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Operational Transresistance Amplifier Based PID Controller

Article in Advances in Electrical and Electronic Engineering · June 2015

DOI: 10.15598/aeee.v13i2.1164

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THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 13 | NUMBER: 2 | 2015 | JUNE

Operational Transresistance Amplifier Based PID

Controller

Rajeshwari PANDEY 1 , Neeta PANDEY 1 , Saurabh CHITRANSHI 1 , Sajal K. PAUL 2

1
Department of Electronics and Communication Engineering, Shahbad Daulatpur, Delhi Technological
University, Bawana Road, DL - 42, Delhi, India
2
Department of Electronics Engineering, Indian School of Mines,
Dhanbad – 826004, Jharkhand, India

rpandey@dce.ac.in, neetapandey@dce.ac.in, chitransi.dtu@gmail.com, sajalkpaul@rediffmail.com

DOI: 10.15598/aeee.v13i2.1164

Abstract. This paper presents Operational transresis- ical examples of conventional controllers, and neuro-
tance amplifier (OTRA) based proportional-integral- fuzzy controllers are representatives of the unconven-
derivative (PID) controller with independent electronic tional class. The controllers based on proportional-
tuning of proportional, integral, and derivative con- integral-derivative (PID) algorithm are most popularly
stants. The configuration can be made fully integrated used in the process industries. These are used to con-
by implementing the resistors using matched transistors trol various processes satisfactorily with proper tuning
operating in the linear region. Theoretical propositions of controller parameters. Generally operational ampli-
are verified through SPICE simulations using 0.18 µm fiers (OPAMPs) are used to design classical analog con-
process parameters from MOSIS (AGILENT). In or- trollers [1], [2]. However the OPAMPs, being voltage
der to demonstrate the workability of the proposed con- mode circuit, have their limitations of constant gain
troller, its effect on step response of an OTRA based bandwidth product (fT ) and low slew rate. This in-
second order system is analyzed and presented. accurately limits the speed of the OPAMP-based con-
trollers and might influence the dynamics of the system
[3]. It is well known that inherent wide bandwidth al-
most independent of closed loop gain; greater linearity
Keywords and large dynamic range are the key performance fea-
tures of current mode technique [4]. Therefore, the
OTRA, PD, PI, PID, second order system. current mode building blocks would be a good alter-
native of OPAMP for designing the analog controllers.
Literature survey reveals that number of current mode
circuits have been reported relating to PID controllers
1. Introduction [3], [5], [6], [7], [8]. Operational transconductance am-
plifier (OTA) based controllers are proposed in [5] and
A controller monitors and modifies the operational con- are electronically tunable. However, these provide volt-
ditions of a given dynamical system. These opera- age output at high impedance making a buffer nec-
tional conditions are referred to as measured output essary to drive the voltage input circuits. The cur-
variables and can be modified by adjusting certain in- rent difference buffered amplifier (CDBA) based PID
put variables. The controller calculates the difference controller presented in [6] uses an excessively large
between a measured output variable and a desired set number of active and passive components. References
point as an error value and attempts to minimize the [3], [7], [8] present current conveyor II (CCII) based
error by adjusting the process control inputs. In gen- PID controllers. Two different structures are proposed
eral controllers can be classified as (i) conventional and for voltage and current outputs respectively in [7], [8]
(ii) non-conventional controllers. For conventional con- whereas [3] presents only voltage output configuration.
trollers, such as PID controller, a prior knowledge of All the CCII based voltage mode designs deliver output
the mathematical model of the process to be controlled voltage at high impedance and are thus not suitable for
is required in order to design a controller whereas for driving voltage input circuits. The OTRA is yet an-
unconventional controllers this information is gener- other, relatively recently proposed current mode build-
ally not needed. P, PI, PD, and PID are few typ-

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Tab. 1: Comparison of proposed work with existing literature.

