State-space Self-tuning Control Research Articles

Novel state-space self-tuning control for two-dimensional linear discrete-time stochastic systems

Novel state-space self-tuning control for two-dimensional linear discrete-time stochastic systems

A NARMAX model-based state-space self-tuning control for nonlinear stochastic hybrid systems

A novel state-space self-tuning control methodology for a nonlinear stochastic hybrid system with stochastic noise/disturbances is proposed in this paper. via the optimal linearization approach, an adjustable NARMAX-based noise model with estimated states can be constructed for the state-space self-tuning control in nonlinear continuous-time stochastic systems. Then, a corresponding adaptive digital control scheme is proposed for continuous-time multivariable nonlinear stochastic systems, which have unknown system parameters, measurement noise/external disturbances, and inaccessible system states. The proposed method enables the development of a digitally implementable advanced control algorithm for nonlinear stochastic hybrid systems.

An Active Fault-Tolerant PWM Tracker for Unknown Nonlinear Stochastic Hybrid Systems: NARMAX Model and OKID-Based State-Space Self-Tuning Control

An active fault-tolerant pulse-width-modulated tracker using the nonlinear autoregressive moving average with exogenous inputs model-based state-space self-tuning control is proposed for continuous-time multivariable nonlinear stochastic systems with unknown system parameters, plant noises, measurement noises, and inaccessible system states. Through observer/Kalman filter identification method, a good initial guess of the unknown parameters of the chosen model is obtained so as to reduce the identification process time and enhance the system performances. Besides, by modifying the conventional self-tuning control, a fault-tolerant control scheme is also developed. For the detection of fault occurrence, a quantitative criterion is exploited by comparing the innovation process errors estimated by the Kalman filter estimation algorithm. In addition, the weighting matrix resetting technique is presented by adjusting and resetting the covariance matrix of parameter estimates to improve the parameter estimation for faulty system recovery. The technique can effectively cope with partially abrupt and/or gradual system faults and/or input failures with fault detection.

Low-order self-tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems

Based on the modified state-space self-tuning control (STC) via the observer/Kalman filter identification (OKID) method, an effective low-order tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems is proposed in this paper. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). Then, the above identified model in a general coordinate form is transformed to an observer form to provide a computationally effective initialization for a low-order on-line “auto-regressive moving average process with exogenous (ARMAX) model”-based identification. Furthermore, the proposed approach uses a modified Kalman filter estimate algorithm and the current-output-based observer to repair the drawback of the system multiple failures. Thus, the fault-tolerant control (FTC) performance can be significantly improved. As a result, a low-order state-space self-tuning control (STC) is constructed. Finally, the method is applied for a three-tank system with various faults to demonstrate the effectiveness of the proposed methodology.

Lower-order state-space self-tuning control for a stochastic chaotic hybrid system

In this paper, subject to acceptable closed-loop performance, an effective lower-order tuner for a stochastic chaotic hybrid system is designed using the observer/Kalman filter identification (OKID) method, in which the system state in a general coordinate form is transformed to one in an observer form. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm. Moreover, it provides a lower-order realization of the tracker, with computationally effective initialization, for on-line “auto-regressive moving average process with exogenous model” -based identification and a lower-order state-space self-tuning control technique. Finally, the chaotic Chen's system is used as an illustrative example to demonstrate the effectiveness of the proposed methodology.

State-Space Self-Tuning Control for Stochastic Fractional-Order Chaotic Systems

Based on the modified state-space self-tuning control (STC), a novel low-order tuner via the modified observer/Kalman filter identification (OKID) is proposed for stochastic fractional-order chaotic systems. The OKID method is a time-domain technique that identifies a discrete input-output map by using known input-output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). First, the estimated system in the general coordinate based on the conventional OKID method is transformed to the one in an observer form to fit the state-space innovation form for the STC. Then, in stead of the conventional recursive least squares (RLS) identification algorithm used for STC, the Kalman filter as a parameter estimator with the state-space innovation form is presented for effectively estimating the time-varying parameters. Besides, taking the advantage of the digital redesign approach, the derivation of the current-output-based observer is proposed for the modified STC. As a result, the low-order state-space self-tuner with the high-gain controller property is then proposed for stochastic fractional-order chaotic systems, which the fractional operators are well approximated using the standard high integer-order operators. Finally, the fractional-order Chen and Roumlssler systems with stochastic system process and measurement noises are used as illustrative examples to demonstrate the effectiveness of the proposed methodology

Active fault tolerant control using state-space self-tuning control approach

This paper presents a new fault tolerant control scheme for unknown multivariable stochastic systems by modifying the conventional state-space self-tuning control approach. For the detection of faults, a quantitative criterion is developed by comparing the innovation process errors occurring in the Kalman filter estimation algorithm, which, for faulty system recovery, a weighting matrix resetting technique is developed by adjusting and resetting the covariance matrices of the parameter estimate obtained in the Kalman filter estimation algorithm to improve the parameter estimation of the faulty systems. The proposed method can effectively cope with partially abrupt and/or gradual system faults and/or input failures with fault detection. The modified state-space self-tuning control scheme can be applied to the multivariable stochastic faulty system without requiring prior knowledge of system parameters and noise properties.

