAS) in the sensorless-vector-controlled linear induction motor (LIM) drives for medium-low speed maglev applications. A state space-vector model of the LIM considering the dynamic end effects is rearranged in order to be represented by the form of the super-twisting algorithm (STA). Then, an STA-SMO-based stator current observer of the LIM with Popov's hyperstability theory is designed, which is used to replace the reference model of the MRAS-based scheme. Correspondingly, the actual stator current model is regarded as the adaptive model of the MRAS for speed estimation. Meanwhile, because the variation of stator resistance associated with stator temperature may lead to a large estimated error and even system instability, a parallel stator resistance on-line identification scheme is adopted in the proposed speed estimation scheme to reduce the speed error and improve the stability of the sensorless control system. Compared to the speed estimation schemes based on the Luerberger observer with MRAS and the single-manifold SMO, the proposed speed estimation scheme exhibits better estimated performance. The effectiveness and feasibility of the proposed speed estimation scheme have been verified by simulation and hardware-in-the-loop tests.

Direct Torque Control of Six-Phase Induction Motor With a Novel MRAS-Based Stator Resistance Estimator

Any mismatch between the real and tuned values of the stator resistance ( $R_s$ ) leads to a degraded performance of the direct torque control (DTC) strategy. The underestimation of $R_s$ causes an error in the stator flux and torque estimations, thereby weakening the DTC performance; however, an overestimation of $R_s$ can make the DTC unstable. The main objective of this paper is to present a novel estimator based on the model reference adaptive system (MRAS) for online estimation and tracking of $R_s$ in the DTC of six-phase induction motors (6PIMs). Voltage and current vectors of 6PIM are mapped into $\alpha -\beta$ , $z_1-z_2$ , and $o_1-o_2$ subspaces, where only the $\alpha -\beta$ components are related to electromechanical energy conversion. The proposed technique uses additional degrees of freedom, i.e., the $z_1-z_2$ subspace to estimate $R_s$ . The attained merits include simplicity, low computation burden, and low sensitivity to other parameters of the 6PIM. The adaptation law is derived from the Lyapunov stability theory and Popov hyperstability theory. The proposed technique is applied under a duty cycle control based DTC, where $z_1-z_2$ currents possess reduced amplitudes in comparison with the conventional DTC. The validity of the proposed system is verified by simulation and experimental results.

Sliding‐mode observer‐based speed‐sensorless vector control of linear induction motor with a parallel secondary resistance online identification

This study proposes a speed estimation scheme for the sensorless-vector-controlled linear induction motor (LIM) drives for medium-low-speed maglev applications, which is composed of two parts: (i) a sliding mode model reference adaptive system observer for speed estimation; and (ii) a parallel secondary resistance online identification for achieving the improvements of the proposed speed estimation scheme performance. The sliding mode observer (SMO) is established on the basis of the state space-vector model of the LIM considering the dynamic end effect. Based on SMO, both speed and secondary resistance estimation algorithms are obtained by utilising Popov's hyperstability theory. Moreover, the Lyapunov stability theory is adopted for the stability analysis of the proposed speed estimation scheme. The effectiveness of the proposed speed estimation algorithm has been verified and compared with the performance of the conventional speed estimation scheme based on single-manifold SMO by the simulation and hardware-in-the-loop tests.

Speed Sensorless Control of a Doubly Fed Induction Motor Drives using MRAS Estimator

In this paper, direct vector control by rotor flux orientation for doubly fed induction motor without mechanical sensor based on the MRAS estimator is discussed, this method consists in developing two models one of reference and the other adjustable for the estimation of the two components of the rotor flux from the measurement of currents, statoric and rotor voltages respectively, the speed estimated is obtained by canceling the difference between the rotor flux of the reference model and the adjustable one, while using the theory of hyperstability to obtain the adaptive mechanism the simulation results are presented to validate the proposed method.

