### Table 1: Voltage percent error in the non-linear low load zone with PID and PID-GMR

in Systems

"... In PAGE 10: ... This test has been done again, both with the PID and the PID-GMR scheme, in the linear zone of the cell characteristics and in the non-linear ones at very low and very high loads to check the improvements of the control accuracy achievable with the PID-GMR scheme. Table1 , 2, 3 show the voltage reference, the load current and the corresponding voltage percent error (difference between the reference and the real voltage) obtained with both the PID and the PID-GMR scheme respectively in the non-linear low load zone, the linear zone and the non-linear high load zone. These tables show that the PID-GMR scheme overcomes the PID one in terms of voltage error, with a resulting real voltage which better approximates the reference one.... ..."

### Table 4: PID controller

"... In PAGE 16: ...specified the equation 13 gives the following solution a33 a5a4 a1 a3 a5 a0 a4 a7 a20 a8 a17 a6a5 a15 a31 a9a8 a0 a2 a10a5 a31 a20 a8 a17 a12 a5 a15 a12a11 Example 3 Combined amplitude and phase margin specification A design method based on the requirement that the Nyquist curve intersects the circle with radius a8 a15 a1 a10 a12 and an angle of a5 a15 a27 a3 a7a25a9 a11 a1a6a27 a3 a3 a5 a25a11 is given. Specifying a5 a2a1 a0 gives the following PID controller a33 a5a4 a1 a10 a15 a14a13 a12 a15 a14 a33 a4 a33 a34 a1 a0 a25a33a5a4 a21 a1 a13 a12 a15 a21 a4 Table4 compares the coefficients found by this method to the coefficients found by Ziegler-Nichols ultimate period method. a21 a4 and a33 a4 may be determined by relay feed- back.... ..."

### Table 1 - Manipulator parameters and control gains used in the simulations. length mass inertia PID control gains

"... In PAGE 9: ...gains are shown in Table1 , where KP, KD and KI are proportional, derivative and integral control gains. Table 1 - Manipulator parameters and control gains used in the simulations.... ..."

### Table 1: An empirical comparison of both PD and PI type FLCs and PID controller.

"... In PAGE 14: ... It is interesting to conclude that both FLCs achieves better performance as compared with a best-tuned PID controller. Table1 summarizes these results. 10 Conclusions In this paper, a complete tuning procedure guide- line and root locus stability evaluation for fuzzy logic control systems were presented.... ..."

### Table 2. An optimized program for the PID controller

2005

"... In PAGE 7: ... The reader can easily appreciate that the process of writing, modifying and optimizing such programs manually is error prone and that it would be much safer to derive it automatically from the high-level Simulink model. We have derived a program similar to the program in Table2 from the Simulink model of Figure 2 in two steps. First, the Simulink-to-Lustre translator [6] was used to... ..."

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### Table 1. Stability regions of some nonlinearities.

"... In PAGE 2: ...not necessarily its satisfaction. The stability condition (4) has been evaluated for frequently applied nonlinearities and the resulting stability regions are given in Table1 . For those nonlinear functions with two entries in the stability-condition column, the first one is an unconditional stabil- ity condition, whereas the second entry is conditioned on satisfy-... In PAGE 3: ...1. Difficult distributions From Table1 it becomes clear, that if a non-Gaussian distri- bution exists that is neither separable by CVB4D9B5 BP D9 BF nor by CVB4D9B5 BP CPD8CPD2CWB4D9B5, it has to show a positive kurtosis, since CVB4D9B5BPD9 BF covers all negative-kurtosis distributions, but the sta- bility region of CVB4D9B5BPCPD8CPD2CWB4D9B5 does not include all positive- kurtosis distributions. One such peculiar distribution was given by Douglas [5].... ..."

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### Table 1. A program realizing a PID controller

2005

"... In PAGE 6: ... These variables con- tinue to exist between successive invocations of the program (like latches in sequential digital circuits when the clock signal is low). The program shown in Table1 is a result of a rather straightforward transformation of (1).... ..."

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### Table 2: A 3-D FAM for fuzzy PID type controller

### Table 2. Step changes imposed in the inlet product temperature to evaluate the PID/feedback and PID/feedback/feedforward controllers

"... In PAGE 5: ...5o C. Table2 shows the magnitude of the step changes made in the system after the controllers tuned. The controllers were evaluated and compared through the behaviors of the manipulated variables, after disturbances in the product inlet temperature and through performance indices IAE (Integral Absolute Error), ITAE (Integral Time Absolute Error) e ISE (Integral Square Error) calculated according to Coughanowr amp; Koppel (1978).... In PAGE 5: ... The controllers were evaluated and compared through the behaviors of the manipulated variables, after disturbances in the product inlet temperature and through performance indices IAE (Integral Absolute Error), ITAE (Integral Time Absolute Error) e ISE (Integral Square Error) calculated according to Coughanowr amp; Koppel (1978). As shown in Table2 , the step changes made were not the same. This fact is due to the experimental difficulties to control the temperature in the jacket of the raw product tank.... ..."

### Table 1. The reactive plan for controlling a manipulator

2002

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