Free-model based neural network for dynamic systems

The precise position control for electro-hydraulic servo system (EHSS) is a key technical problem for modern industry control. This paper presents a model reference adaptive control (MRAC) strategy combining fractional order calculus theory and neural network to solve the high nonlinearity and parameter uncertainties in the EHSS. The reference model in the MRAC strategy is a fractional second-order model and the controller with adaptive law is designed by a Wiener recurrent neural network (WRNN). Simulations indicate the validity and superiority of the proposed fractional MRAC strategy.

The active control technology was carried out on the marine diesel two-stage vibration isolation system (MDTVIS); the active control technology was able to make up for passive vibration isolation technology in the low-frequency range. The construction of a secondary path was one of the most important sectors, which had a full impact on active vibration isolation performance. Nonlinear components comprised the secondary path, which were principally the nonlinear vibration of multi-degrees of freedom in the practical MDTVIS and the nonlinear control path in the hydraulic servo actuator. The nonlinearity was not ignorable in coping with the second path, so that the vibration isolation performance was greatly influenced by the secondary path in the active control technology with the classic adaptive comb-type filter. By combining the model reference adaptive inverse control strategy with the nonlinear robust control technology, the linearity control algorithm was designed, and then the classic adaptive comb-type filter algorithm was carried out for the new system; herein the hybrid control strategy was constructed to apply to the secondary path in the practical MDTVIS. The proposed hybrid control strategy was able to improve the initial active vibration isolation control algorithm with an adaptive comb-type filter and overcome shortcomings of the vibration strengthened in some multi-harmonic-frequency sites in the low-frequency range. The total performance of vibration isolation coupling with multi-path was improved in balance.

It is well-known that the controls of neural network require that all the inputs of their input layer are available. Under this circumstance, the architecture of the neural network is constrained. Hence, this kind of neurocontrol cannot apply to a wide class of nonlinear and unknown dynamical systems, or the control system that requires more sensors. Although the unknown system state and the unknown system dynamics can be achieved from an adaptive observer and a learning neural network, respectively, the simultaneous existence of the estimated state error and the modeling error makes the control system more likely to be unstable. In this paper, a novel neurocontroller based on the concept of sliding mode with estimated state is constructed to tackle a wide class of unknown and nonlinear dynamical systems. The focal stability of the overall system can be verified by the Lyapunov stability criteria. Finally, simulations are presented to verify the usefulness of the proposed method.

Partial-state feedback multivariable MRAC and reduced-order designs

Recently, a class of adaptive control schemes called L1 Adaptive Control (L1-AC) has been proposed and widely advertised in aerospace control for achieving fast and robust adaptation and better performance than the existing Model Reference Adaptive Control (MRAC) Schemes. The L1-AC scheme is designed mainly for plants with full state measurement even though the name L1-AC has been used as an umbrella name for more general classes of plants. In this paper, we show that the L1-AC for plants with measured states is simply a standard MRAC with a low pass filter inserted in front of the control input. The analysis of the scheme is almost identical to that of MRAC as the same Lyapunov function is used to establish stability. The motivation for using the filter is the fact that for this class of adaptive schemes i.e. MRAC for plants with full state measurement the tracking error can be made arbitrarily small during transient by increasing the adaptive gain. A high adaptive gain however makes the differential equation of the adaptive law or estimator very stiff and leads to numerical problems that cause high oscillations in the estimated parameters leading to loss of adaptivity and deviations from what the theoretical properties dictate. The L1-AC approach mistook these numerical oscillations as properties of the adaptive scheme and inserted an input low pass filter in order to filter them out. While the filter helps reduce the frequency of these oscillations in the control law the price paid is high. First the numerical instability does not go away and the estimated parameters continue to oscillate without converging to the true parameters even in the presence of sufficiently rich signals. Second, due to the filter the tracking error is no longer guaranteed to converge to zero and the transient bounds for the tracking error also depend on the filter. As a result, the tracking properties of the L1-AC scheme are worse than what a simple MRAC scheme can generate with adaptive gains that could be high but away from the region of numerical instability. In addition, the presence of the filter reduces the robust stability margins in the presence of unmodeled dynamics and provides literally no advantage as simple robust MRAC techniques can solve the same problem achieving much better properties. The authors of L1-AC often compare the properties of a numerically unstable MRAC due to extremely high adaptive gains something that is prohibited by robust adaptive control with those of the filtered MRAC aka L1-AC to show that L1-AC performs better. Such comparisons are not only misleading but do not reveal what causes what giving the reader a false impression of a new theory that results to new performance and robustness improvements. The use of filters in adaptive control is not new and they are used to improve the performance and robustness of certain adaptive control schemes without destroying their ideal tracking properties. In this paper we present such a scheme that guarantees good transient performance and robustness and reveals the trade off between transient performance and robust stability.