No. of
Active Passive Output Electronic
Reference Active Outputs
block used elements Impedance Tunability
block used
[1] Opamp 4 8R, 2C Voltage Low No
[3] Opamp 1 3R, 3C Voltage Low No
[5] OTA 8 2C Voltage High Yes
[6] CDBA 4 8R, 2C Voltage Low No
Fig. 2: Current High No
[7] CCII 3 4R, 2C
Fig. 3: Voltage High No
Fig. 2: Current High No
[8] CCII 3 4R, 2C
Fig. 3: Voltage High No
Proposed
OTRA 2 4R, 3C Voltage Low Yes
work

ing block which is a high gain current input, voltage

output amplifier [9].
Being a current processing analog building block,
it inherits the advantages of the current mode tech-
nique. Additionally it is also free from the effects of
parasitic capacitances at the input due to virtually in-
ternally grounded input terminals [10] and hence the Fig. 1: The OTRA circuit symbol.
non-ideality problem is less in circuits implemented us-
ing OTRA. Therefore, this paper aims at presenting
OTRA based PID controller with orthogonally tunable
proportional, integral and derivative constants. The
proposed circuit can be made fully integrated by imple-
menting the resistors using MOS transistors operating
in the non-saturation region. This also facilitates elec-
tronic tuning of the controller parameters. A detailed
comparison of the PID controllers available in the lit-
erature is given in Tab. 1 which suggests that OTRA
based structure is the most suitable choice for voltage
mode operation.
Fig. 2: Block diagram of a closed loop system with PID con-
troller.
2. Proposed Circuits
of achieving the complete improvement in system per-
The OTRA is a three terminal device shown symboli- formance [11]. This leads to the motivation of using
cally in Fig. 1 and its port relations can be character-a PID controller so that the best features of each of
ized by the matrix as follows: the PI and PD controllers are utilized. In a PID con-
  
Vp 0 0 0
 
Ip troller as shown in Fig. 2 the proportional, integral and
Vn  =  0 0 0 In  , (1)the derivative of the error signal E (s) are summed up
V0 Rm −Rm 0 I0 to calculate the output actuating signal U (s) of the
controller which controls the plant’s (GP (s)) function.
Thus, the transfer function GC (s) of the PID controller
where Rm is the transresistance gain of the OTRA. For
can be written as:
ideal operations, Rm approaches infinity and forces the
input currents to be equal. Thus, OTRA must be used
in a negative feedback configuration [9], [10]. Ki
GC (s) = Kp + + sKd , (2)
s
where Kp , Ki , and Kd are the proportional, integral
2.1. PID Controller
and derivative constants respectively.
In a given system the proportional action improves the In the following subsection first an OTRA based PI
rise time of the system, the integral action improves controller is introduced followed by a PD controller.
the steady-state error whereas the derivative action im- By combining these two controllers, the proposed PID
proves the degree of stability. So, none alone is capable controller is designed.

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1) Proposed PI Controller
Rf
Kp = , Kd = s · C · R. (8)
The PI controller comprises of proportional and in- R
tegral actions and can be derived from the controller
From Eq. (8) it is clear that by varying R, Kp value
block of Fig. 2 if the derivative block is excluded. The
can be adjusted independently of Kd and by simulta-
transfer function GP I (s), of the PI controller so ob-
neous variation of Rf and R such that Rf /R remains
tained is given by:
constant, Kd can be independently controlled.
Ki
GP I (s) = Kp + . (3)
s

The OTRA based proposed PI controller is shown in

Fig. 3.

Fig. 4: Proposed PD controller.

3) Proposed PID Controller

Fig. 3: Proposed PI controller.
The proposed OTRA based PID Controller can be de-
rived by combining the proposed PI and PD controllers
Using routine analysis the voltage transfer function
and is shown in Fig. 5. The routine analysis of this cir-
of the proposed controller can be as expressed as:
cuit gives the transfer function of the controller as:
Vo C 1
 
