Novel Voltage-Mode PID Controller Using a Single CCTA and All Grounded Passive Components

: A compact voltage-mode proportional-integral-derivative (PID) controller based on the utilization of a single current conveyor transconductance amplifier (CCTA) is presented in this paper. The presented active PID controller is made up of a single CCTA, and four truly grounded passive components, i.e. two resistors, and two capacitors. The design consideration of the controller parameters has been examined. Besides, the crucial sensitivity performances of the controller parameters for ideal and non-ideal conditions have also been discussed. An application on the closed-loop test system is demonstrated to validate the practicability of the proposed PID controller circuit. To confirm the theoretical behavior, the proposed circuit is simulated with the PSPICE program using TSMC 0.35-μm CMOS process technology. Experimental test results based on commercially available CFOA AD844 and OTA CA3080 integrated circuits are also provided to demonstrate the practicality of the proposed circuit.


Introduction
Proportional-Integral-Derivative (PID) controllers are the most commonly employed control actions in feedback control systems, and process industries [1].They have been extensively utilized for several decades since they feature a variety of desired properties, including design simplicity, low cost, robustness, and broad application, as well as easy parameter tuning [2].Their wide range of applications have stimulated and sustained the design and invention of various PID controller circuits and sophisticated hardware modules.Over the last two decades, the enormous literature on PID process controllers has featured a wide range of design techniques based on numerous active compo-nents, such as operational transconductance amplifiers (OTAs) [3], second generation current conveyors (CCIIs) [4]- [5], current feedback operational amplifiers (CFOAs) [6]- [9], current differencing buffered amplifiers (CDBAs) [10], differential voltage current conveyor transconductance amplifiers (DVCCTAs) [11], current follower transconductance amplifiers (CFTAs) [12]-13], voltage differencing transconductance amplifiers (VDTAs) [14], voltage differencing current conveyors (VDCCs) [15], and second generation voltage conveyors (VCIIs) [16].In [3]- [4], [6], [9]- [10], the PID controllers designed with the signal-flow graph approach have been proposed.However, for the realizations in [3]- [4], [9]- [10], [16], at least four active components were required.Furthermore, PID controller realizations of [4]- [6], [9]- [11], [13]- [15] include a number of passive components, i.e., at least five passive components, some of which are also floating.Floating passive components were used to design single active element-based PID controller circuits in [7]- [8], [12]- [13], [15]- [16].Active circuit structures with all grounded passive elements are well recognized to be useful for fully integrated circuit (IC) design as well as IC hybrid fabrication processes.This is due to the fact that the usage of grounded passive elements is helpful for the electronic adjustability and permits the elimination/accommodation of various parasitic effects for IC implementation.Another point to note is that the performance and application of the previously discussed controllers [3]- [7], [10]- [15] were evaluated solely through computer simulations.For acceptability purposes, experimental measurements are the important method to evaluate the practicability of the circuit.
The current conveyor transconductance amplifier (CCTA) is a contemporary versatile active circuit block that is a cascade of a CCII and an OTA [17].The CCTA has been extensively used in the design of analog signal processing circuits and solutions like as analog filters [18]- [20], sinusoidal oscillators [21]- [22], resistor-less inductance simulator [23], and high-frequency active meminductor emulator [24].Therefore, this work aims at proposing a CCTA-based voltage-mode PID controller with a canonic and lowcomponent count.It is made up of only one CCTA as an active component and all grounded passive components, such as two resistors and two capacitors.There is no element-equality criteria required for the controller realization.Non-ideal gain effects on the controller performance and sensitivity analysis are also investigated.The functionality of the proposed PID controller is evaluated in a closed-loop system.As an example plant circuit, a second-order lowpass filter was built to design the closed-loop system.To test the behavior of the proposed PID controller circuit, some computer simulations using the PSPICE software and experimen-tal measurement data using off-the-shelf integrated circuits AD844 and CA3080 are presented.
Table 1 illustrates the comparative analysis of all previously mentioned PID controllers as having the following desirable properties to substantiate the proposition of the proposed controller: (i) the number of active elements, (ii) the number of passive elements, (iii) the use of all grounded passive elements, (iv) electronic tunability, (v) simulation technology, (vi) simulation supply voltages, (vii) simulated total power consumption, (viii) experimental technology, and (ix) experimental supply voltages.

