Hyperstability Theory Research Articles

ADAPTIVE CONTROL FOR UNCERTAIN SYSTEMS WITH SECTOR-LIKE BOUNDED NONLINEAR INPUTS

In this paper, a general approach to the synthesis of model reference adaptive control systems is proposed for uncertain time -delay systems with the so-called sector-like bounded nonlinear inputs via hyperstability theory. In the presence of system parameter variations and external disturbances, it can be ensured that the system output can track the reference model output asymptotically. Finally, some computer simulations are given to illustrate the performance of the proposed adaptive control scheme.

Robust Model Following Control for Uncertain Systems with Input Nonlinearities.

In this paper, a robust model following control law based on hyperstability theory will be derived for uncertain systems with input nonlinearities. Under the upper bound assumption for system uncertainties, it is proved that the stability of the proposed control system is insensitive to system parameter variations, unmodelled dynamical errors, and external disturbances by mathematical analyses. It also ensures that the system output can track the desired model output asymptotically and all signals in the proposed control scheme are bounded. Furthermore, some computer simulation results will be presented to illustrate the performance of the proposed robust model following control scheme.

Popov Theories and Qualitative Behavior of Dynamic and Control Systems

This paper is an attempt to summarize some problems that may be solved within the framework of the Popov and Popov-like theories. Besides classical absolute stability problem, problems as forced oscillations, systems with multiple equilibria, dissipativity (ultimate boundedness) are considered. The Popov theory and results are viewed as emerging in three stages: the first one is concerned with the discovery of the frequency domain inequality connected with integral equations, the second one corresponds to the generalization of Yakubovich Kalman lemma to the multivariable case as well as to hyper stability theory formulation, and the third stage incorporates results on various qualitative behavior for systems with multiple equilibria (mutability-dichotomy and gradient like behavior).

Non-Linear Control with Adaptive Observer for the Sensorless Induction Speed Drives

In the framework of the sensorless non-linear control of a PWM fed induction motor drive, an original strategy is proposed. The latter is an association of the control based on the Inputs-Outputs (I/O) system lineatharion [2], with a MRAS (Model Reference Adaptive System) state observer [7]. The observer design and synthesis uses Popov’s hyper-stability theory. For the sensorless drive, the rotation speed adaptive law is proposed [5]. All control and observation parameters are determined analytically. The precise simulations of the global system allow to testing the basic Operation functions of this drive and especially the good behaviour at very low rotation speed. Significant experimental results are discussed to illustrate the dynamic performances of this induction motor drive in the four quadrants of the torque – speed plane.

Hyperstability approach to the synthesis of adaptive controller for uncertain time-varying delay systems with sector-bounded non-linear inputs

In this paper, a general approach is taken to the synthesis of model reference adaptive controllers for uncertain time-varying delay systems with sector-bounded non-linear inputs via hyperstability theory. It is ensured that the proposed control system is asymptotically hyperstable for the time-varying delay system with system parameter variations, modelling errors and external disturbances. Finally, some computer simulations are given to illustrate the performance of the proposed adaptive control scheme.

An Adaptive Controller for Improving Dynamic Stability of Synchronous Power System

This paper presents a new adaptive control approach for improving dynamic stability of power systems. The adaptive control structure is based on hyperstability theory. The design method of the closed loop system does not need the specification of weighting matrices. The eigenvalues of electromechanical mode of the system is shifted to a prespecified vertical strip. The control is constructed so that the closed loop system is hyperstable, guaranteeing the dynamic stability improvement of power systems. The changeable gains generated specifically but not uniquely by a nonlinear time varying function act as adaptive mechanism. Compared with MRAC or STAC, the proposed control structure avoids the difficulty of choosing an appropriate reference model and the burden of implementing an online parameter estimator. The power system under investigation consists of a synchronous machine connected to an infinite bus. It has both voltage regulator and speed governor controls. The effectiveness of the controller for damping machine oscillations caused by power system disturbances is verified by simulation studies.

A decentralized adaptive controller for multimachine power systems

This paper presents a new adaptive controller via multilevel technique. The control strategy is based on decomposing control signals into two components: the first one balances the effect of interconnections between the subsystems, while the second one is a local adaptive controller based on hyperstability theory for the decentralized subsystems. The changeable gains generated by a non-linear time-varying function act as the adaptive mechanism. Compared with MRAC or STAC the proposed control avoids the difficulty in choosing an appropriate reference model and the burden of implementing an online parameter estimator. The local control is constructed so that the closed-loop system is hyperstable guaranteeing the dynamic stability improvement of each subsystem in the multimachine power system. A guarantee of stability of the overall system is also given. Simulation results of a numerical example of a multimachine power system reveal that the low frequency oscillations can completely be eliminated using the proposed control scheme.

Frequency domain evaluation of circle criterion, Popov criterion and off-axis circle criterion in the MIMO case

Many control applications can be described as non-linear feedback systems whose stability properties can, for example, be analysed with the circle criterion, the Popov criterion or the off-axis circle criterion. In the SISO case these sector criteria became very popular because of their simple graphic interpretations; the criteria's significance for multivariable feedback systems remained rather poor since there are almost no practicable ways to evaluate them. In this paper the MIMO versions of the three stability criteria are derived using Popov's theory of hyperstability. The main contribution is the presentation of new methods for a frequency domain evaluation of the sector criteria in the multivariable case. The new methods are based on graphic elements: the 'positivity curves'.

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.

Instrumentation architecture and sensor fusion for systems control

This paper presents a systematic approach for the design of an instrumentation architecture and a sensor data fusion concept which together enable the robust control of complex electromechanical systems. The development is based on the theory of hyperstability. Earlier results are generalized and previous restrictions on sensors are relaxed to broaden the applicability of the proposed method. Experimental results validate the methodology and confirm its efficacy in practical applications.