Vo R4 R4 · C1
GP I (s) = = + . (4) GP ID (s) = == +
Vi Cf s · Cf · R Vi R2 R3 · C1
(9)
From Eq. (4) the controller parameters can be com- R4
puted as: + + s · C 2 · R4 ,
s · C3 · R1 · R3
C 1
Kp = , Ki = . (5)
Cf R · Cf from Eq. (9) the controller parameters can be identified
as:
It is clear from Eq. (5) that Kp value can be ad-
R4 · C 1 R4 R4
justed independently of Ki by varying C, and Ki can Kp = + , Ki = ,
be independently controlled by varying R. R 3 · C 3 R 2 C3 · R 1 · R3
(10)
Kd = C2 · R4 .
2) Proposed PD Controller
It is observed from Eq. (10) that the Kp value can
A PD controller can be obtained if proportional and be adjusted independently by varying R2 , independent
derivative actions only are taken into consideration in tuning of Ki is possible through R1 variation whereas
Fig. 2. Transfer function of a PD Controller GP D (s), Kd can be controlled independently by simultaneous
can be represented as: variation of R2 , R3 and R4 , such that R4 /R2 and
R4 /R3 remain constant.
GP D (s) = Kp + s · Kd . (6)

Figure 4 shows the proposed PD controller circuit 2.2. MOS-C Implementation and
and the transfer function of this controller is obtained Electronic Tuning of the
as: Proposed Controllers

Vo Rf It is well known that the linear passive resistor con-

GP D (s) = = + s · C · R. (7) sumes a large chip area as compared to the linear resis-
Vi R
tor implementation using transistors operating in the
The controller parameters can be expressed as: non-saturation region. The differential input of OTRA

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(a)

Fig. 5: Proposed PID controller.

allows the resistors connected to the input terminals of

OTRA to be implemented using MOS transistors with
complete non-linearity cancelation [10]. Figure 6(a)
shows a typical MOS implementation of resistance con-
nected between negative input and output terminals of
OTRA. The resistance value may be adjusted by ap-
propriate choice of gate voltages thereby making con-
troller parameters electronically tunable. The value of
resistance so obtained is given by:

1 (b)
R=   , (11)
W
µn · Cox · · (Va − Vb ) Fig. 6: MOS implementation of (a) linear resistance, (b) pro-
L posed PID controller.

where Va and Vb are control gate voltages; the param-

eters µn , Cox , W , and L represent electron mobility,
oxide capacitance per unit gate area, effective channel 3. Nonideality Analysis of PID
width, and effective channel length respectively and Controller
their value are expressed as:

The non-idealities associated with OTRA based cir-

µ0
µn = , (12) cuits may be divided into two groups. The first group
θ (VGS − VT ) results due to finite trans-resistance gain whereas the
second one concerns with the nonzero impedances of p
εox and n terminals of OTRA.
Cox = , (13)
tox

W = WDrawn − 2WD , (14)

3.1. Nonideality due to Finite
L = LDrawn − 2LD , (15) Transresistance Gain

Here the effect of finite transresistance gain (Rm ) on

where the symbols have their usual meaning.
PID controller is considered, and passive compensa-
The MOS transistors based implementation of lin- tion is employed for high-frequency applications. Ide-
ear resistors not only reduces the chip area but also ally the Rm is assumed to approach infinity. However,
makes controller parameters electronically tunable. practically Rm is a frequency dependent finite value.
The MOS-C implementation of the circuit of Fig. 5 Considering a single pole model for the trans-resistance
is shown in Fig. 6(b). gain, it can be expressed in Eq. (16):

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R0
Rm = , (16)
1 + ωs0
1
Rm (s) ≈ . (17)
s · Cp
 
Vo R4 R4 · C 1
GP ID (s)N I = = +
Vi R2 · (1 + s · Cp2 · R4 ) R3 · (C3 + Cp1 ) · (1 + s · Cp2 · R4 )
(18)
R4 s · C 2 · R4
+ + ,
s · R1 · R3 · (C3 + Cp1 ) · (1 + s · Cp2 · R4 ) (1 + s · Cp2 · R4 )
Vo R4 R4 · C 1
= +
Vi R2 · (1 + s · (Cp2 − Y ) · R4 ) R3 · (C3 + Cp1 ) · (1 + s · (Cp2 − Y ) · R4 )
(19)
R4 s · C2 · R4
+ + .
s · R1 · R3 · (C3 + Cp1 ) · (1 + s · (Cp2 − Y ) · R4 ) (1 + s · (Cp2 − Y ) · R4 )

