Zi-Jiang Yang

A Novel Robust Nonlinear Motion Controller With Disturbance Observer

In this brief, a novel robust nonlinear motion controller with disturbance observer (DOB) for positioning control of a nonlinear single-input-single-output (SISO) mechanical system is proposed. The controller is designed in a backstepping manner. First, a proportional-integral (PI) controller is designed to stabilize the position error. Consequently, a novel robust nonlinear velocity controller with DOB is designed to stabilize the velocity error. With the help of nonlinear damping terms, the input-to-state stability (ISS) property of the overall nonlinear control system is proven, which leads to a major contribution of construction of a theoretically guaranteed robust nonlinear controller with DOB. The performance of the proposed controller is verified through application to a magnetic levitation system. Comparative studies with an adaptive robust nonlinear controller are also carried out. It is shown that the proposed novel controller while being simple is superior over the adaptive robust nonlinear controller for the experimental setup under study.

Brief Adaptive robust nonlinear control of a magnetic levitation system

This paper proposes an adaptive robust nonlinear controller for position tracking problem of a magnetic levitation system, which is governed by an SISO second-order nonlinear differential equation. The controller is designed in a backstepping manner based on the nonlinear system model in the presence of parameter uncertainties. At the first step, a PI controller is designed to stabilize the position error of the levitated object. Then at the second step, an adaptive robust nonlinear controller composed of an adaptive feedback linearization control term and a robust nonlinear damping term is designed, to attenuate the effects of parameter uncertainties. The combined adaptive and robust approach helps to overcome some well-known practical problems such as high-gain feedback of the robust controller, and poor transient performance of the adaptive controller, so that better control performance can be achieved compared to the case where either is employed alone. Experimental results are included to show the excellent position tracking performance of the designed control system.

Decentralized Adaptive Robust Control of Robot Manipulators Using Disturbance Observers

In this paper, we propose a decentralized adaptive robust controller for trajectory tracking of robot manipulators. In each local controller, a disturbance observer (DOB) is introduced to compensate for the low-passed coupled uncertainties, and an adaptive sliding mode control term is employed to handle the fast-changing components of the uncertainties beyond the pass-band of the DOB. In contrast to most of the local controllers using DOB for robot manipulators that are based on linear control theory, in this study, by some special nonlinear damping terms, the boundedness of the signals of the overall nonlinear system is first ensured. This paves the way to analyze how the DOB and adaptive sliding mode control play in a cooperative way in each local subsystem to achieve an excellent control performance. Simulation results are provided to support the theoretical results.

Adaptive Robust Output-Feedback Control of a Magnetic Levitation System by K-Filter Approach

This work proposes an adaptive robust output feedback controller for position-tracking problem of a magnetic levitation system with a current feedback power amplifier. The controller is designed by a backstepping procedure with robustifying modification of the k-filter approach. The boundedness and guaranteed transient performance of the error signals are achieved by the nonlinear damping terms. And the ultimate position-tracking error is reduced by the adaptive laws. Experimental results are included to show the excellent control performance of the designed controller.

Dynamic surface control approach to adaptive robust control of nonlinear systems in semi-strict feedback form

This article considers the adaptive robust control of a class of single-input-single-output nonlinear systems in semi-strict feedback form using radial basis function (RBF) networks. It is well known that the standard backstepping design may suffer from “explosion of terms”. To overcome this problem, the recently developed dynamic surface control technique which employs a first-order low-pass filter at each step of the backstepping design procedure is generalized to the nonlinear system under study. Our attention is paid to achieve guaranteed transient performance of the adaptive controller. At each step of design, a feedback controller strengthened by nonlinear damping terms to counteract nonlinear uncertainties is designed to guarantee input-to-state practical stability of the corresponding subsystem, and then parameter adaptations are introduced to reduce the ultimate error bound. Furthermore, for the output trajectory tracking problem, it is recommended to adopt the partial adaptation policy to reduce the computational burden due to “curse of dimension” of the RBF networks. Finally, numerical examples are included to verify the results of theoretical analysis.

