Modified integral action with time-varying forgetting function for tracking control

2019 ◽  
Vol 234 (6) ◽  
pp. 715-725
Author(s):  
Fernando Villegas ◽  
Rogelio Hecker ◽  
Miguel Peña
Keyword(s):  
Stability Analysis ◽  
Tracking Error ◽  
Control Law ◽  
Time Varying ◽  
Forgetting Factor ◽  
Robust Controller ◽  
Integral Action ◽  
Abrupt Changes ◽  
New Type ◽  
And Control

While the use of integral action in control is quite common, in part due to its benefits for output regulation, it can also be counterproductive when abrupt changes in disturbance occur during tracking. In order to mitigate its counterproductive effect while at the same time maintaining its advantages for regulation, this work proposes a new type of integral action, including a time-varying forgetting factor suited to the expected behavior of the disturbance during tracking. Also, Lyapunov stability techniques are used to derive general results aiming to reduce the complexity of stability analysis and control design when the proposed integral action is included in a control law. In particular, these results are used for stability analysis when the proposed integral action is implemented in a deterministic robust controller for a linear motor system. Furthermore, the controller is implemented in the corresponding experimental setup, resulting in an improvement on maximum tracking error of up to 32%.

A Robust Delay Compensator for Uncertain Nonlinear Systems With Unknown Time-Varying Input Delay

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Ashish Kumar Jain ◽  
Shubhendu Bhasin
Keyword(s):  
Stability Analysis ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Tracking Error ◽  
Input Delay ◽  
Control Law ◽  
Time Varying ◽  
Uncertain Nonlinear Systems ◽  
Uniformly Ultimately Bounded ◽  
Simulation Results

This paper proposes a robust compensator for a class of uncertain nonlinear systems subjected to unknown time-varying input delay. The proposed control law is based on the integral of past values of control and a novel filtered tracking error. Sufficient gain conditions dependent on the known bound of the delay are derived using a Lyapunov-based stability analysis, where Lyapunov–Krasovskii (LK) functionals are used to achieve a global uniformly ultimately bounded (GUUB) tracking result. Simulation results for a nonlinear system are used to evaluate the performance and robustness of the controller for different values of time-varying input delay.

Robust Adaptive Control of Nonlinear Systems with Uncertainties

2014 ◽  
Vol 568-570 ◽  
pp. 1108-1112
Author(s):  
Ning Liu ◽  
Yu Sheng Liu ◽  
Qiang Yang
Keyword(s):  
Nonlinear Systems ◽  
Tracking Error ◽  
Robust Adaptive Control ◽  
Design Parameters ◽  
Unmodeled Dynamics ◽  
Time Varying ◽  
Mean Square ◽  
Robust Controller ◽  
The Mean ◽  
Robust Adaptive

This paper proposes a robust adaptive robust controller for nonlinear systems represented by input-output models with unmodeled dynamics. Under the circumstances that the output of the system is bounded, the proposed controller can guarantee that all the variables of the system are bounded in the presence of unmodeled dynamics and time-varying disturbances. The scheme does not need to generate an additional dynamic signal to dominate the effects of the unmodeled dynamics. It is shown that the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately.

Design of a Linear Controller for Robust Tracking and Model Following

1990 ◽  
Vol 112 (4) ◽  
pp. 552-558 ◽  
Author(s):  
T. H. Hopp ◽  
W. E. Schmitendorf
Keyword(s):  
Uncertain Systems ◽  
Feedforward Control ◽  
Tracking Error ◽  
Control Law ◽  
Time Varying ◽  
Robust Tracking ◽  
Matching Conditions ◽  
Nonlinear Controllers ◽  
Model Following ◽  
Tracking And Model Following

We consider a class of linear systems in which there is time-varying uncertainty. These linear uncertain systems can be divided into two types. Systems in which the structure of the uncertainty satisfies certain matching conditions are called matched, and those systems in which the uncertainty does not satisfy the matching conditions are called mismatched. A linear control law is determined which produces tracking of dynamic inputs. The tracking error does not asymptotically decrease to zero because the systems are uncertain, instead the error is bounded. In the case of matched systems this error bound can be made arbitrarily small, and the system is said to practically track the input. In mismatched systems, the tracking error cannot be made arbitrarily small, and the system is said to ε-track the input. Previously published theory requires nonlinear controllers for practical tracking. Here, we derive a linear feedforward control law. Several examples illustrate the results.