where R0 is dc transresistance gain. For high-

frequency applications the transresistance gain reduces
to Eq. (17).
The term Cp represents parasitic capacitance associ-
ated with OTRA and is given by Cp = R0 ω0 . Taking
this effect into account Eq. (9) modifies to Eq. (18),
where Cp1 and Cp2 are the parasitic capacitances of
OTRA1 and OTRA2 respectively.
For high-frequency applications, compensation
methods must be employed to account for the error in-
troduced in Eq. (9). The effect of Cp1 can be eliminated
by pre-adjusting the value of capacitors C3 and thus
achieving self-compensation. The sCp2 term appear-
ing in parallel to R4 will result in the introduction of a
parasitic pole having radian frequency as ω = 1/R4 Cp2 .
The effect of Cp2 can be eliminated by connecting an Fig. 7: Compensated PID controller.
admittance Y between the non-inverting terminal and
the output as shown in Fig. 7. Considering the circuit Vi · s · C3
of Fig. 7, Eq. (18) modifies to Eq. (19). Ip1 = , (21)
1 + s · C3 · Rn1
By taking Y = sCp2 , Eq. (19) reduces to Eq. (9)
where Ip1 and In1 are the currents and Rp1 and Rn1 are
thus eliminating the effect of Cp2 and hence achieving
the input resistances of p and n terminals respectively
the passive compensation.
of OTRA 1. Considering Rm1 to be the transresistance
gain and Ro1 is the output resistance of OTRA1, the
output voltage of OTRA1, can be computed as:
3.2. Effect of Nonzero Impedances of
p and n Terminals V1 0 = Rm1 (Ip1 − In1 ) − R0 · In1 , (22)

V1 0 = Rm1 · Ip1 − (Rm1 + R0 ) · In1 , (23)

Ideally the input as well as output resistances of an
OTRA are assumed to be zero. Considering the in- as Rm1 >> Ro1 , so Rm1 + Ro1 ≈ Rm1 and hence:
put (Rn and Rp ) and output (Ro ) resistances of the
OTRA to be finite, the equivalent model of proposed V1 0 = Rm1 · (Ip1 − In1 ) , (24)
PID controller can be drawn as shown in Fig. 8. 0
V1 Rm1 · (1 + s · C1 · R1 )
Routine analysis of circuit of Fig. 8 results in termi- =
Vi R1 + Rp1 + s · C1 · R1 · Rp1
nal currentsIp1 and In1 as: (25)
1 + s · C3 · Rm1
Vi · (1 + s · C1 · R1 ) · ,
Ip1 = , (20) 1 + s · C3 (Rm1 + Rn1 )
R1 + Rp1 + s · C1 · R1 · Rp1

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V1 0 (1 + s · C1 · R1 ) · (1 + s · C3 · Rm1 )
=  , (26)
Vi 1
R1 · (1 + s · C1 · Rp1 ) · Rm1 + s · C3

(1 + s · C1 · R1 ) · (1 + s · C3 · Rm1 ) · Vi
Vi 0 = , (27)
R1 · (1 + s · C1 · Rp1 ) · (s · C3 )
V1 0 R2 + Vi R3 (1 + sC2 R2 ) V1 0 R2 + Vi R3 (1 + sC2 R2 )
Ip2 = =
R2 Rp2 + R2 R3 + Rp2 R3 (1 + sC2 R2 ) R2 (Rp2 + R3 ) + Rp2 R3 (1 + sC2 R2 )

V1 0 R2 + Vi R3 (1 + sC2 R2 ) V1 0 R2 + Vi R3 (1 + sC2 R2 )
≈ = (28)
R2 R3 + Rp2 R3 (1 + sC2 R2 ) R3 (R2 + Rp2 ) + sC2 R2 R3 Rp2

V1 0 Vi (1 + sC2 R2 )
≈ + ,
R3 (1 + sC2 Rp2 ) R2 (1 + sC2 Rp2 )
(1 + sC1 R1 )(1 + sC3 Rm1 )Vi Vi (1 + sC2 R2 )
Ip2 = + . (29)
R1 R3 (1 + sC2 Rp2 )(1 + sC1 Rp1 )(sC3 ) R2 (1 + sC2 Rp2 )

