Hyperstability Theory Research Articles

Simulation Modeling of Ball Screw Feed Drive System Based on MRAS

In order to obtain a second-order mathematical model of the ball screw feed drive systems in the designing stage, this paper proposed a simulation modeling method based on model reference adaptive system. In this method, a parallel model reference adaptive system, which regarded the mechanical model as the reference model and regarded a second-order model as the adjustable model, was designed use only input and output measurements based on Popov’s hyperstability theory. And the second-order model’s parameters could be achieved by simulation. The proposed method was confirmed effective through case study. The results show that: the second-order system’s parameters can be identified correctly, and the output of the mathematical model can be followed preferably by the second-order system. The error is less than 0.02mm.

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.

Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems

This paper proposes new stability analysis and convergence results applied to the Iterative Feedback Tuning (IFT) of a class of Takagi–Sugeno–Kang proportional-integral-fuzzy controllers (PI-FCs). The stability analysis is based on a convenient original formulation of Lyapunov’s direct method for discrete-time systems dedicated to discrete-time input affine Single Input-Single Output (SISO) systems. An IFT algorithm which sets the step size to guarantee the convergence is suggested. An inequality-type convergence condition is derived from Popov’s hyperstability theory considering the parameter update law as a nonlinear dynamical feedback system in the parameter space and iteration domain. The IFT-based design of a low-cost PI-FC is applied to a case study which deals with the angular position control of a direct current servo system laboratory equipment viewed as a particular case of input affine SISO system. A comparison of the performance of the IFT-based tuned PI-FC and the performance of the PI-FC tuned by an evolutionary-based optimization algorithm shows the performance improvement and advantages of our IFT approach to fuzzy control. Real-time experimental results are included.

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.

Adaptive law with a new leakage term

The hyperstability theory of adaptive control systems is extended to encompass plants with unmodelled dynamics and disturbances. The analysis not only shows that leakage in the adaptive law is a natural way to avoid robustness problems (which is a known result in adaptive control theory), but also provides a new adaptive law that is a sort of signal-dependent σ-modification. The proposed adaptive law is less conservative than the σ-modification, but still ensures the global stability of the system, which is formally proven in the paper. Since it is shown that the design parameter σ′ of the proposed adaptive law is directly related to the H∞ norm of the parasitic dynamics, the criteria for system stability are derived. Based on these, some guidelines for choosing the leakage parameter σ′ and the bandwidth of the reference model are presented.

A novel robust adaptive control algorithm and application to DTC-SVM of AC drives

In this paper a new robust adaptive control algorithm for AC machine is presented. The main feature of this algorithm is that minimum synthesis is required to implement the strategy. The MCS algorithm is a significant development of MRAC and is similary based on the hyper stability theory of Popov. The hyperstability theory guarantees the global asymptotic stability of the error vector (i.e. the difference between the reference model and system states). Finally, a new approach has been successfully implemented to DTC-SVM. Discussion on theoretical aspects, such as, selection of a reference model, stability analysis, gain adaptive and steady state error are included. Results of simulations are also presented.

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.

Model reference adaptive control for a piezo-positioning system

Piezoelectric (PZT) actuators having the characteristic of infinitely small displacement resolution are popularly applied as actuators in precision positioning systems. Due to its nonlinear hysteresis effect, the tracking control accuracy of the precision positioning system is difficultly achieved. Hence, it is desirable to take hysteresis effect into consideration for improving the trajectory tracking performance. In this paper, a model reference adaptive control scheme based on hyperstability theory is developed for a moving stage system driven by a PZT actuator. It is worth emphasizing that the controller can be constructed without a nonlinear hysteresis dynamic equation to compensate the hysteresis effect. According to simulation results, the tracking error was only nanometer order. Through experimental examinations, the tracking performance was obtained as precision as ten nanometers order which is the resolution limitation of the measurement system. The effectiveness of the proposed adaptive control scheme was validated.

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.

A New Leakage Term in the Adaptive Law

The hyperstability theory of adaptive control systems is extended to encompass plants with unmodelled dynamics and disturbances. The analysis not only shows that leakage in the adaptive law is a natural way to avoid robustness problems (which is a known result in adaptive control theory), but also provides a new adaptive law that is a sort of signal-dependent σ-modification. The proposed adaptive law is less conservative than the σ-modification, but still ensures the global stability of the system, which is formally proven in the paper. Since it is norm of the parasitic dynamics, the criteria for system stability are derived. Based on these, are presented.

PMSM 교류 서보모터의 적응형 전류 제어기 설계

서보 모터의 순시 토크 제어 능력의 개선을 위해 PMSM 서보 모터의 적응형 전류 제어기 설계 방법을 제안한다. 동기좌표 전류 제어기에서 비결합 제어 입력을 이용하여 새로운 제어 입력 항을 얻을 수 있으며 이를 통해 제어기의 원하는 대역폭을 선정할 수 있지만 모터의 파라미터 변화, 데드타임에 의한 인버터의 왜곡 등의 외란에 의해 제어 성능이 저하된다. 이러한 단점을 개선하기 위해 PMSM 서보 모터의 적응형 전류 제어기의 설계 방법을 제안하며 설계 방법이 초안정(hyperstability) 이론에 의해 구해진다. 제안된 제어 방식의 점근안정성을 이론적으로 증명하고 DSP TMS320C31을 이용한 시뮬레이션과 실험을 통해 입증한다.

