Active disturbance rejection control

Last updated

Active disturbance rejection control (or ADRC, also known as automatic disturbance rejection control [1] ) is a model-free control technique used for designing controllers for systems with unknown dynamics and external disturbances. [2] This approach only necessitates an estimated representation of the system's behavior to design controllers that effectively counteract disturbances without causing any overshooting.

Contents

ADRC has been successfully used as an alternative to PID control in many applications, such as the control of permanent magnet synchronous motors, [3] thermal power plants [4] and robotics. [5] In particular, the precise control of brushless motors for joint motion is vital in high-speed industrial robot applications. However, flexible robot structures can introduce unwanted vibrations, challenging PID controllers. ADRC offers a solution by real-time disturbance estimation and compensation, without needing a detailed model. [6]

Disturbance rejection

To achieve robustness, ADRC is based on extension of the system model with an additional and fictitious state variable representing everything that the user does not include in the mathematical description of the base system to be controlled. This virtual state (sum of unknown part of model dynamics and external disturbances, usually denoted as a "total disturbance" [2] or "generalized disturbance" [7] ) is estimated online with an extended state observer and used in the control signal in order to decouple the system from the actual perturbation acting on the plant. This disturbance rejection feature allows users to treat the considered system with a simpler model insofar as the negative effects of modeling uncertainty are compensated in real time. As a result, the operator does not need a precise analytical description of the base system; one can model the unknown parts of the dynamics as internal disturbances in the base system.

Control architecture

The ADRC consists of three main components: a tracking differentiator, a non-linear state error feedback and an extended state observer. [2] [8] The global convergence of ADRC has been proved for a class of general multiple-input multiple-output systems. [9] [10]

The following architecture is known as the output-form structure of ADRC:

Architecture of Active Disturbance Rejection Control.svg

There also exists a special form of ADRC, known as error-form structure, which is used for comparing the ADRC with classical controllers such as PID. [11]

Tracking differentiator

The primary objective of the tracking differentiator is to follow the transient profile of the reference signal, addressing the issue of sudden changes in the set point that occur in the conventional PID controller. [2] Moreover, the tracking differentiator also mitigates the possible noise amplification that affects the derivative term of the PID controller by using numerical integration instead of numerical differentiation. [8]

Extended state observer

An extended state observer (ESO) keeps track of the system's states as well as external disturbances and unknown model's perturbations. As a result, ADRC does not rely on any particular mathematical model of disturbance. Nonlinear ESO (NESO) is a subtype of general ESO that uses a nonlinear discontinuous function of the output estimate error. NESO are comparable to sliding mode observers in that both use a nonlinear function of output estimation error (rather than a linear function as in linear, high gain, and extended observers). A sliding mode observer's discontinuity is at the origin, but the NESO's discontinuity is at a preset error threshold.

Nonlinear state error feedback

The intuitiveness of PID control can be attributed to the simplicity of its error feedback. ADRC extends the PID by employing a nonlinear state error feedback, and because of this, seminal works referred to ADRC as nonlinear PID. [12] Weighted state errors can also be used as feedback in a linearization system.

Related Research Articles

<span class="mw-page-title-main">Control engineering</span> Engineering discipline that deals with control systems

Control engineering or control systems engineering is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlaps and is usually taught along with electrical engineering and mechanical engineering at many institutions around the world.

Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality.

A proportional–integral–derivative controller is a control loop mechanism employing feedback that is widely used in industrial control systems and a variety of other applications requiring continuously modulated control. A PID controller continuously calculates an error value as the difference between a desired setpoint (SP) and a measured process variable (PV) and applies a correction based on proportional, integral, and derivative terms, hence the name.

<span class="mw-page-title-main">System identification</span> Statistical methods to build mathematical models of dynamical systems from measured data

The field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimal design of experiments for efficiently generating informative data for fitting such models as well as model reduction. A common approach is to start from measurements of the behavior of the system and the external influences and try to determine a mathematical relation between them without going into many details of what is actually happening inside the system; this approach is called black box system identification.

<span class="mw-page-title-main">Closed-loop controller</span> Feedback controller

A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller. A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs have an effect on the process outputs, which is measured with sensors and processed by the controller; the result is "fed back" as input to the process, closing the loop.