Substituting Ip1 and In1 , Eq. (24) results in Eq. (25). It is observed from Eq. (34) that the nonzero val-
As R1 >> Rp1 and Rm1 >> Rn1 , Eq. (25) yields to ues of input resistances at n and p terminal of OTRAs
Eq. (26). It can be further simplified to Eq. (27) since result in introduction of parasitic pole and zero in pro-
1/Rm1 << 1. portional and integral terms and the derivative term
consists of a parasitic pole. The numerical values of
From Fig. 8 Ip2 , the p terminal current of OTRA2,
poles and zeros are very high as parasitic resistances
can be written as Eq. (28), where Rp2 is the p terminal
of OTRA are very small. Thus, the parasitic zero and
resistance of OTRA2. Substituting for from Eq. (27)
pole frequencies would not practically influence the sys-
Ip2 can be expressed as Eq. (29)
tem performance.
Similarly considering Rn2 to be the n terminal resis-
tance of OTRA2 the In2 can be represented as Eq. (30)
shown bellow:
Vo 4. Simulation Results
In2 = , (30)
R4 + Rn2
and the output voltage of OTRA2, can be computed The theoretical propositions are verified through
as: SPICE simulations using 0.18 µm CMOS process pa-
Vo = Rm2 (Ip2 − In2 ) − Ro2 In2 , (31) rameters provided by MOSIS. The CMOS implemen-
tation of the OTRA, proposed in [13] with supply
where Rm2 and Ro2 are transresistance gain and output voltages ± 1.5 V was used for simulation. For per-
resistance of OTRA2 respectively. Since Rm2 >> R2 , formance evaluation of the proposed controllers, their
so Rm2 + Ro2 ≈ Rm2 and hence time domain responses are obtained. The ideal and
Vo ≈ Rm2 (Ip2 − In2 ) , (32) simulated time domain responses of the proposed PI
controller of Fig. 3, for a 50 mV step input voltage
R4 (1 + sC1 R1 )(1 + sC3 Rn1 )Vi with 20 ns rise time, are shown in Fig. 9(a). The
Vo =
R1 R3 sC3 (1 + sC1 Rp1 )(1 + sC2 Rp2 ) passive component values of the PI controller are cho-
(33) sen as R = 50 kΩ, C = 4 pF and Cf = 2 pF and
R4 (1 + sC2 R2 )Vi the corresponding controller parameters are computed
+ ,
R2 (1 + sC2 Rp2 ) to be Kp = 2, Ki = 107 s−1 . For transient analy-
and the transfer function Vo /Vi modifies to: sis of PD controller of Fig. 4, a 50 mV peak trian-
  gular input voltage is applied. The ideal and sim-
Vo 1 R4 C1 (1 + sC3 Rn1 ) R4 ulated transient responses are depicted in Fig. 9(b).
= +
Vi (1 + sC2 Rp2 ) R3 C3 (1 + sC1 Rp1 ) R2 The component values for the PD controller are cho-
sen as R = 10 kΩ, Rf = 20 kΩ and C = 20 pF and
R4 (1 + sC3 Rn1 ) the controller parameters are computed to be Kp = 2,
+
R1 R3 sC3 (1 + sC1 Rp1 ) (1 + sC2 Rp2 ) Kd = 0.4 µs. For the PID controller of Fig. 5, values
of the capacitors are taken as C1 = C3 = 10 pF and
sC2 R4 C2 = 0.05 pF. The resistive component values are cho-
+ .
(1 + C2 Rp2 ) sen as R1 = R2 = R3 = R4 = 50 kΩ. Using these
(34) passive component values various controller parame-

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Fig. 8: Equivalent model of proposed PID controller.

(a) PI (b) PD

(c) PID

Fig. 9: Time domain response of the proposed controllers.

