This paper proposes an improved double power reaching law integral SMC algorithm to overcome the chattering, large overshoot, slow response. This improved algorithm has two advantages. Firstly, the designed control law can reach the approaching equilibrium point quickly when it is away from or close to the sliding surface. The chattering and response speed problems can be resolved. Secondly, the proposed algorithm has a good anti-jamming performance, and can maintain a good dynamic quality under the condition of the uncertain external disturbance. Finally, the proposed algorithm is applied to the open-loop unstable magnetic suspension system. Theoretical analysis and Matlab simulation results show that the improved algorithm has better control performances than the traditional SMC and the power reaching law integral SMC algorithm, such as less chattering, smaller overshoots, and faster response speed.

Control Algorithms of Magnetic Suspension Systems Based on the Improved Double Exponential Reaching Law of Sliding Mode Control

This paper studies the problem of parameter estimation for frequency response signals For a linear system, the frequency response is a sine signal with the same frequency as the input sine signal When a multi-frequency sine signal is applied to a system, the system response also is a multi-frequency sine signal The signal modeling for multi-frequency sine signals is very difficult due to the highly nonlinear relations between the characteristic parameters and the model output In order to obtain the parameter estimates of the multi-frequency sine signal, the signal modeling methods based on statistical identification are proposed by means of the dynamical window discrete measured data By constructing a criterion function with respect to the model parameters to be estimated, a hierarchical multi-innovation stochastic gradient estimation method is derived through parameter decomposition Moreover, the forgetting factor and the convergence factor are introduced to improve the performance of the algorithm The simulation results show the effectiveness of the proposed methods

Hierarchical Parameter Estimation for the Frequency Response Based on the Dynamical Window Data

This article studies the parameter estimation to the system response from the discrete measurement data. By constructing the dynamical rolling cost functions and using the nonlinear optimization, t...

The parameter estimation algorithms based on the dynamical response measurement data

This paper considers the parameter estimation problems of two-input single-output Hammerstein finite impulse response systems. A hierarchical least squares algorithm is proposed for improving the computational efficiency through combining the hierarchical identification principle and the identification model decomposition, and a multi-innovation least squares algorithm is proposed for enhancing the parameter estimation accuracy based on the multi-innovation identification theory. The key is to derive two sub-identification models, each of which contains a set of merged parameter vectors. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the over-parametrization identification method, and can be easily extended to multi-input multi-output systems. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.

Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems

This paper considers the parameter identification problems of controlled autoregressive systems using observation information. According to the hierarchical identification principle, we decompose the controlled autoregressive system into two subsystems by introducing two fictitious output variables. Then a two-stage gradient-based iterative algorithm is proposed by means of the iterative technique. In order to improve the performance of the tracking the time-varying parameters, we derive a two-stage multi-innovation gradient-based iterative algorithm based on the multi-innovation identification theory. Finally, an example is provided to illustrate the effectiveness of the proposed algorithms.

Two-stage Gradient-based Iterative Estimation Methods for Controlled Autoregressive Systems Using the Measurement Data

For a multivariable system with moving average noise (i.e., a multivariable controlled autoregressive moving average system), this paper proposes a filtering based extended stochastic gradient (ESG) algorithm and a filtering based multi-innovation ESG algorithm for improving the parameter estimation accuracy. The key is using the filtering technique and the multi-innovation identification theory. The proposed algorithms can identify the parameters of the system model and the noise model. The filtering based multi-innovation ESG algorithm can give more accurate parameter estimates. The numerical simulation results demonstrate that the proposed algorithms work well.

A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems

Hammerstein system identification is difficult because there exist the product items of the parameters between the static nonlinear block and the dynamic linear block. This paper presents a novel parameter separation based recursive least squares (PS-RLS) identification algorithm for resolving this problem. Its basic idea is to use a linear filter to filter the output data and the noise, and then to obtain two new identification submodels in each of which the output is linear in the corresponding parameter vector. Compared with the over-parametrization based recursive least squares method, the proposed algorithm can avoid estimating the redundant parameters and has a higher computational efficiency. The simulation results show that the proposed PS-RLS algorithm can generate highly accurate parameter estimates with less computational effort.

Filtering based least squares parameter estimation algorithms for Hammerstein nonlinear CARMA systems

In this paper, we extends the innovation vector to the innovation matrices and presents a filtering based multi-innovation extended stochastic gradient algorithm for multi-input multi-output controlled autoregressive moving average systems. The basic idea is using the filtering technique to transform a multivariable system into two identification models, then to identify the parameters of these two identification models interactively. The proposed multi-innovation identification algorithm can effectively improve the parameter estimation accuracy.

Multi-innovation extended stochastic gradient algorithm for multi-input multi-output controlled autoregressive moving average systems by using the filtering technique

Xiangkui Wan

Papers

A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems

Two-stage Gradient-based Iterative Estimation Methods for Controlled Autoregressive Systems Using the Measurement Data

Filtering based least squares parameter estimation algorithms for Hammerstein nonlinear CARMA systems

Multi-innovation extended stochastic gradient algorithm for multi-input multi-output controlled autoregressive moving average systems by using the filtering technique