Parameter Identification of an MEMS Vibratory Gyroscope with Hyperstability Theory

Fabrication defects affects the performance of a vibratory MEMS gyroscope sensor, which makes the serious bias. This paper presents a parameter identifier for an MEMS z-axis vibratory gyroscope with Hyperstability theory, investigating the basic control problem of a vibrating MEMS gyroscope, parameter identification including system parameters and rotation angular rate. The parameter identifier is proposed by introducing a Hurwitz matrix to the MEMS state space model for the demand of system’s strictly positive real, and the so-called passivity condition (Popov integral inequality) is guaranteed with the selected common PI adaptive law. Simulation results show the validity and effectiveness of the online identifier.

Stability analysis of q-axis rotor flux based model reference adaptive system updating rotor time constant in induction motor drives

q-axis rotor flux can be chosen to form a model reference adaptive system (MRAS) updating rotor time constant online in induction motor drives. This paper presents a stability analysis of such a system with Popov's hyperstability concept and small-signal linearization technique. At first, the stability of q-axis rotor flux based MRAS is proven with Popov's Hyperstability theory. Then, to find out the guidelines for optimally designing the coefficients in the PI controller, acting as the adaption mechanism in the MRAS, small-signal model of the estimation system is developed. The obtained linearization model not only allows the stability to be verified further through Routh criterion, but also reveals the distribution of the characteristic roots, which leads to the clue to optimal PI gains. The theoretical analysis and the resultant design guidelines of the adaptation PI gains are verified through simulation and experiments.

A Soft Sensor Development for the Rotational Speed Measurement of an Electric Propeller

In recent decades, micro air vehicles driven by electric propellers have become a hot topic, and developed quickly. The performance of the vehicles depends on the rotational speed of propellers, thus, improving the accuracy of rotational speed measurement is beneficial to the vehicle’s performance. This paper presents the development of a soft sensor for the rotational speed measurement of an electric propeller. An adaptive learning algorithm is derived for the soft sensor by using Popov hyperstability theory, based on which a one-step-delay adaptive learning algorithm is further proposed to solve the implementation problem of the soft sensor. It is important to note that only the input signal and the commutation instant of the motor are employed as inputs in the algorithm, which makes it possible to be easily implemented in real-time. The experimental test results have demonstrated the learning performance and the accuracy of the soft sensor.

Nonlinear control systems theory in Romania and the influence of the contributions of V. A. Yakubovich

Theory of automatic control started in Romania as an essentially linear theory based on transfer functions (input/output representations). The introduction of the nonlinear theory started in the late 50ies of the past century by some research papers due to A. Halanay and V. M. Popov -with special reference to absolute stability. But only after the discovery by V.M. Popov of the famous frequency domain absolute stability inequality it became possible to connect his method to the classical ones which relied on Liapunov functions: this led to the assimilation of the results of V.A. Yakubovich on matrix inequalities which grew in the Yakubovich Kalman Popov lemma and the positiveness theory. The positiveness theory at its turn is strongly connected with the hyperstability theory and thus, with dissipativeness and passivity. The next decades witnessed applications to forced oscillations, generalization of the positiveness theory to the indefinite sign case, the start of the rigorous theory for adaptive systems -with some roots in Romania also -and the extension to discrete time and time delay systems. Consideration of the periodic discrete time systems witnessed a return to the book of Yakubovich and Starzhinskii on systems with periodic coefficients and its first extensions to the discrete time case, including some results on discrete time parametric resonance. Worth mentioning that the influence of V.A. Yakubovich generated the opening to the representatives of his school and, in general, to the Sankt Petesburg University school of differential equations and qualitative control theory.