Robust speed control of brushless DC motor using adaptive input–output linearisation technique

A robust speed control scheme for a brushless DC (BLDC) motor using an adaptive input–output linearisation technique is presented. By using this technique, the nonlinear motor model can be linearised in Brunovski canonical form, and the desired speed dynamics can be obtained based on the linearised model. This control technique, however, gives an undesirable output performance under the mismatch of the system parameters and load conditions caused by the incomplete linearisation. For the robust output response, the disturbance torque and flux linkage will be estimated by a model reference adaptive technique. The adaptation laws are derived by the Popov's hyperstability theory and positivity concept. The proposed scheme is implemented on a BLDC motor using the software of DSP TMS320C30 and the effectiveness is verified through the comparative simulations and experiments.

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.

A robust control scheme for asymptotic tracking of robot motion

In this paper, a controller structure is developed to provide for asymptotic tracking of robot motion. The design tool is the theory of hyperstability and the analysis has led to a simple and an easy-to-implement robust version of the inverse dynamics. Simulation studies are worked out to demonstrate the controller performance. A comparison with other methods is done to show the merits of the developed scheme vs. other recently developed schemes. The implementation and computational requirements of the control schemes are determined and shown to be within the capabilities of new control hardware.

Adaptive Control of Robot Manipulators Using a Popov Hyperstability Approach

A general adaptive control approach of robot manipulators using Popov hyperstability is proposed in this paper. The manipulator adaptive control problem is first formulated in a form suitable for the application of hyperstability theory. The adaptive control law is general, and most of the adaptive control laws that have been proposed are special forms of this adaptive control law. The adaptive controller takes advantage of the flexibility in the choice of the adaptive parameters and the controller structure. The adaptive controller guarantees globally asymptotic stability in the hyperstability sense. For input disturbances, the control law, with little modification, maintains satisfactory system performance. Simulation results are presented to evaluate the performance of the adaptive controller for a two link manipulator.

Stabilitätsanalyse von Fuzzy- Mehrgrößenregelungen mit Hilfe der Hyperstabilitätstheorie

In 1973 V. M. Popov introduced a criterion of hyperstability to analyze MIMO-systems as a generalisation of the absolute stability problem. In this paper an easy method to analyze a large class of closed-loop-systems controlled by a non-linear characteristic, especially fuzzy-controllers, using hyperstability theory is presented. The criterion of hyperstability is reduced to a multidimensional sector criterion, which allows an easy analytic and maybe a graphic analysis of the closed-loop system. Because of its clarity the advantage of this method is to give a secure statement concerning the stability behaviour of the closed-loop system after modifying the fuzzy-controller

Adaptive model-following controller for robotic manipulators

A nonlinear state-space model representing the robot dynamics and containing a disturbance term due to gravitational loading is presented. An adaptive model-following control problem satisfying the matching conditions is formulated using a suitable linear time-invariant reference model. The control input is designed to have two components: a non-adaptive linear component to do the task of model-following and a nonlinear unit-vector component based on hyperstability theory to do the adaptive task. An additional integral feedback term is further added and then the overall asymptotic hyperstability is established. Simulation experiments on the first three joints of a PUMA 560 robot manipulator have indicated the potential of our design approach.

A design approach to adaptive model-following control of robotic manipulators

In this paper, the robot dynamics are represented by a nonlinear state-space model containing a disturbance term due to gravitational loading. Using a suitable linear time-invariant reference model, an adaptive model-following control problem is formulated which satisfies the matching conditions. The control input is designed to have two components: a nonadaptive linear component to do the task of model-following and a nonlinear unit-vector component based on hyperstability theory to do the adaptive task. An additional integral feedback term is further superimposed and then the overall asymptotic hyperstability is established. The simulation results on the first three joints of PUMA 560 robot manipulator indicate the potential of our design approach.

A second-order hyperstable adaptive filter for frequency estimation

A second-order adaptive filter structure that can be used for frequency estimation and enhancement of an input sinusoid is proposed. Unlike other gradient-based adaptive line enhancement schemes, this filter has the advantage that it can be made to converge arbitrarily fast by increasing the step size of the update, while still retaining stability. This is possible because the adaptation strategy has its roots in hyperstability theory. A limitation of the scheme is that it gives a biased estimate in the presence of noise; however, some techniques that bring the bias down to a low level are described. >

Model reference adaptive inverse control of a single link flexible robot

A new model reference adaptive inverse control algorithm is proposed for the end point position control of flexible manipulators. This controller forms a series model reference adaptive system where an estimated system inverse is placed in the feed forward path to provide an inverse control through regulation of controller parameters. It differs from other model reference control strategies in that a signal synthesis loop is included to compensate for the estimation error of the inverse controller and the output tracking error, and to improve stability. The stability of the overall control system is shown to be guaranteed using hyperstability theory. The proposed control scheme is applied to control the tip position of a single link flexible robot. A non-dimensionalized model is developed. Its zero-order hold equivalence in discrete time domain is described by an auto-regressive and moving average form. A lattice filter is utilized as a deconvolution filter. The time-delay behavior from the driving torque to the robot tip position due to robot structural flexibility is investigated.

Model Reference Control of Non-Linear Plants in the Presence of Plant Uncertainties

A model reference control (MRC) scheme based on the hyperstability theory for a class of input-output linearizable non-linear plants is proposed. It is shown that a switching slate feedback gain in this algorithm can reject the effect of the plant uncertainties, if the bounds of the plant uncertainties are known. Hence the boundedness of all signals in the proposed MRC system can be ensured.