Circuit description 2.1 CCTA properties
Basically, the CCTA is a versatile active building block designed by the cascade connection of CCII followed by an OTA [17].The schematic symbol of the CCTA is depicted in Fig. 1.The voltage drop at terminal x follows the applied voltage at terminal y in magnitude.The output currents at terminals z and zc follow the current through terminal x in magnitude.The voltage drop at terminal z is converted to an output current at terminal o with the transconductance gain (g m ).The terminal relationship of the ideal CCTA can be described by the following set of equations: In general, the transconductance g m can be modified electronically by adjusting the externally provided current I B .

Proposed single CCTA-based PID controller circuit
In a general PID controller, three modes of controller with proportional, integral, and derivative actions must be incorporated.As a consequence, the transfer function of a standard voltage-mode PID controller is generally defined as follows: [25] where V in (s) is the input voltage, V out (s) is the output voltage, K P is the proportional coefficient, K I is the integral coefficient, and K D is the derivative coefficient.
Fig. 2 shows the proposed voltage-mode PID controller based on CCTA as an active component.The controller comprises only a single CCTA, and all grounded passive components, i.e. two resistors and two capacitors.
From the aspect of an integrated circuit, it is critical to employ all grounded passive components.The circuit analysis of the proposed PID controller in Fig. 2 gives the following voltage transfer function.
By comparing the above obtained function with the general equation of the PID controller given in equation (2), the various coefficients of the proposed controller are determined to be as follows: Ref. [5] in 2006 and As seen from the above expressions, the various gain coefficients of the PID controller can be controlled electronically.The expressions also show that the three coefficients can be determined by appropriately setting the values of g m , R 1 , R 2 , C 1 and C 2 .The design considerations will be outlined in the following section.Because the primary contribution of this work is the design of a compact analog PID controller with a minimal number of active and passive components, independent tuning of the gain coefficients K P , K I and K D is not expected.Due to the low component count, the circuit requires a small chip area.As a result, the production cost is lowered.

Practical design considerations
In order to realize the desired gain parameters of the proposed PID controller indicated in equations ( 4)-( 6), the design procedure for setting the circuit components is described as follows.
From equations ( 5) and ( 6), the values of capacitors C 1 and C 2 so obtained are expressed as and Therefore, substituting these relations into equation (4), we then obtain According to the PID design criteria, the coefficients K I and K D are supposed to be arbitrarily determined parameters.By taking the gain K P modifies to The minimum value of K P derived from equation ( 11) is obtained at and its minimum value can be given below: It can be realized from equation ( 13) that the value of K P(min) is determined by the given values of K I and K D .As a result, the useful value for the gain K P should satisfy the following relationship: Rearranging equation (11), we found that .0 Based on the condition of the K P value specified in equation (14), equation (15) has two real roots, as illustrated below.
Therefore, the basic steps in the sequel are followed to determine the required controller parameters, and satisfy the K P value given in equation (14).

Non-ideal effects
The non-ideal condition of the real CCTA is investigated in this section.The port relationship of the non-ideal  CCTA, including tracking errors, can be modeled by the following matrix equation: By taking the non-ideal CCTA into effect, the voltage transfer function of the proposed PID controller in Fig. 2 can be derived as: In this case, the non-ideal gain parameters of the PID controller can then be obtained as: and The above expressions clearly show that the non-ideal gains β, α and δ of the CCTA have a direct effect on the PID gain parameters K P , K I and K D .The absolute coefficients of the active and passive sensitivity versus PID gain parameters are found to be less than or equal to unity, as shown by the following equations: and

