Closed-loop bandwidth

The error amplifier must add gain to the eventual closed loop function in order to achieve the desired closed loop bandwidth. This gain is... 

The compensation schemes shown in this book are the most common methods. Several of these will work in each applications, but only one for each is considered the optimum method insofar as the dc gain and closed-loop bandwidth aspects are concerned. Tables B-1 and B-2 will help match a possible compensation method with your application. 

The closed-loop bandwidth coa is the Ifequency where 15(/a>) first crosses 1/V2 = 0.707 (w -3dS) from below. 

The gain crossover frequency, at, defined as the frequency where L jcd) first crosses 1 from above, is also used to define closed-loop bandwidth. It has the advantage of being simple to compute, and usually gives a value close to coa. 

While one of the most critical factors that determines the performance of a servo system is the closed-loop bandwidth (Skogestad and Postlethwaite 2005) (i.e., active frequency range, within which disturbance inputs are successfully rejected and reference inputs are accurately followed), there are also important limitations that determine the achievable bandwidth in a servo system arising typically from the dynamics of the plant and controller such as unstable zeros and delays, umnodeled dynamics, vibration modes, actuator saturations, and... 

Furthermore, by observing the DC variation at higher frequencies (e.g., at the closed-loop bandwidth specified), the disturbance directions are identified for which the high-frequency modes are attenuated with difficulty or not at all. 

A remarkable aspect of these results is that the closed-loop bandwidth does not depend, in this somewhat idealized case, on the closed-loop gain G(0). Figure 7.133 shows plots of the magnitude of the gain vs. 

However, no CFB is ideal, and small departures from ideal characteristics have adverse effects on the performance of these operational elements. For example, the output resistance of the buffer between the input leads causes some dependence of the closed-loop bandwidth on the closed-loop gain. Figure 7.134 shows an amplifier that includes a CFB model that accounts for this resistance which is denoted as r. With r included, the closed-loop gain of the noninverting amplifier becomes... 

Equation (7.201) can be used to modify the external resistor of the CFB amplifier of Fig. 7.134 to compensate for bandwidth reduction caused by r. For required closed-loop bandwidth BWcl and low-frequency gain G(0) = 1 -F Rp/Ri,we obtain... 

In a first control structure selection step, the plant dynamics is checked for non-minimum phase elements for all possible structures. For the air separation plant, the possible closed loop bandwidth of several possible control structures is limited by RHP zeros. 6 control structures have very small RHP zeros which make good control of the plant impossible. 6 other structures have no or relatively large RHP zeros and thus are prime candidates The selection... 

In the first selection step, the non-minimum phase behavior of the various combinations was analyzed. For this distillation column, the closed-loop bandwidth is mainly limited by the RHP zeros. Therefore, all combinations with RHP zeros smaller than 0.01 rad/s were rejected and the number of control structures was reduced to seven. 

I am seleeting the bandwidth of the elosed loop (fxo) power supply to be 6 kHz. It eould be as high as 15 to 20 kHz, but there is a double pole at one-half the switehing frequency which, if approached too closely, would ruin the phase and gain margin of the closed loop. 

The current-mode controlled forward converter has one additional consideration there is a double pole at one-half the operating switching frequency. The compensation bandwidth normally does not go this high, but it may cause problems if the closed-loop gain is not sufficiently low enough to attenuate its effects. Its influence on the control-to-output characteristic can be seen in Figure B-14. 

Design a cascade lead compensator that will ensure stability and provide a phase margin of at least 30°, a bandwidth greater than 5rad/s and a peak closed-loop modulus Mp of less than 6dB. 

Closed-loop peak Mp = 5.5 dB Gain margin = 13.75dB Bandwidth = 5.09 rad/s Phase margin = 30.6 ... 

Creates closed-loop Bode Gain Diagrams for K=3.8 and 3.2 %Prints in Command Window Mp,k,wp and bandwidth 0 If... 

The command cloop is used to find the closed-loop transfer function. The command max is used to find the maximum value of 20 logio (mag), i.e. Mp and the frequency at which it occurs i.e. tUp = uj k). A while loop is used to find the —3 dB point and hence bandwidth = ca (n). Thus, in addition to plotting the closed-loop frequency response gain diagrams,/ gd29.7 will print in the command window ... 

In this section we will use PSpice to determine the bandwidth of an op-amp circuit with varying amounts of negative feedback. For an op-amp circuit, the closed-loop gain times the bandwidth is approximately constant. To observe this property, we will run a simulation that creates a Bode plot for several different closed-loop gains. We will use the circuit below ... 

The challenge posed by establishing and maintaining communication between distributed controllers has also stimulated research in the area of networked process control (El-Farra et al. 2005, Mhaskar et al. 2007, Sun and El-Farra 2008, 2010). The central issue of maintaining closed-loop stability in the presence of bandwidth constraints and limitations in transmitter battery longevity is typically addressed by a judicious distribution of computation and communication burdens between local/distributed control systems and a centralized supervisory controller. 

The third class of techniques include a frequency-domain method based on the identification of the sensitivity function S s)) and the complementary sensitivity function T s)) from plant data or CPM of multivariable systems [140]. Robust control system design methods seek to maximize closed-loop performance subject to specifications for bandwidth and peak... 

The amplifier (5) boosts the signal, eliminates temperature coefficients, and adjusts the offset. The low pass filter (6) limits the bandwidth. The drive circuit is a closed loop system to achieve a stable drive oscillation. It consists of a structure (not drawn) that detects the oscillation movement of the drive of the yaw-rate sensor element, a control unit (2), and an actuator (not drawn). The start circuit (9) initiates the drive oscillation at power on. The block (8) generates all necessary adjustment signals and includes the logic circuit for the trim and an EPROM (erasable programmable read-only memory) for the storage of the trim data. 

The single design parameter k determines the location of the closed-loop poles and thus indirectly, the system bandwidth [26]. This relationship is considered further in Section 5.5. 

The quantity ct)cL f is the closed-loop gain-bandwidth product, and so Eq. (7.111) shows that the closed-loop gain-bandwidth product for this ampHfier equals the open-loop gain-bandwidth product. 

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