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Nature Inspired Optimization for Controller Design
Published in Jitendra R. Raol, Ramakalyan Ayyagari, Control Systems, 2020
Jitendra R. Raol, Ramakalyan Ayyagari
Let us now proceed to describe the fuzzy cascade controller. The commonly known ball and beam system is also referred to as a structure that realizes a task of “balancing a ball on a beam.” The problem is generally linked to real-world control problems, such as horizontally stabilizing an airplane during landing and in turbulent airflow and the balance problem dealing with goods to be carried by a moving robot. There are two degrees of freedom in this system. One is the ball rolling up and down the beam and the other is the beam itself rotating through its connected axis.
Fuzzy adaptive event-triggered output feedback control for nonlinear systems with tracking error constrained and unknown dead-zone
Published in International Journal of Systems Science, 2021
In recent decades, intelligent control has drawn wide attention (Askari et al., 2017; Hu et al., 2020; Hu & Lin, 2020; Li & Tong, 2016; Ma et al., 2017; Zhao et al., 2021). Among them, since the adaptive neural network (NN) and fuzzy backstepping control methods don't need the controlled plant to satisfy the matching condition, therefore, they have become one of the most prevalent control strategies and numerous results have been proposed in (Boulkroune et al., 2018; Li et al., 2011; Sun, Yuan et al., 2018; Tong et al., 2010; Wu, 2018; Xia et al., 2019). For the case of measured states, adaptive fuzzy backstepping control schemes of a class of strict feedback nonlinear systems have been proposed in Sun, Yuan et al. (2018), Xia et al. (2019) and Boulkroune et al. (2018). However, in many practical control systems, the states of the controlled plant are unavailable, such as electromechanical system, multi-agents system and cruise control system, etc. The output feedback fuzzy backstepping control schemes have been extensively studied in Tong et al. (2010), Li et al. (2011) and Wu (2018), and various state observers are established to estimate the unavailable states of the original systems. However, there are some practical engineering control systems with non-strict feedback form, such as the helicopter model (Yoneyama, 2011), the ball-and-beam control system (Joo & Lee, 2005), and nonlinear oscillatory model of chemical process (Wang et al., 2015).
Time-response shaping using output to input saturation transformation
Published in International Journal of Control, 2018
E. Chambon, L. Burlion, P. Apkarian
In this section, the assumptions in Section 3.1 are reviewed in the case of the ball and beam example introduced in Section 2.2. As far as the relative degrees are concerned, k = 2 and l = 2 which fulfils Assumptions 3.2 and 3.7.The disturbance and its bounds are represented on Figure 6. They fulfil Assumption 3.3.Assumption 3.4 is satisfied.The state-feedback controller with integral action proposed in Equation (9) asymptotically stabilises the ball and beam system. Hence, Assumption 3.5 is satisfied.The system is equivalent to a double integrator with no transmission zero: . Assumption 3.6 is fulfilled.
On robust approximate feedback linearisation with an event-triggered controller
Published in International Journal of Systems Science, 2023
Ji-Sun Park, Sang-Young Oh, Ho-Lim Choi
For many years and up to date, control problems for approximate feedback linearised systems have been much studied and there have been numerous related results. In these results, there are often certain assumptions pertaining to the perturbed nonlinearity such as lower-triangular(strict-feedback) and upper-triangular(feedforward) nonlinearity. For example, in Bekiaris-Liberis and Krstic (2010), authors consider a class of nonlinear systems with strict-feedback nonlinearity by predictor feedback control. In Chen et al. (2021), they study the global stabilisation of lower-triangular nonlinear systems with uncertain time-varying parameters, and also in Lan and Li (2018), authors assumed lower-triangular conditions. Meanwhile, in Lin and Li (1999), they propose the control for Ball-and-Beam system well known as feedforward system with state feedback controller. In Chang et al. (2021), Koo et al. (2010), and Zhang et al. (2020), authors assumed upper-triangular conditions. So, these results are specifically targeted to either lower-triangular or upper-triangular nonlinear systems, respectively. Meanwhile, regarding the non-triangular nonlinearity, there are independently developed results (Cai et al., 2017; Oh & Choi, 2021; W. Sun et al., 2021). In Oh and Choi (2021), the control problem of global stabilisation for approximate feedback linearised systems with the non-triangular nonlinearity is considered. In Cai et al. (2017), the adaptive backstepping controller for a class of nonlinear systems with non-triangular structural uncertainties is proposed. In common, the results of Cai et al. (2017), Oh and Choi (2021), and W. Sun et al. (2021) are developed by using the traditional time-triggered control approaches.