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ters are computed as Kp = 2, Ki = 2 · 106 s−1 and The standard characteristic polynomial, D(s), of sec-
Kd = 2.5 ns. For time domain analysis, a 50 mV step ond order system [12] is given by:
signal with 10 ns rise time is applied. The transient re-
sponse of proposed PID controller is shown in Fig. 9(c). D(s) = s2 + 2ξωn s + ω 2 n , (37)
It is observed that for all the controllers the simulated
where ωn is the natural frequency of oscillations and ξ
and ideal responses are in close agreement.
represents the damping factor. Comparing the denom-
inator of Eq. (35) with Eq. (37) the ωn and ξ for the
LPF can be computed as:
5. Performance Evaluation of √
K 1
the Proposed Controllers ωn =
RC
and ξ = √ . (38)
2 K
To evaluate the effect of various controllers, the per- In the study that follows, the step response of the
formance of a second order plant is analyzed by form- open loop second order system (LPF) is analysed first
ing a closed loop system as shown in Fig. 10(a) where and then the effect of various proposed controllers on
GP (s) represents the open loop transfer function of a this second order system is observed by forming closed
unity feedback system. For OTRA based realization loop with controllers.
of the closed loop system the low-pass filter (LPF)
presented in [14] is used and is modified as shown For the second order system shown in Fig. 10(b),
in Fig. 10(b). The OTRA1, resistors R1 , R2 , along the passive component values are chosen as
with capacitors C1 and C2 form the second order plant Ra = Rb = 20 kΩ, R1 = R2 = R3 = 2 kΩ, and
whereas OTRA2 along with resistors Ra and Rb is used C1 = C2 = 20 pF. The fn and ξ for the LPF can be
as subtractor thereby forming the error signal. The cir- computed as 3.98 MHz and 0.5 respectively.
cuit of Fig. 10 can also be made electronically tunable
by implementing all the related resistors using MOS
transistors operating in the linear region.

(a) Block diagram.

(a) with fixed ξ

(b) OTRA based realization.

Fig. 10: Second order closed loop system.

The transfer function of the circuit of Fig. 10(b) us- (b) with varying ξ
ing equal component design with R1 = R2 = R and
C1 = C2 = C can be derived as: Fig. 11: Step Response of LPF.

K
Vo (s) R2 C 2
= 2 s K

, (35) To observe the step response of the LPF a step in-
Vi (s) s + CR + R2 C 2 put of 50 mV is applied, and the simulated response is
shown in Fig. 11(a). The effect of damping ratio, ξ on
where
Rb the step response of the second order LPF is shown in
K= . (36) Fig. 11(b). To change ξ, Rb is kept constant while Ra
Ra

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Tab. 2: Performance Comparison of second order system.

Closed loop with

Unity feedback Closed loop with Closed loop with PID controller
Parameter closed loop PD controller PI controller (Kp = 2,
system (Kp = 2, Ki = 107 s−1 ) (Kp = 2, Kd = 0.4 µs) Ki = 2 · 106 s−1 ,
Kd = 2.5 ns)
Overshoot 19.56 % 12.47 % 18.76 % 8.16 %
Peak output 58.26 mV 56.52 mV 57.83 mV 52.59 mV
Rise time 140.43 ns 119.89 ns 112.28 ns 99.75 ns
Settling time 303.12 ns 274.35 ns 266.11 ns 252.27 ns

with the increase in ξ, oscillations are decreasing and

is perfectly in tune with the theoretical concept. The
performance of PI, PD, and PID controllers is evalu-
ated by comparing step responses of closed loop sys-
tems based on these controllers. Figure 12(a) depicts
the effects of proposed PI (Kp = 2, Ki = 107 s−1 )
and PD (Kp = 2, Kd = 0.4 µs) controllers on step
response of the closed loop system. Step response for
(a) with PI and PD controllers. varying values of Ki , while keeping Kp = 2 constant,
is depicted in Fig. 12(b). The effect of variable Kd
on the step response of the system, keeping Kp = 2
constant, is shown in Fig. 12(c). System step response
with PID controller is represented by Fig. 12(d). Per-
formance parameters such as overshoot, peak output,
rise time and settling time of the closed-loop system
with different controllers are measured and tabulated
in Tab. 2. The study of the table clearly suggests that
with the help of controllers the system performance
is improved in a desired manner. The PD controller
prominently improves the overshoot whereas PI con-
troller influences mainly the settling time as compared
(b) with variable Ki for PI controller.
to all other parameters. The PID includes best features
of all individual controllers and results in improvement
of all the performance measure parameters.

