Zero compensation, pole

It is worth reminding the reader that, before getting too excited about poor charge collection, under-compensated pole-zero cancellation will also cause a tail on the low-energy side of peaks. Whatever the circumstances, the FIRST diagnostic check to make should be pole-zero cancellation. 

Locating the compensating poles and zeros in the error amplifier... 

The control-to-output characteristic curves for a current-mode controlled flyback-mode converter, even though it is operating in variable frequency, are of a single-pole nature. So a single pole-zero method of compensation should be used. The placement of the filter pole, ESR zero, and dc gain are... 

The next task is to determine the plaeement of the eompensating zero and pole within the error amplifier. The zero is plaeed at the lowest frequency manifestation of the filter pole. Since for the voltage-mode controlled flyback converter, and the current-mode controlled flyback and forward converters, this pole s frequency changes in response to the equivalent load resistance. The lightest expected load results in the lowest output filter pole frequency. The error amplifier s high frequency compensating pole is placed at the lowest anticipated zero frequency in the control-to-output curve cause by the ESR of the capacitor. In short ... 

Figure B-21 An example of pole-zero compensation used with a voltage/current-mode controlled flyback converter.

We used the term pole-zero cancellation at the beginning of this section. We should say a few more words to better appreciate the idea behind direct synthesis. Pole-zero cancellation is also referred to as cancellation compensation or dominant pole design. Of course, it is unlikely to... 

The materials and structures associated with primary sensors contain dissipative, storage and inertial elements. These translate into the time derivatives appearing in the differential equation that models the sensor system. Hence another major defect is represented by the time (or frequency) response. The means to neutralise this imperfection involves filtering, which may be thought of in terms of pole-zero cancelation. If the device has a frequency response H s) then a cascaded filter of response G s) = 1/H s) will compensate for the non-ideal time response. The realisation of such a filter in analogue form presents a major obstacle that is greatly diminished in the digital case. 

Frequency boost - which is needed when an otherwise acceptable detector is slower than the application requires. Monitoring explosions with a thermal detector is one example. The frequency-boost circuit uses pole-zero compensation at the input and/or in the feedback of a TIA. Note that the S/N ratio is degraded at boosted frequencies. 

To compensate for the double filter pole, I will place two zeros at one-half the filterpole frequency ... 

Locate the compensating error amplifier pole at the lowest anticipated zero frequency caused by the ESR of the capacitor or... 

Locate the compensating error amplifier zero at the location of the lowest manifestation of the filter pole or... 

The form of compensation is the 2-pole-2-zero method of compensation. This is to compensate for the effect of the double pole caused by the output filter inductor and capacitor. One starts by determining the control-to-output characteristic of the open-loop system. 

The more complicated methods of compensation, such as this, allow the designer much more control over the final closed-loop bode response of the system. The poles and zeros can be located independently of one another. Once their frequencies are chosen, the corresponding component values can be easily determined by the step-by-step procedure below. The zero and pole pairs can be kept together in pairs, or can be separated. The high-frequency pole pair appear to yield better results if they are separated and placed as below. The zero pair are usually kept together, but can be separated and placed either side of the output filter pole s corner frequency to help minimize the gain effects of the Q of the T-C filter (refer to Figure B-23). 

Figure B-23 An example of 2-pole-2-zero compensation used with a voltage-controlled forward converter.

The method performed above with the plaeement of the poles and zeroes will yield a minimum value for the exeess phase of 45 degrees, whieh is satisfaetory. If other pole and zero loeations are attempted, then loeate the maximum phase lag point of the L-C filter at the geometrie mean frequency between/ez2 and/epi. This will guarantee the best phase performance. The amount of phase boost of the compensation design will be... 

A compensator, or controller, placed in the forward path of a control system will modify the shape of the loci if it contains additional poles and zeros. Characteristics of conventional compensators are given in Table 5.2. 

The default is a proportional controller, but the K block in Fig. M6.1 can easily be changed to become a PI, PD, or PID controller. The change can be accomplished in different ways. One is to retrieve the compensator-editing window by clicking on the K block or by using the Tools pull-down menu. The other is to use the set of arrow tools in the root locus window to add or move open-loop poles and zeros associated with the compensator. 

Fig. 9.8. Deflection of a bimorph. Two long, thin plates of piezoelectric material are glued together, with a metal film sandwiched in between. Two more metal films cover the outer surfaces. Both piezoelectric plates are poled along the same direction, perpendicular to the large surface, labeled z. (A) By applying a voltage, stress of opposite sign is developed in both plates, which generates a torque. (B) The bimorph flexes to generate a stress to compensate the torque. The neutral plane, where the stress is zero, lies at hi i from the central plane.

Pole and zero placement using a dynamic compensator for an SISO system can be accomplished by specifying analytically the closed loop servo response (e.g., first or second order with deadtime). Suppose that the specified response is defined by P(s) solving the closed loop equation (5) yields an analytical... 

Figure 3.7. Excitation trajectories as a function of resonance offset for (a) a 90° pulse and (b) a 180° pulse. The offset moves from zero (on-resonance) to - -yB Hz in steps of 0.2yB] (as in Fig. 3.6). The 90° pulse has a degree of offset-compensation as judged by its ability to generate transverse magnetisation over a wide frequency bandwidth. In contrast the 180° pulse performs rather poorly away from resonance, leaving the vector far from the target South Pole and with a considerable transverse component.

Note that the integrator has a single-pole — at zero frequency . Therefore, we will often refer to it as the pole-at-zero stage or section of the compensation network. This pole is more commonly called the pole at the origin or the dominant pole. 

Our compensation analysis seems complete. However, there is one last complication still remaining. We may need at least one pole from our compensation network. This is for canceling out the ESR zero coming from the output capacitor. We have been ignoring this particular zero so far, but it is time to take a look at it now. 

There are two poles pi and p2 (besides the pole-at-zero pO ), and two zeros, zl and z2 provided by this compensation. Note that several of the components involved play a... 

Figure 7-18 Type 1, Type 2, and Type 3 Compensation Schemes (poles and zeros arbitrarily placed and displayed)...

Type 1 compensation provides only a pole-at-zero, and in fact can only work with current mode control (that too with the ESR zero below crossover). Note that it is just a simple integrator. 

There is a practical difficulty involved in using the full-blown transconductance op-amp compensation scheme discussed above — because the pole and zero from HI are not independent. They will even tend to coincide if say Rf2 is much smaller than Rfl (i.e. if the desired output voltage is almost identical to the reference voltage). In that case, the pole and zero coming from HI will cancel each other out completely. Therefore, we can t proceed anymore, because we were counting on the zero from HI to change the open-loop gain from —2, to —1, just in time before it crossed over. 

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