Simulation results
The theoretical assumptions are validated through PSPICE simulation utilizing 0.35-μm CMOS process parameters provided by TSMC.For simulation, the CMOS implementation of the CCTA shown in Fig. 3 was used with symmetrical supply voltages of ±1.5 V. Transistor aspect ratios are provided in Table 2.The transconductance of the CCTA is found as: where K = μC ox (W/L).Here, the parameters μ, C ox , W, and L denote electron mobility, oxide capacitance per unit gate area, effective channel width, and effective channel length, respectively.The transconductance g m is dependent on the process parameter K, and the external bias current I B , according to equation (32).The plot in Fig. 4 also illustrates the variations in g m for the CMOS CCTA in Fig. 3, which are relatively dependent on variations in I B .It has been analyzed that, when I B is varied from 40 μA to 230 μA, the percentage inaccuracy in g m is less than 9% compared to the theoretical g m value.Additionally, the temperature-dependent variation of the frequency-domain responses of the proposed PID controller analysis was performed at industrial ranges T = -50°C, 0°C, 27°C, 50°C, and 100°C.The simulation results of the industrial temperature analysis are given in Fig. 7, where it can be observed that the gain characteristic of the controller diminishes with increasing temperature.

Figure 8: Single CCTA-based lowpass filter using only grounded capacitors
For the performance evaluation of the proposed PID controller circuit in Fig. 2, a voltage-mode lowpass filter using a single CCTA and four passive elements is realized as shown in Fig. 8.The voltage transfer function of the filter with R p2 = 1/g m is given by where the pole frequency (ω p ) and the quality factor (Q) are derived as: The negative feedback system has been given to evaluate the practical ability of the proposed PID controller circuit.The block diagram of the closed-loop system is represented in Fig. 9.In the study that follows, the step response of the system is analyzed to observe the effect of the proposed controller on this system.For the lowpass filter in Fig. 8, the component values were set as follows: g m = 0.61 mA/V, R p1 = 1 kΩ, R p2 = 1.5 kΩ, and C p1 = C p2 = 1 nF, giving f p = 124.3kHz and Q = 1.28.Fig. 10 shows the ideal and simulated transient responses of e(t) and u(t) for the closed-loop system in Fig. 9 with the ramp input voltage v in (t) rising time of 3 μs/100 mV.The overall power consumption of the closed-loop system in Fig. 9 is estimated to be 108 mW predicated on simulations.In addition to observing the step response of the system, a step input with amplitude of 100 mV was applied, and the obtained results are displayed in Fig. 11.These results are provided to demonstrate the transient response characteristics of the system for four different values of the tuning controller gain parameters.The first set of gain parameters in Fig. 11(a) for case 1 were K P = 1.9,K I = 0.86 Ms, and K D = 1 μs with g m = 0.86 mA/V, R 1 = R 2 = 5 kΩ, and C 1 = C 2 = 1 nF.The second parameters in Fig. 11(b) were modified to K P = 6.9,K I = 1.9 Ms, and K D = 5 μs by selecting g m = 0.38 mA/V, R 1 = 1 kΩ, R 2 = 5 kΩ, and C 1 = C 2 = 1 nF for case 2. The gain parameters in case 3 of Fig. 11(c) were K P = 8, K I = 3 Ms, and K D = 5 μs with g m = 0.61 mA/V, R 1 = 1 kΩ, R 2 = 5 kΩ, and C 1 = C 2 = 1 nF.For case 4, the gains in Fig. 11(d) were K P = 13.6,K I = 8.6 Ms, and K D = 5 μs by setting g m = 0.86 mA/V, R 1 = 1 kΩ, R 2 = 5 kΩ, C 1 = 1 nF, and C 2 = 0.5 nF.

