Popov's Hyperstability Theory Research Articles

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.

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.

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.

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.

Design of a Robust Model Reference Adaptive Control System

This paper addresses a robust adaptive control system based on Popov hyper-stability theory, which has strong robustness for the particular structure. Introducing the error between model and controlled object into adaptive controller, the system has accurate tracking capability and the convergence even in the presence of external disturbances and uncertainties. Simulations results are given to illustrate the effectiveness of the proposed robust adaptive control law in comparison with PID control.

Adaptive Controller Design for Faulty UAVs via Quantum Information Technology

In this paper, an adaptive controller is designed for a UAV flight control system against faults and parametric uncertainties based on quantum information technology and the Popov hyperstability theory. First, considering the bounded control input, the state feedback controller is designed to make the system stable. The model of adaptive control is introduced to eliminate the impact by the uncertainties of system parameters via quantum information technology. Then, according to the model reference adaptive principle, an adaptive control law based on the Popov hyperstability theory is designed. This law enable better robustness of the flight control system and tracking control performances. The closed-loop system's stability is guaranteed by the Popov hyperstability theory. The simulation results demonstrate that a better dynamic performance of the UAV flight control system with faults and parametric uncertainties can be maintained with the proposed method.

Very low speed and zero speed estimations of sensorless induction motor drives

Recently, speed sensorless control of induction motor drives received great attention to avoid the different problems associated with direct speed sensors. However, low speed operation with robustness against parameter variations remains an area of research for sensorless systems. Stator resistance is of utmost importance for good operation of speed sensorless systems in low speed region. In this paper, a sliding mode current observer for an induction motor is presented. An estimation algorithm based on this observer in conjunction with Popov's hyper-stability theory is proposed to calculate the speed and stator resistance independently. The proposed speed observer with parallel stator resistance identification is first verified by simulation. Experimental results are included as well as to demonstrate the good performance of the proposed observer and estimation algorithms at very low and zero speeds.

Wide-Speed-Range Estimation With Online Parameter Identification Schemes of Sensorless Induction Motor Drives

Recently, the development of speed estimation methods for sensorless control of induction motor drives has found great interest in the research community. Parameter adaptation schemes play an important role for better speed estimation over a wide range from zero to high levels beyond the rated speed. Therefore, parallel identification schemes for both speed and stator resistance of sensorless induction motor drives are proposed for a wide range of speed estimation. These estimation algorithms combine a sliding-mode current observer with Popov's hyperstability theory. Low- and zero-speed operations of the proposed sliding-mode-observer (SMO)-based speed estimation combined with an online stator resistance adaptation scheme are investigated. A modified SMO-based speed estimation scheme for field-weakening operation is also introduced. The mismatch problem of magnetizing inductance in the field-weakening region is treated by an online identification scheme. Magnetizing inductance, estimated in this way, is further utilized within the SMO, so that the main flux saturation variation is taken into consideration. The performance of the proposed SMO and its speed estimation accuracy, with an indirect field-oriented controlled induction motor, are verified by simulation and experimental results over a wide speed range from zero to high values beyond the base speed.

反射とその適応的な抑制による腱駆動型ロボットの軌道追従制御

In this paper, a trajectory tracking control method for the tendon-driven robot is presented. In the human motor control system, it is known that the spinal reflex and the cerebellum play a key role to achieve the desired limb motions and have some characteristic structures different from the conventional robot control systems, such as the internal positive feedback loops. From the viewpoint of control, the positive feedback is inconvenient since it might potentially destabilize the limb motion. However, in the biological system, the positive feedback is actively used rather than avoided and has significant role to achieve the natural human limb motions. Thus, in this paper, we attempted to establish a trajectory tracking controller for the tendon-driven robots with reference to the biological control system composed of the spinal cord and cerebellum. The stability of the controlled system was proven along the Popov's hyper-stability theory. The effectiveness of the proposed controller was demonstrated through some computer simulations and experiments using a 2 link tendon-driven robot.