An industrial process control or simply process control in continuous production processes is a discipline that uses industrial control systems and control theory to achieve a production level of consistency, economy and safety which could not be achieved purely by human manual control. It is implemented widely in industries such as automotive, mining, dredging, oil refining, pulp and paper manufacturing, chemical processing and power generating plants.

Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The main advantage of MPC is the fact that it allows the current timeslot to be optimized, while keeping future timeslots in account. This is achieved by optimizing a finite time-horizon, but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from a linear–quadratic regulator (LQR). Also MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability. MPC is nearly universally implemented as a digital control, although there is research into achieving faster response times with specially designed analog circuitry.

In control theory, a separation principle, more formally known as a principle of separation of estimation and control, states that under some assumptions the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the state of the system, which feeds into an optimal deterministic controller for the system. Thus the problem can be broken into two separate parts, which facilitates the design.

<span class="mw-page-title-main">Static synchronous compensator</span> Power distribution technology

A static synchronous compensator (STATCOM), is a shunt-connected, reactive compensation device used on transmission networks. It uses power electronics to form a voltage-source converter that can act as either a source or sink of reactive AC power to an electricity network. It is a member of the FACTS family of devices.

Neurorobotics is the combined study of neuroscience, robotics, and artificial intelligence. It is the science and technology of embodied autonomous neural systems. Neural systems include brain-inspired algorithms, computational models of biological neural networks and actual biological systems. Such neural systems can be embodied in machines with mechanic or any other forms of physical actuation. This includes robots, prosthetic or wearable systems but also, at smaller scale, micro-machines and, at the larger scales, furniture and infrastructures.

<span class="mw-page-title-main">Excitation (magnetic)</span> Generation of a magnetic field by an electric current

In electromagnetism, excitation is the process of generating a magnetic field by means of an electric current.

A networked control system (NCS) is a control system wherein the control loops are closed through a communication network. The defining feature of an NCS is that control and feedback signals are exchanged among the system's components in the form of information packages through a network.

<span class="mw-page-title-main">Wassim Michael Haddad</span>

Wassim Michael Haddad is a Lebanese-Greek-American applied mathematician, scientist, and engineer, with research specialization in the areas of dynamical systems and control. His research has led to fundamental breakthroughs in applied mathematics, thermodynamics, stability theory, robust control, dynamical system theory, and neuroscience. Professor Haddad is a member of the faculty of the School of Aerospace Engineering at Georgia Institute of Technology, where he holds the rank of Professor and Chair of the Flight Mechanics and Control Discipline. Dr. Haddad is a member of the Academy of Nonlinear SciencesArchived 2016-03-04 at the Wayback Machine for recognition of paramount contributions to the fields of nonlinear stability theory, nonlinear dynamical systems, and nonlinear control and an IEEE Fellow for contributions to robust, nonlinear, and hybrid control systems.

EFOSMO is an abbreviation for encoderless full observer order mode of sliding. It is used to estimate the not measurable variables in drive implement the encoderless control method.

Classical control theory is a branch of control theory that deals with the behavior of dynamical systems with inputs, and how their behavior is modified by feedback, using the Laplace transform as a basic tool to model such systems.

<span class="mw-page-title-main">Synchronverter</span> Type of electrical power inverter

Synchronverters or virtual synchronous generators are inverters which mimic synchronous generators (SG) to provide "synthetic inertia" for ancillary services in electric power systems. Inertia is a property of standard synchronous generators associated with the rotating physical mass of the system spinning at a frequency proportional to the electricity being generated. Inertia has implications towards grid stability as work is required to alter the kinetic energy of the spinning physical mass and therefore opposes changes in grid frequency. Inverter-based generation inherently lacks this property as the waveform is being created artificially via power electronics.

In mathematics, zero dynamics is known as the concept of evaluating the effect of zero on systems.

Linear-quadratic regulator rapidly exploring random tree (LQR-RRT) is a sampling based algorithm for kinodynamic planning. A solver is producing random actions which are forming a funnel in the state space. The generated tree is the action sequence which fulfills the cost function. The restriction is, that a prediction model, based on differential equations, is available to simulate a physical system. The method is an extension of the rapidly exploring random tree, a widely used approach to motion planning.