The purpose of this chapter is to redesign the standard adaptive control schemes by using hybrid structure composed by Model Reference Adaptive Control (MRAC) or Adaptive Pole Placement Control (APPC) strategies, associated to Variable Structure (VS) schemes for achieving non-standard robust adaptive control strategies. The both control strategies is now on named VS-MRAC and VS-APPC. We start with the theoretical base of standard control strategies APPC and MRAC, discussing their structures, as how their parameters are identified by adaptive observers and their robustness properties for guaranteeing their stability. After that, we introduce the sliding mode control (variable structure) in each control scheme for simplifying their design procedure. These design procedure are based on stability analysis of each hybrid robust control scheme. With the definition of both hybrid control strategies, it is analyzed their behavior when controlling system plants with unmodeled disturbances and parameter variation. It is established how the adaptive laws compensates these unmodeled dynamics. Furthermore, by using simple systems examples it is realized a comparison study between the hybrid structures VS-APPC and VSMRAC and the standard schemes APPC and MRAC. As the hybrid structures use switching laws due to the sliding mode scheme, the effect of chattering is analyzed on the implementation and consequently effects on the digital control hardware where sampling times are limiting factor. For reducing these drawbacks it is also discussed possibilities which kind of modifications can employ. Finally, some practical considerations are discussed on an implementation on motor drive systems.

It is shown how to change the primary control structure of a model reference adaptive control (MRAC) scheme from the usual minimum settling time-type algorithm to a ripple-free response control (RFRC) scheme. RFRC does not try to compensate process zeros, avoiding ringing effects (like intersampling ripple). The main issue in the derivation of the RFRC-MRAC scheme is the establishment of a stable adaptive law which guarantees a ripple-free behavior if the error signal tends to zero. In the original MRAC scheme, the error signal consisted of the desired error plus a transient term which tends to zero when adaptation proceeds. In this MRAC scheme, the error consists of a filtered form of the desired RFRC error. Hence, if the error used in the adaption tends to zero, the RFRC behavior is achieved. The scheme avoids ringing effects and can control nonminimum-phase processes. The cost of these advantages is a slowing down of the process response by a number of samples equal to the order of the numerator polynomial. Simulations confirm the RFRC-like characteristics, and practical results on a water level system show the usability of the method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The problem of rejecting unknown sinusoidal disturbances in the output of an unknown LTI system which is also corrupted by wide-band noise has received a lot of interest in the recent years. Most of the successful efforts proposed up to now assume that the model of the LTI system is stable and is known exactly. This paper shows how an overparameterized classical robust model-reference adaptive control (MRAC) scheme can handle the problem of simultaneous reference-model tracking and unknown disturbance suppression. The results are applicable to a plant whose dominant modeled part is unknown and possibly unstable, yet has stable zeros and a known relative degree. Some considerations are taken to avoid boosting broadband noise effects on the plant output and to improve robustness with respect to plant unstructured unmodeled dynamics. The architecture of the classical MRAC is employed together with overparameterization of the controller and an auxiliary control input for performance improvement. The performance and robustness properties of the scheme are discussed and numerical simulations are given to demonstrate the efficacy of the scheme.

In this paper, we present a new approach for modeling the hysteresis nonlinearity of a piezo-positioning systems. Because of its nonlinear hysteresis effect, the tracking control accuracy of the precision positioning system is difficulty achieved. Hence it is desirable to take hysteresis effect into consideration for improving the trajectory performance. A model reference adaptive optimal control scheme based on online actor-critic algorithm is developed. The proposed controller can be constructed without a nonlinear hysteresis dynamic equation to compensate the hysteresis effect. Simulation results show the effectiveness of the new approach.