Adaptive control for uncertain systems with sector-like bounded non-linear inputs

In the current paper, a model reference adaptive controller design based on hyper-stability theory is proposed for the uncertain non-linear system equipped with the so-called sector-like bounded non-linear inputs, which are subject to system uncertainties of the norm-bounded system parameter variations and external disturbances. The control objectives are to achieve an asymptotical tracking of the system output targeted to the desired reference model output and to ensure the bounded condition of all the signals in the controlled system. Finally, some computer simulation results are given to validate the excellent performance of the proposed adaptive control system.

On the design of adaptive autopilots for a launch vehicle

Three efficient and practical approaches for the design of an adaptive autopilot for a launch vehicle (LV) attitude control system during atmospheric flight are presented. The proposed adaptive control schemes are developed on the basis of different combinations of gain scheduling, decoupling, and the model reference adaptive technique. A new adaptation mechanism based on hyperstability theory is developed. Every scheme contains some degree of adaptation, corresponding to its complexity and cost of realization. A six-degree-of-freedom non-linear simulation was used to compare the adaptation characteristics of the proposed schemes in the presence of different disturbances during atmospheric flight of the vehicle.

A Self-Adjusting Simple Hyperstable Adaptive Recursive Algorithm

Adaptive infinite impulse response (IIR), or recursive, filters are less attractive mainly because of the stability and the difficulties associated with their adaptive algorithms. Hyperstability theory when simplified and adapted for digital signal processing offers a new class of IIR filters, simple hyperstable adaptive recursive filters (SHARFs), which is directly related to strictly positive real (SPR) transfer functions. One of the most important drawbacks of the SHARF algorithm is the presence of the unknown denominator in the transfer function that must be SPR in order to ensure convergence. In this paper, SHARF is investigated with SPR transfer functions designed without any priori knowledge of the filter parameters by the pole–zero placement on the unit circle method and made self-adjusting. To demonstrate self-adjustment of the algorithm, SHARF algorithm using constraint least-mean square (LMS) method is applied to a pure four-pole autoregressive process.

Adaptive control for a class of chaotic systems with nonlinear inputs and disturbances

In this paper, an adaptive controller design method based on hyperstability theory is proposed for a class of unified chaotic systems with so-called sector-bounded inputs and disturbances. Under the norm-bounded assumption of disturbances, for the controlled system, system states can be regulated to zero levels asymptotically in the presence of this class of disturbances. To show the validity and feasibility of the proposed adaptive controller, some simulations on controlling different chaotic systems with disturbances, are made and investigated.

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.

PI predictive fuzzy controllers for electrical drive speed control: methods and software for stable development

The paper presents two structures of PI predictive fuzzy controllers (PI-P-FCs) with first- and second-order prediction. The PI-P-FCs are meant for the speed control of electrical drives with variable inertia used in several industrial applications. The new development method for these PI-P-FCs is based on guaranteeing a desired domain for the “phase margin” of the fuzzy control systems (FCSs) with PI-P-FCs when they are considered to be equivalent to the linear control systems with linear (conventional) PI controllers. It is also proposed a stability analysis method for the FCSs with PI-P-FCs employing Popov’s hyperstability theory and a discrete-time state space mathematical model of the controlled plant. A software tool for the stability analysis of the FCSs, developed in the Matlab and Simulink environment, is presented.

The error-based minimal control synthesis algorithm with integral action

This paper presents a new form of the direct adaptive minimal control synthesis (MCS) algorithm. As its name suggests, the error-based minimal control synthesis with integral action (Er-MCSI) algorithm is solely driven by error signals that are generated within the closed-loop system, and contains an explicit integral gain term. The purpose of this new structure is, respectively, to remove the problem of variable adaptive effort with changes in the operating set point, and to remove gain ‘wind-up’ effects due to plant disturbances and signal offsets. The core of this paper contains a proof of stability for Er-MCSI, based on hyperstability theory, together with supporting simulation and implementation studies.

Sensorless MRAS‐based induction motor control with parallel speed and stator resistance estimation

AbstractThis paper proposes a novel MRAS‐based speed controller for the induction motor drive without shaft sensor, with the integral adaptation mechanism for on‐line tuning of the stator resistance (Rs). For an accurate estimate of the shaft speed (ω) even at near zero speeds, proposed Rs estimator running parallel in order to compensate for the RS thermal variation. In an intent to accurately estimate the ω at low speeds, without deterioration the drive performance, parallel with the ω estimation the Rs is also estimated to compensate Rs thermal variation. The reference and adjustable models of MRAS‐based ω estimator change their roles in the Rs estimator context. The dynamics of the ω derivation and the Rs estimation are investigated for a wide range of operating conditions and straightforward design procedure is proposed, derived from the hyperstability theory. Extensive computer simulations prove the effectiveness of the proposed solution.