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Design Methods
Published in William S. Levine, The Control Handbook: Control System Fundamentals, 2017
R.H. Middleton, Stefan F. Graebe, Anders Ahlén, Jeff S. Shamma
Conceptually, gain scheduling allows for greater operating regions than a design based on a single equilibrium. However, since the scheduling variable is no longer constant, the gain schedule introduces time variations in the overall control system. Such time variations typically are not addressed in the original frozen-equilibrium design. One consequence is possible degradation in performance or even instability of the gain-scheduled system. Another consequence is that the state of the nonlinear system while in transition need not be close to any of the equilibrium points, and hence outside of the design regions of the linearized controllers. However, the effects of these phenomena are reduced in the case of slow transitions among the operating conditions. In the end, the quality of a gain-scheduled design is typically inferred from extensive computer simulations.
Introduction
Published in Guoliang Wei, Zidong Wang, Wei Qian, Nonlinear Stochastic Control and Filtering with Engineering-Oriented Complexities, 2016
Guoliang Wei, Zidong Wang, Wei Qian
On the other hand, for the purpose of designing a controller/filter with less conservatism for LPVSs, it’s natural to construct the novel Lyapunov functions with scheduling parameters, which are usually called the parameter-dependent Lyapunov functions. Very recently, the parameter-dependent Lyapunov function approach has been applied to deal with the gain-scheduled control/filtering problems, and some results have been reported in the literature [5, 153, 171, 229]. It should be noticed that, in order to design an appropriate controller/filter for LPVSs, the gain-scheduling approach has been proved to be an effective one in this process. The idea of the gain-scheduling approach is to design controller/filter gains as functions of the scheduling parameters, which are supposed to be available in real time and can be utilized to adjust the controller/filter with hope to get the better performance. Therefore, the gain-scheduling control and filtering problems for LPVSs have stirred a great deal of interest in these years; see, e.g. [153, 171, 229]. In addition, several successful applications of the gain-scheduling approach for LPVSs have been discussed in the survey paper [136].
Multi-Objective Particle Swarm Optimization Fuzzy Gain Scheduling Control
Published in Nadia Nedjah, Luiza De Macedo Mourelle, Heitor Silverio Lopes, Evolutionary Multi-Objective System Design, 2020
Edson B. M. Costa, Ginalber L. O. Serra
The pioneer research in gain scheduling control occurred in the early 1950s motivated mainly by the design of autopilots for high-performance aircraft. The main complexities in such projects are the wide range of speeds and altitudes that the aircraft operates, nonlinear dynamics, and time varying characteristics. In general, gain scheduling is a nonlinear control approach that uses a set of linear controllers for various operating conditions of the system. In this approach, one or more measurable variables, called scheduling variables, are used to determine what operating condition the system is currently in and to enable the appropriate linear controller.
Design of gain schedule fractional PID control for nonlinear thrust vector control missile with uncertainty
Published in Automatika, 2018
Mohamed Fawzy Ahmed, Hassen Taher Dorrah
In many situations, the dynamics of plants are varied with the operating conditions of the process. It is possible to vary the parameters of the controller by seeing the operating conditions of the process. This technique is called gain scheduling. Gain scheduling is simple to process in computer controlled systems. Gain scheduling depends on measurements of procedures of the process and it is the best way to compensate for varying process parameters or unknown nonlinearities. If the familiar definition of the adaptive controller is utilized, Gain schedule is a very helpful procedure for decreasing the effects of parameter variations. There are several commercial process control systems that utilize gain schedule to compensate for dynamic and static nonlinearities. It is possible to decrease the effects of parameter variations by varying the parameters of the controller as functions of the additional variables.
Self-tuning state-feedback control of a rotary pendulum system using adjustable degree-of-stability design
Published in Automatika, 2021
Omer Saleem, Mohsin Rizwan, Khalid Mahmood-ul-Hasan
The self-tuning adaptive controllers provide a pragmatic approach to strengthen the closed-loop system's immunity against bounded exogenous disturbances, under every operating condition, by dynamically reconfiguring the controller's behaviour [14,15]. They adopt well-postulated state-driven analytical (or logical) rules to automatically modify the controller's operational parameters which renders a robust control yield [16]. A plethora of adaptive state-feedback control schemes for multivariable under-actuated systems has been proposed in the literature [17]. The model-reference adaptive systems track the output of a reference model to reconfigure the behaviour of the operational controller [18]. However, identifying the adaptation-rates for the Lyapunov gain-adjustment law is a cumbersome task [19]. The gain-scheduling technique dynamically modifies the controller-parameters by commuting between a predefined set of distinct linear controllers, each designed to address a specific operating condition, which is usually selected via a state-error dependent look-up table(s) [20]. Postulating distinct linear controllers and guaranteeing their asymptotic-stability, for every operating condition, is a laborious task that often leads to the degradation of control quality [21]. The State-Dependent-Riccati-Equation based control schemes offer to generate robust effort to regulate the performance of inherently unstable and nonlinear systems [22]. However, the accurate definition of state-dependent-coefficient matrices to fully realize the nonlinear characteristics of the system is difficult due to the system's complex dynamics [23].
Improving the nonlinear control performance of the supply fan at air handling units using a gain scheduling control strategy
Published in Science and Technology for the Built Environment, 2022
Zufen Wang, Rodney Hurt, Li Song, Gang Wang
The designed gain scheduling controller can effectively compensate for the system gain variation and approximately maintain the identical control behaviors under variable operation conditions. By applying the gain scheduling controller, the oscillation range under the same operation condition can be reduced by up to 74% for the duct static pressure and by up to 81% for the fan speed. In addition, the RMSE of the duct static pressure can also be reduced by 24 Pa (0.043 inch of water).