Control of Four Switch Three Phase Inverter Fed Induction Motor Drives Based Speed and Stator Resistance Estimation

This paper presents sensorless position and speed control for a four-switch three-phase inverter (FSTPI) fed induction motor drive. Accurate knowledge of stator resistance is of utmost importance for correct operation of a number of speed sensorless induction motor control schemes in the low speed region. Since stator resistance inevitably varies with operating conditions, stable and accurate operation at near-zero speed requires an appropriate identification algorithm for the stator resistance. The paper proposes such an identification algorithm, which is developed for the rotor flux based model reference adaptive system (MRAS) type of the speed estimator in conjunction with a rotor flux oriented control scheme. In this speed estimation method only one (out of the two available) degree of freedom is utilized for speed estimation. It is utilize the second available degree of freedom as a mean for adapting the stator resistance. The parallel stator resistance and rotor speed identification algorithm is developed in a systematic manner, using Popov’s hyper stability theory. It increases the complexity of the overall control system insignificantly and enables correct speed estimation and stable drive operation at near-zero speeds. The proposed speed and position estimator with parallel stator resistance identification for FSTPI fed induction motor at very low speed under high load operation is verified by simulation and experimental results. The results show the robustness of the proposed method with FSTPI. DOI: http://dx.doi.org/10.11591/ijpeds.v4i2.5057

Multi-channel wide area adaptive damping control for suppressing low-frequency and sub-synchronous oscillation

A model reference adaptive control scheme is developed based on hyper-stability theory and is proved. Both of reduced order models of the power system and relevant oscillation frequencies are acquired by TLS-ESPRIT algorithm. The band-pass filters (Butterworth) are utilized to decompose oscillation frequencies into different channels and controllers are designed for each oscillation mode based on adaptive control method, thus reducing the influences of the various controllers. Xiangjiaba-Shanghai DC link under island operation condition is simulated using electromagnetic transient program PSCAD/EMTDC to demonstrate proposed control strategy. The results validate that the proposed method is able to suppress low-frequency oscillation and sub-synchronous oscillation simultaneously and the proposed method has better control performance than the traditional PID control. The problem will lead to controller performance deterioration caused signal transmission delay in system and it is resolved by phase compensation.

Switched adaptive tracking control of robot manipulators with friction and changing loads

A switched adaptive controller is designed for robot manipulators with friction and changing loads. The nonlinear friction is depicted by a nonlinear friction model, and a switched nonlinear system is used to model the parameter jump caused by load change. Hyperstability theory is used in the designing procedure, which provides more options for adaptive laws than Lyapunov theory. In the presence of friction and changing loads, asymptotic tracking is achieved under arbitrary switching, which is not able to accomplish by a non-switched adaptive controller. The proposed method is validated by a simulation of a 2 degree of freedom manipulator.

An Improved Flux Observer for Sensorless Permanent Magnet Synchronous Motor Drives with Parameter Identification

This paper investigates an improved stator flux linkage observer for sensorless permanent magnet synchronous motor (PMSM) drives using a voltage-based flux linkage model and an adaptive sliding mode variable structure. We propose a new observer design that employs an improved sliding mode reaching law to achieve better estimation accuracy. The design includes two models and two adaptive estimating laws, and we illustrate that the design is stable using the Popov hyper-stability theory. Simulation and experimental results demonstrate that the proposed estimator accurately calculates the speed, the stator flux linkage, and the resistance while overcoming the shortcomings of traditional estimators.

The Research of Electro-Hydraulic Proportional Control on Copper Anode Lifting Platform

This paper introduces the structure and working principle of the designed copper anode lifting platform. According to the actual working conditions and the structure of the lifting device, hydraulic system of electro-hydraulic proportional synchronous lifting device is designed and its working principle is analyzed. This paper takes the electro-hydraulic synchronization system as a research subject, whose mathematic model is established. To solve the synchronization accuracy of the hydraulic cylinder movement in the lifting process, a model reference adaptive controller is designed which is based on hyperstability theory. Both system simulation models of traditional PID control and adaptive control are established respectively in the software of Matlab/Simulink. Through the simulation result we can learn that adaptive control is batter than the PID control. Two hydraulic cylinders synchronization error is less than 0.02mm.