On-line identification of continuous time-delay systems combining least-squares techniques with a genetic algorithm

This paper proposes a new approach to on-line identi® cation of continuous timedelay systems from sampled input± output data. In order to track the time-varying time-delay and system parameters, the linear recursive least-squares (RLS) method is combined in a bootstrap manner with the genetic algorithm (GA) which has a high potential for global optimization. The time-delay is coded into binary bit strings and searched by the GA, while the system parameters are updated by the RLS method. Since only the time delay is searched by the GA, a small population size for the GA is suc cient and hence it is possible to implement the algorithm on line on the digital computers. Furthermore, this method (GALS method) is hybridized with the sequential nonlinear least-squares method which is eŒective in local search, to improve the speed of convergence. Simulation results show that both the GALS and the hybrid methods are quite ec cient. It is also veri® ed that, since the hybrid method is eŒective in both global and local optimizations, it has superior tracking performance over the GALS method especially in the case where the system parameters and time delay vary continuously with time.

Identification of continuous systems using digital low-pass filters

Direct methods for recursive identification of continuous systems from sampled input–output data using digital low–pass filters are discussed. The digital low–pass filters are introduced to avoid direct approximations of system signal derivatives from sampled data. Using a pre–designed digital low–pass filter, an approximated discrete–time estimation model is constructed easily. Thus the system parameters can be identified directly by recursive identification algorithms. Numerical results, show that the parameter estimates are not so sensitive to the pass-band of the filter, and if the filter is designed so that its pass-band matches that of the system closely and thus the noise effects are sufficiently reduced, accurate estimates can be obtained by recursive identification algorithms. Two classes of filters (FIR digital filter and IIR digital filter) are considered. It is shown that some other methods can be unified to be either the IIR or the FIR filtering approach.

Brief paper: Identification of continuous-time systems with multiple unknown time delays by global nonlinear least-squares and instrumental variable methods

This paper considers the identification problem of multiple input single output (MISO) continuous-time systems with unknown time delays of the inputs, from sampled input-output data. An iterative global separable nonlinear least-squares (GSEPNLS) method which estimates the time delays and transfer function parameters separably is derived to significantly reduce the possibility of convergence to a local minimum, by using the stochastic global-optimization techniques. Furthermore, the GSEPNLS method is modified to a novel global separable nonlinear instrumental variable (GSEPNIV) method to remove the biases of the estimates in the presence of high measurement noise. Simulation results show that the proposed algorithms work quite well.

An Adaptive Robust Nonlinear Motion Controller Combined With Disturbance Observer

Parameter adaptation and disturbance observer (DOB) have been considered as two contrastively different approaches to handle uncertainties in motion control problems. The purpose of this brief is to merge both techniques into one control design with theoretically guaranteed performance. It is shown that the DOB compensates low-passed components of the lumped uncertainties without the necessity of parameterization, whereas the adaptive mechanism is only automatically activated in the cases where the fast-changing components of the uncertainties beyond the pass-band of the DOB can be parameterized by unknown parameters. It is thus shown theoretically how the DOB and adaptive mechanism play in a cooperative way so that the controller is more effective than the individual ones. Simulation results are provided to support the theoretical results.

Distributed robust control for synchronised tracking of networked Euler–Lagrange systems

In this paper, we propose a distributed robust control method for synchronised tracking of networked Euler–Lagrange systems, where the time-varying reference trajectory is sent to only a subset of the agents. It is assumed that the agents can exchange information with their local neighbours on a bidirectionally connected communication graph. In the local controller equipped in each generalised coordinate of the agents, a disturbance observer is introduced to compensate for the low-passed-coupled uncertainties, and a sliding mode control term is employed to handle the uncertainties that the disturbance observer cannot compensate for sufficiently. By some damping terms, the boundedness of the signals of the overall networked nonlinear systems is first ensured. Then we show how the disturbance observer and sliding mode control term play in a cooperative way in each local generalised coordinate to achieve an excellent synchronised tracking performance. Simulation results are provided to support the theoretical results.