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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.
Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
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.
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system can be divided and allocated to different sources of uncertainty in its inputs. This involves estimating sensitivity indices that quantify the influence of an input or group of inputs on the output. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem.
Industrial process control (IPC) or simply process control is a system used in modern manufacturing which uses the principles of control theory and physical industrial control systems to monitor, control and optimize continuous industrial production processes using control algorithms. This ensures that the industrial machines run smoothly and safely in factories and efficiently use energy to transform raw materials into high-quality finished products with reliable consistency while reducing energy waste and economic costs, something which could not be achieved purely by human manual control.
Intelligent control is a class of control techniques that use various artificial intelligence computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, reinforcement learning, evolutionary computation and genetic algorithms.
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.
Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain. For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions. Adaptive control is different from robust control in that it does not need a priori information about the bounds on these uncertain or time-varying parameters; robust control guarantees that if the changes are within given bounds the control law need not be changed, while adaptive control is concerned with control law changing itself.
A microgrid is a local electrical grid with defined electrical boundaries, acting as a single and controllable entity. It is able to operate in grid-connected and off grid. A stand-alone or isolated microgrid only operates off-the-grid and cannot be connected to a wider electric power system. Very small microgrids are called nanogrids.
In control theory, robust control is an approach to controller design that explicitly deals with uncertainty. Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some set. Robust methods aim to achieve robust performance and/or stability in the presence of bounded modelling errors.
In control theory, advanced process control (APC) refers to a broad range of techniques and technologies implemented within industrial process control systems. Advanced process controls are usually deployed optionally and in addition to basic process controls. Basic process controls are designed and built with the process itself, to facilitate basic operation, control and automation requirements. Advanced process controls are typically added subsequently, often over the course of many years, to address particular performance or economic improvement opportunities in the process.
Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the input using feedback, feedforward, or signal filtering. The system to be controlled is called the "plant". One way to make the output of a system follow a desired reference signal is to compare the output of the plant to the desired output, and provide feedback to the plant to modify the output to bring it closer to the desired output.
In control theory a self-tuning system is capable of optimizing its own internal running parameters in order to maximize or minimize the fulfilment of an objective function; typically the maximization of efficiency or error minimization.
In recent years, the use of biologically inspired methods such as the evolutionary algorithm have been increasingly employed to solve and analyze complex computational problems. BELBIC is one such controller which is proposed by Caro Lucas, Danial Shahmirzadi and Nima Sheikholeslami and adopts the network model developed by Moren and Balkenius to mimic those parts of the brain which are known to produce emotion.
Miroslav Krstić is an American control theorist and Distinguished Professor of Mechanical and Aerospace Engineering at the University of California, San Diego (UCSD). Krstić is also the director of the Center for Control Systems and Dynamics at UCSD and a Senior Associate Vice Chancellor for Research. In the list of eminent researchers in systems and control, he is the youngest.
Linear parameter-varying control deals with the control of linear parameter-varying systems, a class of nonlinear systems which can be modelled as parametrized linear systems whose parameters change with their state.
System identification is a method of identifying or measuring the mathematical model of a system from measurements of the system inputs and outputs. The applications of system identification include any system where the inputs and outputs can be measured and include industrial processes, control systems, economic data, biology and the life sciences, medicine, social systems and many more.
Machine learning control (MLC) is a subfield of machine learning, intelligent control, and control theory which aims to solve optimal control problems with machine learning methods. Key applications are complex nonlinear systems for which linear control theory methods are not applicable.
Frank L. Lewis is an American electrical engineer, academic and researcher. He is a professor of electrical engineering, Moncrief-O’Donnell Endowed Chair, and head of Advanced Controls and Sensors Group at The University of Texas at Arlington (UTA). He is a member of UTA Academy of Distinguished Teachers and a charter member of UTA Academy of Distinguished Scholars.
Chance Constrained Programming (CCP) is a mathematical optimization approach used to handle problems under uncertainty. It was first introduced by Charnes and Cooper in 1959 and further developed by Miller and Wagner in 1965. CCP is widely used in various fields, including finance, engineering, and operations research, to optimize decision-making processes where certain constraints need to be satisfied with a specified probability.
References
- ↑ "Survey of Gain-Scheduling Analysis & Design" (PDF). Retrieved 1 November 2012.
- ↑ Hosseini, Ehsan; Aghadavoodi, Ehsan; Fernández Ramírez, Luis M. (September 2020). "Improving response of wind turbines by pitch angle controller based on gain-scheduled recurrent ANFIS type 2 with passive reinforcement learning". Renewable Energy. 157: 897–910. Bibcode:2020REne..157..897H. doi:10.1016/j.renene.2020.05.060.
- ↑ Yeh, Yi-Liang; Yang, Po-Kai (2021-11-26). "Design and Comparison of Reinforcement-Learning-Based Time-Varying PID Controllers with Gain-Scheduled Actions". Machines. 9 (12): 319. doi: 10.3390/machines9120319 . ISSN 2075-1702.
- ↑ Gutiérrez-Oribio, Diego; Stathas, Alexandros; Stefanou, Ioannis (2024-12-17). "AI-Driven Approach for Sustainable Extraction of Earth's Subsurface Renewable Energy While Minimizing Seismic Activity". International Journal for Numerical and Analytical Methods in Geomechanics. doi:10.1002/nag.3923. ISSN 0363-9061.