Skip to content

CFOA-Based Fractional Order PIλDδ Controller

MetadataDetails
Publication Date2017-07-14
JournalElectronics ETF
AuthorsTada Comedang, Pattana Intani
AnalysisFull AI Review Included

Technical Documentation & Analysis: CFOA-Based Fractional Order PID Controller

Section titled “Technical Documentation & Analysis: CFOA-Based Fractional Order PID Controller”

6CCVD Material Scientist Analysis: This research demonstrates the successful implementation of a Fractional-Order Proportional Integral Derivative (FO-PID) controller using a modified Current Feedback Operational Amplifier (CFOA). The core innovation relies on using high-speed “Diamond Transistors” (DT, specifically the OPA 860) to achieve electronic controllability and wide bandwidth (up to 185 MHz). While the paper utilizes commercial silicon-based components, the application—high-frequency analogue signal processing and robust control systems—is perfectly aligned with the superior electronic and thermal properties of MPCVD Diamond. 6CCVD offers the foundational materials necessary to transition this technology from commercial silicon components to ultra-stable, high-power diamond-based integrated circuits.


  • Application Focus: Successful design and experimental verification of a Fractional-Order PID (FO-PID) controller for robust analogue signal processing and control systems.
  • Core Component: A modified Current Feedback Operational Amplifier (CFOA) is used, achieving electronic controllability by integrating high-speed “Diamond Transistors” (DT, OPA 860).
  • Performance Gain: The FO-PID controller significantly outperforms the traditional Integer-Order PID, demonstrating shorter rise time, settling time, and reduced steady-state error (e.g., 269.06 µs settling time vs. 445.43 µs simulated).
  • Methodology: Fractional-order behavior is approximated using a passive domino ladder circuit network (fractance circuit) composed of discrete resistors and capacitors.
  • Frequency Range: The proposed CFOA topology is confirmed to be useful for the frequency range of units and tens of megahertz (MHz), demanding materials with excellent high-frequency characteristics.
  • 6CCVD Value Proposition: MPCVD Diamond (SCD/PCD) offers the ultimate platform for replicating and extending this research, providing superior thermal management, higher breakdown voltage, and unmatched stability required for next-generation high-power, wide-bandwidth analogue circuits.

The following data points were extracted from the simulation and experimental results comparing the Fractional-Order PID (FO-PID) controller against the Integer-Order PID (IO-PID) controller.

ParameterValueUnitContext
CFOA Voltage Transfer Bandwidth184.92MHzY and X ports (Simulation)
CFOA Current Transfer Bandwidth81.09MHzX and Z ports (Simulation)
Supply Voltage (VCC)±5VSymmetrical bias used for CFOA
Input Voltage Linearity (VZ)-4 to 4VHigh linearity DC transfer characteristic
Fractional Order Approximation (α)0.2-Used for domino ladder fractance circuit
Simulated Performance (Unit Step Response)
Max Overshoot (FO-PID)2.24%Lower than IO-PID (2.36 %)
Settling Time (FO-PID)269.06µsFaster than IO-PID (445.43 µs)
Steady-State Error (FO-PID)553.66µsLower than IO-PID (654.49 µs)
Experimental Performance (Closed-Loop)
Max Overshoot (FO-PID)8.11%Lower than IO-PID (12.17 %)
Settling Time (FO-PID)490µsFaster than IO-PID (950 µs)
Steady-State Error (FO-PID)750µsLower than IO-PID (1.25 ms)

The experimental realization of the CFOA-Based Fractional Order PID Controller involved the following steps:

  1. CFOA Modification: The conventional CFOA was modified to achieve electronic controllability by incorporating commercially available high-speed bipolar operational transconductance amplifiers (OTAs) and voltage buffers (OPA 860, referred to as “Diamond Transistors”).
  2. Transconductance Control: The transconductance gain (gm) of the CFOA was electronically adjusted using bias currents (IQ1, IQ2) and adjustable resistors (RL).
  3. Fractional Order Approximation (Fractance): The fractional-order integral and derivative terms (orders λ and δ, approximated at α = 0.2) were realized using a passive domino ladder circuit network.
  4. Component Selection: The fractance circuit utilized specific discrete resistor and capacitor values (e.g., R1=51 Ω, C1=470 pF, R5=820 kΩ, C4=820 pF) to achieve the desired impedance characteristics.
  5. Controller Integration: Three modified CFOAs were combined with the grounded domino ladder fractance network and various resistors (R1-R8) to construct the full analogue FO-PID controller circuit prototype.
  6. System Validation: The controller was tested in a closed-loop system using a 2nd-order Sallen-Key low-pass filter as the plant, and performance metrics were verified against simulation results.

