ABSTRACT
In electromechanical systems, signal processing, signal conditioning, and other tasks are accomplished by ICs. The digital controllers and filters are implemented using microcontrollers and DSPs. Electromechanical systems are predominantly continuous, and analog controllers and filters can be implemented utilizing operational amplifiers and specialized ICs. These controllers and filters are integrated within power amplifiers. The electromechanical motion devices and solid-state devices are continuous. The use of digital controllers and sensors results in the so-called hybrid closed-loop electromechanical systems as introduced in Chapter 1, see system configurations documented in Figures 1.2 and 1.4. As reported in Chapters 3 and 4, in electromechanical systems, analog proportional-
integral-derivative controllers are implemented using operational amplifiers. This section examines and documents the use of operational amplifiers to implement various analog controllers and filters with specified transfer functions. Various operations on signals and variables may be required. For example, sensors convert time-varying physical quantities (displacement, velocity, acceleration, force, torque, pressure, temperature, and others) in electric signals (voltage or current). The signal-level sensor output must be amplified and filtered. The single operational amplifier is a two-port network which has noninverting and inverting input terminals (3 and 2) as well as one output terminal (6) as depicted in Figure 7.1. Two (or one) DC voltages are needed, and terminal 7 is connected to a positive voltage uþ, while a negative voltage (or ground) u is supplied to the terminal 4. The pin connections of the single, dual, and quad low-power operational amplifiers MC33171, MC33172, and MC33174 are reported in Figure 7.1, which also illustrates 8-and 14-pin plastic packages (cases 626 and 646). These operational amplifiers are also available in the surface mount packages (cases 751 and 948). Operational amplifiers, which consist of dozens of transistors, are fabricated using the complementary metal oxide semiconductor (CMOS) or biCMOS fabrication technologies [1]. Figure 7.1 depicts the representative schematic diagram. The amplifier output is the difference between two input voltages, u1(t) and u2(t),
applied to the inverting input terminal and the noninverting input terminal, multiplied by the differential open-loop coefficient kog. That is, the resulting output voltage is
u0(t) ¼ kog u2(t) u1(t)½
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The differential open-loop coefficient is positive. The value of kog is very large, and kog varies as [1 105 to 1 107]. The general purpose operational amplifiers have input and output resistances [1 105 to 1 1012] and [10, 1000] ohm, respectively. The inverting and noninverting input terminals are distinguished using ‘‘’’ and ‘‘þ’’ signs. Supplying the signal-level input voltage u1(t) to the inverting input terminal using external resistor R1, and grounding the noninverting input terminal, one can find the differential closed-loop coefficient kcg if a negative feedback is used. The output terminal is connected to the inverting input terminal, and the resistor R2 is inserted as depicted in Figure 7.2. To find the differential closed-loop coefficient kcg, one has to obtain the ratio between
the output and input voltages u0(t) and u1(t). The voltage between two input terminals is u0(t)=kog, and the voltage at the inverting input terminal is u0(t)=kog because the
noninverting input terminal is grounded. Therefore, we have i1(t) ¼ u1(t)þ u0(t)kog
R1 , and the
output voltage is u0(t) ¼ u0(t)kog u1(t)þ u0(t)kog
R1 R2. Hence, the differential closed-loop coef-
ficient is found to be kcg ¼ u0(t)u1(t) ¼ R2 R1
1þ 1 kog
þ R2 kogR1
.
