China
Africa
Explore chapters and articles related to this topic
Practical Design Considerations for Switched-Capacitor Filters
Published in John T. Taylor, Qiuting Huang, CRC Handbook of ELECTRICAL FILTERS, 2020
The previous sub-chapters have been concerned with synthesizing discrete-time transfer functions and signal flow graphs, and implementing them with switched-capacitor (SC) building blocks such as stray-insensitive SC integrators. Under the assumption that the switches and op amps used are ideal, the description of an SC filter is nearly the same as that of a digital filter in the sense that signal processing takes place in discrete time which can be described by difference equations. Since each sample in an SC filter is held constant for the clock period, the transfer function of an SC filter is similar to an A/D converter, digital filter plus D/A converter combination. The first-order hold function, which an SC filter has in common with a D/A converter, introduces a 2 sin(ωT/2)/ωT modification to the exact transfer function. This should be taken into account during the filter synthesis if the clock-to-bandedge-frequency ratio is not very high.1 Capacitance ratio inaccuracies were mentioned, reflecting the analog nature of SC circuits, to justify the use of ladder structures.
Advanced Numerical Integration
Published in Harold Klee, Randal Allen, Simulation of Dynamic Systems with MATLAB® and Simulink®, 2018
The analytical expression for the piecewise continuous output of the first-order hold is given by u˜(t)=un+un−un−1T(t−nT),nT≤t<(n+1)T(n=0,1,2,…) where u−1 is assumed to be zero. A derivation of G(z) based on a first-order hold approximation is possible using a similar approach to the derivation leading to the z-domain transfer function in Equation 8.419 using the zero-order hold approximation. However, it is quite laborious and unnecessary, since the “c2d” function includes the first-order hold approximation method. The approximation is invoked by issuing also the command sysd = c2d(sysc,T,‘foh’).
Design of Actuator Servo Controller
Published in Abdullah Al Mamun, GuoXiao Guo, Chao Bi, Hard Disk Drive, 2017
Abdullah Al Mamun, GuoXiao Guo, Chao Bi
One possibile solution for this problem is to use a notch filter whose center frequency and width of the notch can be easily modified. From this point of view, digital notch filters are prefered over their analog counterparts. The parameters of a digital filter and, therefore, its properties can be changed easily. These filters are easily implementable in the firmware of the microprocessor used in digital control system or even using programmable digital hardware. One can substitute s in equation (3.17) with s=2Tsz−1z+1 as indicated in equation (3.1) to find the digital version of the notch filter. Many design softwares provide appropriate functions to convert an analog filter into a digital filter. For example, the command c2dm of MATLABTM can be used to convert a continuous-time LTI (Linear Time Invariant) systems to equivalent discrete-time LTI system. One can use either a zero-order hold (ZOH), or a first-order hold (FOH) for plant discretization with this MATLAB function, and use the bilinear (Tustin) approximation to discretize the controller.
Self-triggered model predictive control for nonlinear continuous-time networked system via ensured performance control samples selection
Published in International Journal of Control, 2022
Choose , based on the designed parameters, using MATLAB package, the self-triggered MPC strategy can be conducted. To compare with the traditional MPC methods, we degrade the first-order hold method in Ning et al. (2018) to zero-order hold method in average N sampling times between two samples case, and two figures herein are illustrate the results, Figure 2 shows the comparison of displacements of system (24) between the optimal sampling time and the average sampling time, and Figure 3 shows the comparison of velocities of the system (24) between the optimal sampling time and the average sampling time. From these two pictures, it can be seen that the system performance of two state trajectories of and are nearly the same, and we can obtain the results from Theorem 4.1 that the self-triggered MPC strategy is feasibility and from Theorem 4.2 that the state and are asymptotically stable, and when t goes to infinity, and both go to stable state 0. The total cost function of these two methods are shown in Table 1, and we can see the total cost of the optimal sampling time is hugely less than the average one with same communication frequency. In conclusion, the proposed self-triggered MPC strategy with optimal sampling time is more effective, and can save total cost while guaranteeing the system performances.