STATE-SPACE SELF-TUNING CONTROL FOR NONLINEAR STOCHASTIC AND CHAOTIC HYBRID SYSTEMS

This paper presents a new state-space self-tuning control scheme for adaptive digital control of continuous-time multivariable nonlinear stochastic and chaotic systems, which have unknown system parameters, system and measurement noises, and inaccessible system states. Instead of using the moving average (MA)-based noise model commonly used for adaptive digital control of linear discrete-time stochastic systems in the literature, an adjustable auto-regressive moving average (ARMA)-based noise model with estimated states is constructed for state-space self-tuning control of nonlinear continuous-time stochastic systems. By taking advantage of a digital redesign methodology, which converts a predesigned high-gain analog tracker/observer into a practically implementable low-gain digital tracker/observer, and by taking the non-negligible computation time delay and a relatively longer sampling period into consideration, a digitally redesigned predictive tracker/observer has been newly developed in this paper for adaptive chaotic orbit tracking. The proposed method enables the development of a digitally implementable advanced control algorithm for nonlinear stochastic and chaotic hybrid systems.

Hybrid state-space self-tuning control of uncertain linear systems

The paper presents a hybrid state-space self-tuner using a new dual-rate sampling scheme for digital adaptive control of continuous-time uncertain linear systems. A state-space-based recursive least-squares algorithm, together with a variable forgetting factor, is used for direct estimations of both the equivalent discrete-time uncertain linear system parameters and the associated discrete-time state of a continuous-time uncertain linear system from the sampled input and output data. An analogue optimal regional pole-placement design method is used for designing an optimal observer-based analogue controller. A suboptimal observer-based digital controller is then designed from the designed analogue controller using digital redesign technique. To enhance the robustness of parameter identification and state estimation algorithms, a dynamic bound for a class of uncertain bilinear parameters and a fast-rate digital controller are developed at each fast-sampling period. Also, to accommodate computation loads and computation delay for developing the advanced hybrid self-tuner, the designed analogue controller and observer gains are both updated at each slow-sampling period. This control technique has been successfully applied to benchmark control problems.

Hybrid state-space self-tuning control using dual-rate sampling

This paper presents a hybrid state-space self-tuning control scheme using dual-rate sampling for suboptimal digital adaptive control of linear time-invariant continuous-time multivariable stochastic systems with unknown parameters. An equivalent fast-rate discrete-time state-space innovation model (with estimated states) of the continuous-time system is constructed by using the estimated system parameters and Kalman gain. To utilize the existing optimal regional-pole assignment method developed in the continuous-time domain, the constructed fast-rate discrete-time model is converted into an equivalent continuous-time model for the development of a state-feedback optimal control law with pole placement in a specific region. The developed analog optimal control law is then converted into an equivalent pseudo-slow-rate digital control law via the proposed digital redesign technique, which can be realized via slow-rate digital electronics. The proposed method enables the development of a digitally implementable advanced control algorithm for digital adaptive control of continuous-time multivariable stochastic systems which may be unstable and/or have nonminimum phase.

Using the filtered CARMA and CARIMA models for state-space self-tuning control

Design procedures of state-space self-tuning controllers are described for both the filtered CARMA and CARIMA models. While closely resembling the generalized approach of Clarke-Kanjilal-Mohtadi (CKM), the proposed methods use the minimum possible dimension for the associated implicit-delay state-space model, and practical issues such us feedforward for linearization, regulation, servo-following, disturbance and offset elminution are considered. The resulting conipart-mental design allows the adjustment of tuning parameters to affecl different control characteristics. For the state-space self-tuners based on the filtered CARIMA model, two different forms can be distinguished: the normal form resembles the controller configuration based on the CARMA model, while the integrating form resembles the CKM self-tuner. Satisfactory results are observed in a simulation study of using the proposed self-tuners to control the steam temperature of a solar central receiver.

State-space self-tuning regulators for general multivariable stochastic systems

The paper presents a state-space approach for the self-tuning control of general linear multivariable discrete-time stochastic systems with the number of inputs (controllability indices) equal to or different from the number of outputs (observability indices). The dynamic system is represented in the state-space innovation form with the Luenberger's canonical structure. The model parameters, as well as the Kalman gain, are identified via the least-squares ladder algorithm, without utilising the standard stateestimation algorithm. Also, to avoid the direct use of the Luenberger's canonical transformations, a long division method is introduced for quickly converting a reducible or irreducible left matrix fraction description (LMFD) to an irreducible right matrix fraction description (RMFD) and for constructing the Luenberger's transformation matrices. In conjunction with the state-space selftuning control, an integral control is used so as to eliminate the steady-state errors and render the closed-loop system less sensitive to modelling errors. The proposed method will enhance the application of the state-space self-tuning concepts to a general class of multivariable stochastic systems.

State-space Self-tuning Control with Application to End Milling

An algorithm for self-tuning control of an immeasurable physical state of linear system is introduced. The control objective is specified by time-varying external reference signals The suggested algorithm can be considered as a concatenation of the Recursive Prediction Error (RPE) method for joint state and parameter estimation of state innovations model and state feedback control law with pole-zero placement.The practical usefulness of the algorithm is demonstrated by application to surface accuracy control in end milling process.

Modified approach to state-space self-tuning control with pole assignment

The paper presents a modified approach to state-space self-tuning pole-assignment control. The recursive prediction error method is used for joint state and parameter estimation in the controllable canonical form. This simplifies the state feedback law by eliminating the online computation of transformation matrices. The resulting algorithm is thus a feasible solution to the adaptive control of nonminimum-phase systems.