Complex Order Control (CLOC)



Project term


Nima Karbasizadeh Esfahani (PhD), Dr. Niranjan Saikumar (PD)

Dr. Hassan HosseinNia, Prof. dr. ir. Just Herder


 The high-tech industry in The Netherlands is highly competitive and requires machines to run with ever- increasing speed and precision. The need for high speed has resulted in system design favouring mass re- duction of moving parts. This increases their compliance which leads to reduced achievable speed. Further the performance specifications of control have also become extremely demanding. Classical Proportional- Integral-Derivative (PID) control still applied in 95% of the high-tech industry is no longer sufficient to meet these challenges. Its linearity is particularly not suited to handle precision, speed and stability simulta- neously. In spite of great efforts in nonlinear robust control, such as adaptive control and sliding mode control, these techniques remain complex to implement or are highly depending on the application, and are incompatible with industry standards.

The novel control technique developed in CLOC will overcome these limitations by unifying advanced control concepts such that the resulting design is compatible with current industry standards. The key concepts are (i) applying fractional order calculus to overcome limitations of integer-order control, and (ii) selecting reset strategies as primary nonlinear techniques to overcome the limitations of linear controllers. While we recently explored their combination in fractionalizing reset control, CLOC will go beyond this by realizing complex-order integral using reset nonlinearities applied to fractional order approximation techniques. This will result in the first successful practical realization and implementation of complex order controllers that can be directly adopted by the industry.

The novel controller will improve precision and speed, while simultaneously be capable of maintaining high levels of robustness. We will demonstrate the validity and generality of the developed concepts through experimental verification on high-speed positioning stages to assess overall performance. 


  1. AA Dastjerdi, A Astolfi, N Saikumar, N Karbasizadeh, D Valerio, Closed-Loop Frequency Analysis of Reset Control Systems
  2. N Saikumar, K Heinen, SH HosseinNia, Loop-shaping for reset control systems: A higher-order sinusoidal-input describing functions approach, Control Engineering Practice 111, 104808, 2021.
  3. AA Dastjerdi, SH Hosseinnia, A Frequency-Domain Tuning Method for a Class of Reset Control Systems, IEEE Access 9, 40950-40962, 2021.
  4. N Karbasizadeh, N Saikumar, SH HosseinNia, Fractional-order single state reset element, Nonlinear Dynamics, 1-15, 2021.
  5. AA Dastjerdi, A Astolfi, SH HosseinNia, A Frequency-Domain Stability Method for Reset Systems, 59th IEEE Conference on Decision and Control, 2020.
  6. Niranjan Saikumar, Duarte Valerio, S. Hassan HosseinNia, Complex order control for improved loop-shaping in precision positioning, CDC 2019, France.
  7. Duarte Valerio, Niranjan Saikumar, Ali Ahmadi Dastjerdi, Nima Karbasizade, S. Hassan HosseinNia, Reset control approximates complex order transfer functions, Journal of Nonlinear Dynamics, 2019.
  8. N Saikumar, RK Sinha, SH HosseinNia, 'Constant in gain Lead in phase' element- Application in precision motion control, IEEE/ASME Transactions on Mechatronics, 201