Hassan K. Khalil is an Egyptian-born American electrical engineer. He was named Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 1989 for contributions to singular perturbation theory and its application to control.

<span class="mw-page-title-main">Saverio Mascolo</span> Italian information engineer

Saverio Mascolo is an Italian information engineer, academic and researcher. He is the former Head of the Department of Electrical Engineering and Information Science and the professor of Automatic Control at Department of Ingegneria Elettrica e dell'Informazione (DEI) at Politecnico di Bari, Italy.

References

  1. ↑ Su, Yu Xin; Zheng, Chun Hong; Duan, Bao Yan (2005-05-31). "Automatic disturbances rejection controller for precise motion control of permanent-magnet synchronous motors". IEEE Transactions on Industrial Electronics. IEEE. 52 (3): 814–823. doi:10.1109/TIE.2005.847583.
  2. 1 2 3 4 Han, Jingqing (2009). "From PID to Active Disturbance Rejection Control". IEEE Transactions on Industrial Electronics. 56 (3): 900–906. doi:10.1109/TIE.2008.2011621. ISSN   1557-9948. S2CID   206698917.
  3. ↑ Sira-Ramirez, Hebertt; Linares-Flores, Jesus; Garcia-Rodriguez, Carlos; Contreras-Ordaz, Marco Antonio (2014). "On the Control of the Permanent Magnet Synchronous Motor: An Active Disturbance Rejection Control Approach". IEEE Transactions on Control Systems Technology. 22 (5): 2056–2063. doi:10.1109/TCST.2014.2298238. ISSN   1063-6536. S2CID   1000762.
  4. ↑ Wu, Zhenlong; Gao, Zhiqiang; Li, Donghai; Chen, YangQuan; Liu, Yanhong (2021). "On transitioning from PID to ADRC in thermal power plants". Control Theory and Technology. 19 (1): 3–18. doi:10.1007/s11768-021-00032-4. ISSN   2095-6983. S2CID   233709932.
  5. ↑ Fareh, Raouf; Khadraoui, Sofiane; Abdallah, Mahmoud Y.; Baziyad, Mohammed; Bettayeb, Maamar (2021). "Active disturbance rejection control for robotic systems: A review". Mechatronics. 80: 102671. doi:10.1016/j.mechatronics.2021.102671. S2CID   244183528.
  6. ↑ "Beyond PID: Exploring Alternative Control Strategies for Field-Oriented Controllers". www.mathworks.com. Retrieved 2023-08-19.
  7. ↑ Herbst, Gernot (2015). "Practical active disturbance rejection control: Bumpless transfer, rate limitation, and incremental algorithm". IEEE Transactions on Industrial Electronics. IEEE. 63 (3): 1754–1762.
  8. 1 2 Dong Sun (2007). "Comments on Active Disturbance Rejection Control". IEEE Transactions on Industrial Electronics. 54 (6): 3428–3429. doi:10.1109/TIE.2007.909047. ISSN   0278-0046.
  9. ↑ Guo, Bao-Zhu; Zhao, Zhi-Liang (2011). "On convergence of tracking differentiator". International Journal of Control. 84 (4): 693–701. Bibcode:2011IJC....84..693G. doi:10.1080/00207179.2011.569954. ISSN   0020-7179. S2CID   31030254.
  10. ↑ Guo, Bao-Zhu; Zhao, Zhi-Liang (2013). "On Convergence of the Nonlinear Active Disturbance Rejection Control for MIMO Systems". SIAM Journal on Control and Optimization. 51 (2): 1727–1757. doi:10.1137/110856824. ISSN   0363-0129. S2CID   5740371.
  11. ↑ Madonski, Rafal; Herbst, Gernot; Stankovic, Momir (2023). "ADRC in output and error form: connection, equivalence, performance". Control Theory and Technology. 21 (1): 56–71. arXiv: 2211.07427 . doi:10.1007/s11768-023-00129-y. ISSN   2095-6983. S2CID   253510300.
  12. ↑ Han, J. (1994). "Nonlinear PID controller". Acta Automatica Sinica. 20 (4): 487–490.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.