6. Conclusion

(c) with variable Kd for PD controller. Operational transresistance amplifier based PI, PD and
PID controllers have been presented which possess the
feature of independent tuning of proportional (Kp ),
derivative (Kd ) and integral (Ki ) constants. By imple-
menting the resistors using MOS transistors operating
in linear region MOS-C equivalent of the controllers
can be obtained which are suitable for full integration.
This also results in reduced chip area and power con-
sumption as compared to passive resistors. To verify
the functionality of the proposed controllers their ef-
(d) PID controller. fect on a second order closed loop system was analyzed
through simulations. The simulated results are in line
Fig. 12: Response of a second order system. with the proposed theory. The performance analysis
reveals that PD controller improves percentage over-
shoot, PI controller refines settling time while PID as
is varied electronically by changing gate voltages of the a combination of the two, enhances transient as well as
transistors used for implementing it. It is observed that the steady-state response of the system.

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About Authors
[6] KESKIN, A. U. Design of a PID Controller
Circuit Employing CDBAs. International Jour- Rajeshwari PANDEY did B.Tech. (Electronics and
nal of Electrical Engineering Education. 2006, Telecommunication) from University of Allahabad,
vol. 43, no. 1, pp. 48–56. ISSN 0020-7209. India, M.E. (Electronics and Control) from Birla In-
DOI: 10.7227/IJEEE.43.1.5 stitute of Technology and Sciences, Pilani, Rajasthan,
and Ph.D. from Delhi University, India.Currently, she
[7] MINAEI, S., E. YUCE, S. TOKAT and O.
is Associate Professor in Department of Electronics
CICEKOGLU. Simple Realizations of Current-
and Communication Engineering, Delhi Technological
Mode and Voltage-Mode PID, PI and PD Con-
University, Delhi. Her research interests include
trollers. In: Proceedings of the IEEE International
Analog Integrated Circuits, and Microelectronics.
Symposium on Industrial Electronics. Dubrovnik:
IEEE, 2005, pp. 195–198. ISBN 0-7803-8738-4.
Neeta PANDEY did M.E. in Microelectronics
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from Birla Institute of Technology and Sciences,
[8] YUCE, E., S. TOKAT, S. MINAEI and O. Pilani, Rajasthan, India and Ph.D. from Guru Gobind
CICEKOGLU. Low-Component-Count In- Singh Indraprastha University Delhi, India. At
sensitive Current-Mode and Voltage-Mode present she is Associate Professor in Department of
PID, PI and PD Controllers. Frequenz. 2006, Electronics and Communication Engineering, Delhi
vol. 60, no. 3–4, pp. 65–70. ISSN 2191-6349. Technological University, Delhi. A life member of
DOI: 10.1515/FREQ.2006.60.3-4.65. ISTE, and member of IEEE, USA, she has published
papers in International, National Journals of repute
[9] CHEN, J. J., H. W. TSAO and C. C. and conferences. Her research interests are in Analog
CHEN. Operational transresistance amplifier us- and Digital VLSI Design.
ing CMOS technology. Electronics Letters. 1992,
vol. 28, no. 22, pp. 2087–2088. ISSN 0013-5194. Saurabh CHITRANSI did B.Tech. (Electronics
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 THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 13 | NUMBER: 2 | 2015 | JUNE

University of Lucknow, India and M.Tech. (VLSI De- (IGNOU), Kolkata; Advanced Training Institute for
sign and Embedded System) from Delhi Technological Electronics and Process Instrumentation(ATI-EPI),
University, Delhi, India. Currently, he is Executive Hyderabad; North Eastern Regional Institute of Sci-
Engineer in Diffusion and CVD Department, SITAR, ence Technology(NERIST), Nirjuli and Delhi College
DRDO, Bangalore, India. His research interests of Engineering(DCE), Delhi in various capacities. He
include Analog Integrated Circuits, MEMS and Silicon has served the Department of Electronics Engineering,
process integration. Indian School of Mines, Dhanbad as Head of the
Department and at present Professor of the same
Sajal K. PAUL did B.Tech., M.Tech., and Ph.D. in department. His research interest includes Microelec-
Radio Physics and Electronics from the Institute of toncic Devices, Electronic Properties of Semiconductor
Radio Physics and Electronics, University of Calcutta. and Bipolar and MOS Analog Integrated Circuits. He
He has served Webel Telecommunication Industries, has more than 60 research publications in International
Kolkata; Indira Gandhi National Open University and National journals of repute and conferences.

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