Iterative learning identification and control for point-to-point tracking of linear time-varying systems with unknown parameters and stochastic noise

2017 ◽  
Vol 40 (13) ◽  
pp. 3834-3845 ◽  
Author(s):  
Yan Geng ◽  
Xiaoe Ruan
Keyword(s):  
Linear Time ◽  
Tracking Error ◽  
Iterative Learning ◽  
Time Varying ◽  
Unknown Parameters ◽  
Point Tracking ◽  
Time Varying Systems ◽  
System Output ◽  
Point To Point ◽  
And Control

In this paper, an interactive iterative learning identification and control (ILIC) scheme is developed for a class of discrete-time linear time-varying systems with unknown parameters and stochastic noise to implement point-to-point tracking. The identification is to iteratively estimate the unknown system parameter matrix by adopting the gradient-type technique for minimizing the distance of the system output from the estimated system output, whilst the control law is to iteratively upgrade the current control input with the current point-to-point tracking error scaled by the estimated system parameter matrix. Thus, the iterative learning identification and the iterative learning control are scheduled in an interactive mode. By means of norm theory, the boundedness of the discrepancy between the system matrix estimation and the real one is derived, whilst, by the manner of the statistical technique, it is conducted that the mathematical expectation of the tracking error monotonically converges to nullity and the variance of the tracking error is bounded. Numerical simulations exhibit the validity and effectiveness of the proposed ILIC scheme.

Cross-Coupled Control of Biaxial Feed Drive Servomechanisms

1990 ◽  
Vol 112 (2) ◽  
pp. 225-232 ◽  
Author(s):  
K. Srinivasan ◽  
P. K. Kulkarni
Keyword(s):  
Stability Analysis ◽  
High Speed ◽  
Tracking Error ◽  
Time Varying ◽  
Tracking Accuracy ◽  
Contouring Error ◽  
Feed Drive ◽  
Straight Line ◽  
Controller Performance ◽  
Contouring Accuracy

A cross-coupled controller, designed to improve high-speed contouring accuracy independently of tracking accuracy in biaxial machine tool feed drive servomechanisms, is presented here. The controller parameters depend on the instantaneous slope of the desired contour and hence vary with time for curved contours, resulting in a time-varying controller. An approximate stability analysis of the controller is presented. The proposed controller is evaluated experimentally on a microcomputer controlled two-axis positioning table and compared to a more traditional uncoupled controller. Controller performance is evaluated for straight line, cornering and circular contours at feed rates varying from 2.25 m/min to 7.2 m/min. The experimental results show that the proposed controller reduces contouring error as compared to the uncoupled controller and leaves the tracking error practically unchanged. The cross-coupled controller is simple to implement and is practical.

scholarly journals Quantum genetic sliding mode controller design for depth control of an underwater vehicle

2018 ◽  
Vol 51 (7-8) ◽  
pp. 336-348 ◽  
Author(s):  
Zahra Tavanaei-Sereshki ◽  
Mohammad Reza Ramezani-al
Keyword(s):  
Genetic Algorithm ◽  
Controller Design ◽  
Sliding Mode ◽  
Tracking Error ◽  
Underwater Vehicle ◽  
Small Population ◽  
Control Law ◽  
Quantum Genetic Algorithm ◽  
Depth Control ◽  
New Type

Quantum genetic algorithm (QGA) is an optimization algorithm based on the probability that combines the idea of quantum computing and traditional genetic algorithm. In this paper, a new type of control law is developed for an underwater vehicle along with the desired path. The proposed controller is based on sliding mode control (SMC) in which the reaching law is modified to overcome two challenging problems, chattering, and sensitivity against noise. The disturbance is considered as a set of sinus waves with different frequencies which its parameters are estimated by Particle Swarm Optimization (PSO). Since QGA has some advantages such as fast convergence speed, small population size, and strong global search capabilities, we use QGA to determine the gain of the proposed controller. Finally, the Lyapunov theorem is used to prove that trajectory-tracking error converges to zero. Simulation results show that QGA can converge to the optimal response with a population consist of one chromosome.

Sign in / Sign up

Export Citation Format

Share Document