SummaryIn this paper, a novel robust model reference adaptive impedance control (RMRAIC) scheme is presented for an active transtibial ankle prosthesis. The controller makes the closed loop dynamics of the prosthesis similar to a reference impedance model and provides asymptotic tracking of the response trajectory of this impedance model. The interactions between human and prosthesis are taken into account by designing a second-order reference impedance model. The proposed controller is robust against parametric uncertainties in the nonlinear dynamic model of the prosthesis. Also, the controller has robustness against bounded uncertainties due to unavailable ground reaction forces and unmeasurable feedbacks of accelerations at the socket place. Moreover, an appropriate Series Elastic Actuator (SEA) mechanism for the prosthetic ankle is included in this work and its effects are discussed. Tracking performance and stability of the closed-loop system are proven via the Lyapunov stability analysis. Using simulations on an overall amputee prosthetic foot system, the effectiveness of the proposed RMRAIC controller is investigated for the task of level ground walking.

Inspired from complex human brain architecture, parallel processing and learning capabilities, Artificial Neural Networks (ANN) has emerged as a new data processing paradigm. Image Association, Image Recognition, Function Approximation, Beam Forming are some of the fields that appealed many researchers to use Neural Networks. Generalization capability of Neural Networks also makes it appurtenant to Plant Control as superior control strategy than traditional Proportional-Integrator-Derivative (PID) Controllers. The research aims to design Neural Network architecture to identify whether this strategy can be employed to control a non-linear dynamic model. For this purpose well-known Vertical Take Off and Landing (VTOL) vehicle known as Quadrotor is used as a plant. Direction Cosine Matrix Inertial Measurement Unit (DCM IMU) Theory is used for attitude estimation of the flying robot. Neural Network Predictive Control and Model Reference Adaptive Control (MRAC) strategy is selected to achieve attitude control of Quadrotor. Levenberg-Marquardt algorithm is used as backpropagation technique for training of the neural network architecture. Quadrotor plant modeling, Neural Network training and an effective controller is implemented in Matlab Simulink environment and their pros and cons are reviewed. Project files are open source and available publicly on to fuel further research in area.

A stochastic, fuzzy, neural network (SFNN) to model unknown nonlinear dynamic systems is developed. In this network, a non-singleton fuzzifier with Gaussian membership functions instead of the singleton fuzzifier in the fuzzy logic is introduced. Based on these membership functions, an online supervised parameter learning algorithm of the SFNN is proposed to overcome the local minimum of learning process in current neural networks, and an off-line algorithm for the structure learning of the SFNN is presented to reduce the amount of computation of the SFNN. This new network provides a universal approximator and it is also applicable to stochastic control and decision systems and the identification of chaos in nonlinear systems.

A desire to improve the positioning accuracy of ball screws prompted an investigation into the dynamics of nanometer motion. Characterization of the ball screw indicated that nanometer motion is possible prior to friction breakaway via elastic deformation of the frictional contacts. The observed dynamics are nonlinear, and consequently result in inconsistent and unpredictable closed-loop response while under PI position control. A model reference adaptive control (MRAC) strategy is adopted and a Lyapunov design technique is applied to derive the adaptive laws. The digital signal processor (DSP) implementation of the scheme is discussed. Experimental results show the MRAC scheme results in a more predictable and consistent closed-loop response than the PI scheme.

On the hybrid MRAC-PID control: A comparison study

This paper discusses adaptive control method used in high performance servo system based on Cerebellar Model Articulation Controller(CMAC). It analyzes the uncertain and nonlinear factors of the servo system, studies the modeling method using the frequency property of the system, and then uses an additional item to instead of the non-modeling factor. In the proposed control scheme, the CMAC controller is able to learn the unknown model dynamics, parameter variation and disturbance of the system on line. The model reference adaptive control (MRAC) scheme is used to give better solutions with online adaptation. It contemporarily improved the conception mapping algorithm of the Cerebellar Model Articulation Controller Neural Network(CMACNN), which gave a determined expression of the physical memory size and designed a physical memory address function. Experiment results verify that the proposed strategy can achieve high tracking precision for real-time position close-loop servo system.