Estimation and rejection of sinusoidal disturbance with unknown frequency using cascade disturbance observer

A disturbance rejection approach is presented for a class of uncertain systems subject to sinusoidal disturbance with unknown frequency. The proposed disturbance estimation method includes two types of observers that are connected in cascade form. The disturbance property is excited through an auxiliary filter, and then a frequency factor observer is constructed to generate the information required by full-order state observer. Thus, with the disturbance and system state estimation values, the composite control structure including a cascade disturbance observer (CDO) and a robust feedback controller is designed. As a result, the uncertain system with unknown-frequency sinusoidal component can be controlled within the disturbance observer-based control (DOBC) framework, where the asymptotic stability performance can be guaranteed.

Proxy-Based Sliding Mode Vibration Control with an Adaptive Approximation Compensator for Euler-Bernoulli Smart Beams

Proxy-based sliding mode control PSMC is an improved version of PID control that combines the features of PID and sliding mode control SMC with continuously dynamic behaviour. However, the stability of the control architecture maybe not well addressed. Consequently, this work is focused on modification of the original version of the proxy-based sliding mode control PSMC by adding an adaptive approximation compensator AAC term for vibration control of an Euler-Bernoulli beam. The role of the AAC term is to compensate for unmodelled dynamics and make the stability proof more easily. The stability of the proposed control algorithm is systematically proved using Lyapunov theory. Multi-modal equation of motion is derived using the Galerkin method. The state variables of the multi-modal equation are expressed in terms of modal amplitudes that should be regulated via the proposed control system. The proposed control structure is implemented on a simply supported beam with two piezo-patches. The simulation experiments are performed using MATLAB/SIMULINK package. The locations of piezo-transducers are optimally placed on the beam. A detailed comparison study is implemented including three scenarios. Scenario 1 includes disturbing the smart beam while no feedback loop is established (open-loop system). In scenario 2, a PD controller is applied on the vibrating beam. Whereas, scenario 3 includes implementation of the PSMC+AAC. For all previously mentioned scenarios, two types of disturbances are applied separately: 1) an impulse force of 1 N peak and 1 s pulse width, and 2) a sinusoidal disturbance with 0.5 N amplitude and 20 Hz frequency. For impulse disturbance signals, the results show the superiority of the PSMC+AAC in comparison with the conventional PD control. Whereas, both the PSMC+ACC and the PD control work well in the case of a sinusoidal disturbance signal and the superiority of the PSMC is not clear.

Parameters Estimation Algorithm for an Unmeasured Sinusoidal Signal with Time-Varying Amplitude

In this paper the problem of identification algorithm for unknown frequency of a sinusoidal disturbance for a linear plant was considered. This problem is solved in the class of plants with known parameters and a measured of state variables. Regarding the frequency of the sinusoidal disturbance was assumed that the it upper limit is known. Despite the seeming triviality the considered problem is difficult. Using of numerous methods for parameters identification of the measured sinusoidal signals does not give success if the amplitude of sinusoidal disturbance is time-varying. In this paper we will assume that amplitude is the product of an unknown constant by a known strictly positive function of time. For the time-varying strictly positive function we will suppose that the upper boundary of its derivative is known. We note that such assumption on the amplitude of a time-varying sinusoidal disturbance is not a mathematical abstraction. Similar models arise in fault-detection strategy in DC/ AC conversion. It is well known that alternative energy sources require a high level of integration into the electrical power grids. For this purpose, DC/AC and AC/AC power converter are used to provide the coupling, synchronization and appropriate power flow to the electrical networks. These power converters employ high-frequency switching to manipulate the energy conversion process. As a result of a constant operation and load transients, the power switches in the DC/AC and AC/AC topologies are facing voltage, current and temperature stresses that could lead to a fault. After a fault, the DC/AC and AC/AC power converter will not be able to provide a symmetric voltage and current to the electrical network and, consequently, the faulty converter will induce harmonic noise. By evaluating such harmonic noise / disturbance, emergency situations can be avoided. In this paper the asymptotic convergence of the estimation of the frequency of the perturbing effect to the true value is proven. For clarification of design procedure of estimation algorithm and performance illustration an example was presented. The computer simulation results are demonstrating the achievement of a given purpose.