Experimental results
In experimental measurements, the CCTA has been practically constructed with commercially available ICs such as AD844s [26] and CA3080 [27], as depicted in Fig. 12.In this case, the CCTA's transconductance gain (g m ) is proportional to the external bias current (I B ) and has the following relationship: g m = 20I B [27].The symmetrical bias voltages of the AD844s and CA3080 were set at ±5V.Also, for the laboratory testing circuit, the active and passive elements were chosen as g m = 0.86 mA/V (I B = 43 μA), R 1 = R 2 = 5 kΩ, and Proposed PID controller (Fig. 2) Gc(s) Lowpass Filter (Fig. 8 3.As observed in Table 3, the use of the proposed PID controller clearly improves the system's performance in the desired manner. On the other hand, the ideal, simulated and measured frequency-domain responses of the closed-loop system in Fig. 9 for the four mentioned cases of the controller gain values are given in Fig. 15.The experimental results validate the ideal responses within the working range of the proposed PID controller.Nevertheless, the slight deviation in these responses is mostly due which leads to K P = 1.9,K I = 0.86 Ms, and K D = 1 μs as in case 1.A step input voltage with amplitude of 100 mV was applied to the input of the experimental test circuit.Fig. 13 shows the measured input voltage and associated output waveforms for the uncontrolled filter v op (t) and the controlled filter v out (t).
To evaluate the impact of the proposed PID controller on the step response of the closed-loop system in Fig. 9, the measured transient responses for three different controller gains are given in Fig. 14.The experimental test results were obtained using the same component settings as in simulation verification, namely  to the non-ideal characteristics of AD844s and CA3080 in Fig. 12, such as non-ideal transfer gains and parasitic impedances.Some techniques [28]- [29] that reduce non-ideal transfer gains and parasitic elements can be used to minimize the difference between ideal and measured responses.

Conclusions
This paper suggests a novel voltage-mode PID controller based on CCTA.A single CCTA, two resistors, and two capacitors are used in the suggested circuit.Because all of the passive components in this realization are grounded, it is ready for further integration.The implementation does not need element-matching requirements and can be simply accomplished using commercially available integrated circuits.The controller gain parameters K P , K I , and K D are all adjustable.An application example of the proposed PID controller as the closed-loop system is included.The analysis of the theoretically proposed circuit has been validated through simulation findings and experimental test results.

Acknowledgments
This work was supported by Rajamangala University of Technology Rattanakosin (RMUTR).The support by School of Engineering, King Mongkut's Institute of Technology Ladkrabang (KMITL), is also gratefully acknowledged.

Conflict of Interest
The authors confirm that this article content has no conflict of interest.

Figure 1 :
Figure 1: Schematic symbol for the CCTA

Figure 2 :
Figure 2: Proposed single CCTA-based PID controller using all grounded passive elements.
β = 1 -ε v and α = 1 -ε i are the non-ideal gains.The parameters ε v (| ε v | << 1) and ε i (| ε i | << 1) represent the voltage and current tracking errors from the y to the x terminals and from the x to the z and zc terminals, respectively.The non-ideal gain δ = 1 -ε gm , where ε gm (| ε gm | << 1) is the transconductance tracking error between the z and o terminals.

Figure 4 :. 3 Firstly
Figure 4: g m plot for variations in I B for the CMOS CCTA in Fig.3

Figure 9 :
Figure 9: Feedback control system to evaluate the performance of the proposed PID controller.

Figure 10 :
Figure 10: Ramp-input responses of e(t) and u(t) for the closed-loop system in Fig.9.

Table 1 :
Comparative features of the proposed circuit with previously reported PID controllersCircuit

Table 2 :
Aspect ratios of the transistors of CMOS CCTA in Fig.3 P. Mongkolwai et al.; Informacije Midem, Vol.52, No. 3(2022), 169 -179 case 2, case 3, and case 4. From Figs.13 and 14, the performance comparison in terms of delay time (t d ), rise time (t r ), peak time (t p ), peak output (p o ), maximum overshoot (M p ), and settling time (t s ) are also measured and summarized in Table

Table 3 :
Comparison of the performance of the uncontrolled filter and the controlled filter