A stator resistance estimation scheme for speed sensorless rotor flux oriented induction motor drives

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 online 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 degree of freedom (out of the two available) is utilized for speed estimation. It is proposed to utilize the second available degree of freedom as a means for adapting the stator resistance online. The parallel stator resistance and rotor speed identification algorithm is developed in a systematic manner, using Popov's hyperstability 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 estimator with parallel stator resistance identification is at first verified by simulation. Extensive experimentation is conducted next at low speeds of rotation and successful stator resistance identification is achieved down to 0.5-Hz frequency of rotation.

New sensorless control for brushless DC motors using disturbance observers and adaptive velocity estimations

A brushless DC motor has been represented by a nonlinear equation. Therefore, it has been difficult to apply linear control theory to brushless DC motor systems. In this paper, to apply the linear control theory to brushless DC motor systems, the authors propose considering the nonlinear term of the equation as a disturbance and to realize a sensorless control of the brushless DC motor using both the disturbance observer and the adaptive velocity estimation. With proper pole locations of the disturbance observer, stability of the position estimation is guaranteed, and stability of the adaptive velocity estimation is also guaranteed by Popov's hyperstability theory. The experimental results show that the proposed method is very useful.

Stability analysis of a robust PD control law for robot manipulators

The purpose of this article is to examine the stability of a robust and decentralized PD control law for robot manipulator control. The control law, which was developed by the authors, has been shown experimentally to be extremely simple to implement and highly accurate for position and force tracking in the presence of robot model uncertainty and payload variation. However, stability analysis has been difficult due to the nonlinearity of robot dynamics and the use of time-delayed measurements of joint torques and joint accelerations in the control law. A rigorous stability analysis is presented in this article using Popov's hyperstability theory. A sufficient condition for global stability is obtained that supports previous theoretical and experimental results. © 1996 John Wiley & Sons, Inc.

An experimental study on model reference adaptive control for robot manipulators

Model reference adaptive control based on Popov's hyperstability theory is applied to the trajectory tracking control of a two-link SCARA-type manipulator, and its effectiveness is examined experimentally. A linearized state equation with an optimal state feedback is used as a reference model. The similarity of the structure of the model and a real system like this is useful for simplifying the design of the adaptive control system. Further, by introducing a new adaptation law which consists of a combination of linear and non-linear control, it is possible to reduce high frequency chattering in the control inputs. The results of a simulation and experiment show that by adding a rather simple adaptation mechanism to a conventional state feedback, the effects of Coulomb frictions and parameter identification errors are removed and the accuracy of trajectory tracking is greatly improved.

Model Reference Adaptive Control for Manipulators–A Review

Based on the model reference approach and Popov's hyperstability theory, several adaptive control laws are derived in a simple and unified manner. The concepts of hyperstabi1ity theory and model reference adaptive control systems are introduced by means of a first order constant linear system. The theory is then applied to the design of adaptive controllers for manipulators having complex and nonlinear dynamics.

DISCRETE ADAPTIVE CONTROL OE A MANIPULATOR ARM

SUMMARYA discrete‐time adaptive control algorithm is presented which overcomes the difficulties encountered when one attempts to control a manipulator arm. The algorithm is based upon MRAC techniques combined with Popov's hyperstability theory, and simulations presented here show that excellent control can be achieved.

Extension of V.M. Popov's Hyperstability Theory and its Application in Adaptive System Design

The extension of V.K. Popov's hyperstability theory is presented in chis paper. It has been proved that a system is asymptotically stable by the definition of hyperstability if all the poles and zeros of the linear part of a system are in the left half complex plane. If in this case the transfer function of the system is not positive real, then a Eurwitz differential operator of proper degree can be introduced to reform the characteristic of nonlinear part of the system. A design of model reference adaptive control system is suggested by using the theorem obtained in this paper. Both “integration” and “proportion plus integration” parameter adaptation rules are used.