This document describes a mixed-mode PIDA controller circuit employing OTAs. It introduces PID and PIDA controllers and discusses their limitations. It then presents the proposed mixed-mode PIDA controller circuit design using OTAs which allows for either current or voltage input/output signals and independent adjustment of gain parameters. Simulation results show the circuit performs as theoretically expected with good agreement between ideal and simulated frequency responses. The circuit offers advantages over conventional controller designs and can be applied in closed-loop control systems.
5. THE SYNTHESIS OF ELECTRONIC CONTROLLER
CIRCUITS
using op-amp and passive element [3]-[4], they consume
high power and their frequency response is limited by
GBP
6. PIDA circuits using OTA (Operational
Transconductance Amplifier), CFOA
(Current Feedback Operational Amplifier),
and CCII (second generation current
conveyor) were proposed [5], [6], and [7].
This controller is more advantageous than
conventional controllers.
Since the inputs and output of proposed
controller can be either current signal or
voltage signal, the application of circuitry
will be more flexible
7.
8. PRINCIPLE OF THE PROPOSED CIRCUIT
Figure 1. Operational transconductance amplifiers.
)a (The single output OTA.
(b (The dual output OTA.
IB
iO2
IB
-
+
V+
V-
iO1
iO1
-
+
V+
V-
Operational transconductance
amplifier:OTA
(1)
9. PIDA CONTROLLER
Transfer function of PIDA is given as
Since the poles d, e are greater than zero, these
poles are non-dominant poles, and can be
ignored.
(3)
(2)
10. The transfer function of proposed PIDA controller
will be shown by
Vin
Iin
iout
Vout
s
K I
D
sK
D
A
K
sK
P
K
m
g
1
m
g
1
Figure 2. Block diagram of proposed PIDA controller.
(4)
12. The output voltage of PIDA occurs from summation of IP,
II,ID, and IA at OTA_10, and can be expressed as
The output current of PIDA can be expressed
as
(5)
(6)
if , the transfer function will be
if , the transfer function will be
if , the transfer function will be
if , the transfer function will be
13. THE GAINS OF THE VOLTAGE MODE PIDA
CONTROLLER IN THE FOLLOWING EQUATIONS
(9)
(8)
(10)
(7)
17. Frequency
1Hz 10Hz 100Hz 1kHz 10kHz 100kHz
-200dB
-100dB
0dB
50dB
Simulated IP
Simulated II
Simulated ID
Simulated IA
Ideal ID
Ideal IA
Ideal IP
Ideal II
Figure 6. ideal and simulated frequency response of
each PIDA elements
18. PERFORMANCE ANALYSIS
(12)
(11)
The input resistance of CMOS OTA is very high, and
capacitors CI, CD, and CA are greater than parasitic
capacitors. Therefore these effect can be ignored. The
output resistance of OTA is a main factor that affects the
proposed PIDA
19. APPLICATION
The close loop control system with Proportional
controller
RS
CP1
CP3
CP2
gmp1
gmp3
gmp2
gmS
VS
Vo
VE
Time
0s 2ms 4ms 6ms
-100mV
0V
100mV
200mV
300mV
Vs
Vo, RS=160kΩ
Vo, RS=40kΩ Vo, RS=80kΩ
22. CONCLUSION
its input signal and output signal can
be either current or voltage.
the gains KP, KI, KD, and KA can be
independently controlled by adjusting
bias currents.
grounded capacitors are only used .
no resistor is required.
simulation results agree well with the
theoretical anticipation.
This paper has proposed the PIDA
controller circuit which has the following
features
