Output Adaptive Observers Design for Linear Non-Stationary Systems with Polynomial Parameters

2021 ◽  
Vol 22 (8) ◽  
pp. 404-410
Author(s):  
K. B. Dang ◽  
A. A. Pyrkin ◽  
A. A. Bobtsov ◽  
A. A. Vedyakov ◽  
S. I. Nizovtsev
Keyword(s):  
Linear Time ◽  
State Observer ◽  
Observer Design ◽  
Model Parameters ◽  
Time Varying ◽  
State Variables ◽  
Unknown Constant ◽  
Established Method ◽  
Time Varying Parameters ◽  
True Values

The article deals with the problem of state observer design for a linear time-varying plant. To solve this problem, a number of realistic assumptions are considered, assuming that the model parameters are polynomial functions of time with unknown coefficients. The problem of observer design is solved in the class of identification approaches, which provide transformation of the original mathematical model of the plant to a static linear regression equation, in which, instead of unknown constant parameters, there are state variables of generators that model non-stationary parameters. To recover the unknown functions of the regression model, we use the recently well-established method of dynamic regressor extension and mixing (DREM), which allows to obtain monotone estimates, as well as to accelerate the convergence of estimates to the true values. Despite the fact that the article deals with the problem of state observer design, it is worth noting the possibility of using the proposed approach to solve an independent and actual estimation problem of unknown time-varying parameters.

Identification of Linear Time-Varying Parameters of Nonstationary Systems

2019 ◽  
Vol 20 (5) ◽  
pp. 269-265
Author(s):  
V. T. Le ◽  
M. M. Korotina ◽  
A. A. Bobtsov ◽  
S. V. Aranovskiy ◽  
Q. D. Vo
Keyword(s):  
Linear Time ◽  
Control Object ◽  
Time Interval ◽  
Identification Algorithm ◽  
Time Varying ◽  
State Variables ◽  
Unknown Parameters ◽  
Technical Problems ◽  
True Values ◽  
Stationary Control

The paper considers the identification algorithm for unknown parameters of linear non-stationary control objects. It is assumed that only the object output variable and the control signal are measured (but not their derivatives or state variables) and unknown parameters are linear functions or their derivatives are piecewise constant signals. The derivatives of non-stationary parameters are supposed to be unknown constant numbers on some time interval. This assumption for unknown parameters is not mathematical abstraction because in most electromechanical systems parameters are changing during the operation. For example, the resistance of the rotor is linearly changing, because the resistance of the rotor depends on the temperature changes of the electric motor in operation mode. This paper proposes an iterative algorithm for parameterization of the linear non-stationary control object using stable LTI filters. The algorithm leads to a linear regression model, which includes time-varying and constant (at a certain time interval) unknown parameters. For this model, the dynamic regressor extension and mixing (DREM) procedure is applied. If the persistent excitation condition holds, then, in the case the derivative of each parameter is constant on the whole time interval, DREM provides the convergence of the estimates of configurable parameters to their true values. In the case of a finite time interval, the estimates convergence in a certain region. Unlike well-known gradient approaches, using the method of dynamic regressor extension and mixing allows to improve the convergence speed and accuracy of the estimates to their true values by increasing the coefficients of the algorithm. Additionally, the method of dynamic regressor extension and mixing ensures the monotony of the processes, and this can be useful for many technical problems.

Using Sliding Mode Control to Adjust Drum Level of a Boiler Unit With Time Varying Parameters

2010 ◽  
Author(s):  
Hamed Moradi ◽  
Firooz Bakhtiari-Nejad ◽  
Majid Saffar-Avval ◽  
Aria Alasty
Keyword(s):  
Water Level ◽  
Transfer Functions ◽  
Sliding Mode ◽  
Operating Conditions ◽  
Model Parameters ◽  
Feed Water ◽  
Time Varying ◽  
Boiler Unit ◽  
Varying Parameters ◽  
Time Varying Parameters

Stable control of water level of drum is of great importance for economic operation of power plant steam generator systems. In this paper, a linear model of the boiler unit with time varying parameters is used for simulation. Two transfer functions between drum water level (output variable) and feed-water and steam mass rates (input variables) are considered. Variation of model parameters may be arisen from disturbances affecting water level of drum, model uncertainties and parameter mismatch due to the variant operating conditions. To achieve a perfect tracking of the desired drum water level, two sliding mode controllers are designed separately. Results show that the designed controllers result in bounded values of control signals, satisfying the actuators constraints.

Linear Approximations for Swing Leg Motion During Gait

1984 ◽  
Vol 106 (2) ◽  
pp. 137-143 ◽  
Author(s):  
W. H. Lee ◽  
J. M. Mansour
Keyword(s):  
Linear Systems ◽  
System Analysis ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
State Variables ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Leg Motion ◽  
Time Invariant

The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.

State-Observer Design of a PDE-Modeled Mining Cable Elevator With Time-Varying Sensor Delays

2020 ◽  
Vol 28 (3) ◽  
pp. 1149-1157
Author(s):  
Ji Wang ◽  
Yangjun Pi ◽  
Yumei Hu ◽  
Zhencai Zhu
Keyword(s):  
State Observer ◽  
Observer Design ◽  
Time Varying

scholarly journals Time-Varying Uncertainty in Shock and Vibration Applications Using the Impulse Response

2012 ◽  
Vol 19 (3) ◽  
pp. 433-446 ◽  
Author(s):  
J.B. Weathers ◽  
Rogelio Luck
Keyword(s):  
Linear Time ◽  
Nonlinear Differential Equations ◽  
Uncertainty Propagation ◽  
External Input ◽  
Simulation Software ◽  
Model Parameters ◽  
Time Varying ◽  
Principle Of Superposition ◽  
Dynamic Simulations ◽  
Uncertainty Model

Design of mechanical systems often necessitates the use of dynamic simulations to calculate the displacements (and their derivatives) of the bodies in a system as a function of time in response to dynamic inputs. These types of simulations are especially prevalent in the shock and vibration community where simulations associated with models having complex inputs are routine. If the forcing functions as well as the parameters used in these simulations are subject to uncertainties, then these uncertainties will propagate through the models resulting in uncertainties in the outputs of interest. The uncertainty analysis procedure for these kinds of time-varying problems can be challenging, and in many instances, explicit data reduction equations (DRE's), i.e., analytical formulas, are not available because the outputs of interest are obtained from complex simulation software, e.g. FEA programs. Moreover, uncertainty propagation in systems modeled using nonlinear differential equations can prove to be difficult to analyze. However, if (1) the uncertainties propagate through the models in a linear manner, obeying the principle of superposition, then the complexity of the problem can be significantly simplified. If in addition, (2) the uncertainty in the model parameters do not change during the simulation and the manner in which the outputs of interest respond to small perturbations in the external input forces is not dependent on when the perturbations are applied, then the number of calculations required can be greatly reduced. Conditions (1) and (2) characterize a Linear Time Invariant (LTI) uncertainty model. This paper seeks to explain one possible approach to obtain the uncertainty results based on these assumptions.

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