The research highlights the critical need for high-performance, wide-bandwidth components capable of stable operation in complex analogue signal processing environments. While the paper uses commercial silicon-based “Diamond Transistors” (OPA 860), 6CCVD provides the actual MPCVD Diamond materials necessary to push the limits of this technology, offering superior thermal and electronic performance for next-generation FO-PID systems.

Material GradeRecommendationRationale for FO-PID Application
Electronic Grade SCDPrimary RecommendationIdeal for fabricating high-speed, high-power Diamond Transistors (DTs) and FETs. SCD offers the highest thermal conductivity and electron mobility, crucial for maintaining stability and maximizing the bandwidth (185 MHz demonstrated) of the CFOA in high-frequency control loops.
Heavy Boron-Doped Diamond (BDD)Integrated Passive ComponentsBDD allows for the creation of highly stable, integrated resistors and capacitors directly on the diamond substrate. This is essential for realizing the complex, low-drift fractance circuits (domino ladder networks) used to approximate the fractional order, replacing bulky, discrete passive components.
Optical Grade SCD/PCDThermal SubstratesFor high-power analogue systems, diamond substrates (up to 10 mm thick) provide unmatched heat spreading, ensuring the stability of the integrated CFOA and fractance components, minimizing temperature-induced drift in the PID parameters (Kp, Ki, Kd).

Customization Potential for Analogue IC Prototyping

Section titled “Customization Potential for Analogue IC Prototyping”

To transition this FO-PID design from a discrete prototype (as shown in Fig. 19) to a robust, integrated circuit, 6CCVD offers specialized fabrication services:

  • Custom Dimensions: We provide SCD and PCD plates/wafers up to 125 mm in diameter, allowing researchers to scale up complex analogue designs like the three-CFOA FO-PID controller (Fig. 13).
  • Precision Thickness Control: We supply SCD layers from 0.1 µm (for active device fabrication) up to 500 µm, and substrates up to 10 mm thick for optimal thermal management.
  • Advanced Metalization: The integration of active and passive components requires precise contact layers. 6CCVD offers in-house metalization services including Ti/Pt/Au, W, Pd, and Cu, essential for creating low-resistance ohmic contacts and interconnects for high-frequency operation (81 MHz current transfer).
  • Ultra-Low Roughness Polishing: For high-quality device fabrication and lithography, we guarantee surface roughness (Ra) of < 1 nm for SCD and < 5 nm for inch-size PCD, ensuring reliable device performance.

The successful realization of the fractional-order PID controller relies on precise material selection and fabrication tolerances. 6CCVD’s in-house PhD team specializes in the electronic and thermal properties of MPCVD diamond. We can assist researchers in:

  • Optimizing the Boron doping profile for BDD to achieve specific resistance values required for the fractance circuit approximation.
  • Designing the optimal diamond substrate thickness and metalization scheme for high-power, wide-bandwidth analogue signal processing projects.
  • Consulting on the fabrication of high-performance Diamond Transistors (DTs) to replace the commercial silicon OPA 860, thereby maximizing the frequency range and stability of the CFOA.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Conventional Current Feedback Operational Amplifier (CFOA) is not current controllable or not electronically controllable. It is thus of interest to add a current mirror into the CFOA in order to make it current controllable. This modification can be achieved by using Diamond Transistor (DT) instead of going through complicated IC fabrication process. This work applies the modified CFOA in fractional-order proportional integral derivative (PIλDδ) controller. Both simulation and experimental results confirm that the modified CFOA is electronically controllable.