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Dynamic modelling of a projectile launcher with controlled double inverted pendulum
Published in Alka Mahajan, Parul Patel, Priyanka Sharma, Technologies for Sustainable Development, 2020
P.S. Savnani, M.M. Chauhan*, A.I. Mecwan, R.N. Patel
The mechanism is assumed to be a controlled double inverted pendulum (Zhong & Rock, 2001) as shown in Figure 1 and the mathematical model is generated on this hypothesis. A double inverted pendulum is a system having two pendulums attached end to end with each other and it exhibits periodic, quasi-periodic and chaotic behaviour (Rafat, Wheatland, & Bedding, 2009). Here, the first pendulum is a continuous mass system while the second pendulum is a lumped mass system. Double pendulum’s motion is highly dynamic and nonlinear in nature (Ohlhoff & Richter, 2000), therefore its trajectory is difficult to predict. Here, Euler-Lagrange Equations (Morin, 2007) (Widnall, 2009) are used to derive the mathematical model of the dynamic system.
Sliding Mode Control of Pendulum Systems
Published in Vadim Utkin, Jürgen Guldner, Jingxin Shi, Sliding Mode Control in Electro-Mechanical Systems, 2017
Vadim Utkin, Jürgen Guldner, Jingxin Shi
As addressed by Widjaja [1994], the inverted pendulum system includes several control problems: swing-up, balancing, and both swing-up and balancing. In this section, we will concentrate on a sliding mode controller for balancing the pendulum. The swing-up algorithm in the experiments will be directly taken from the work by Widjaja [1994]. First, we will try to stabilize the system such that the pendulum is in the unstable vertical position θ1 = 0 and allow the base to be at an arbitrary fixed position. Then, the design method will be generalized to drive both the pendulum and the rotating base to the equilibrium point θ1 = θ0 = 0 and maintain it there.
Reasoning and Control of Qualitative Knowledge
Published in Deyi Li, Yi Du, Artificial Intelligence with Uncertainty, 2017
In the development of automatic control theory and technology, the correctness of a certain theory is usually verified through the control of an object by a controller designed according to this theory. The inverted pendulum is one that has had perpetual popularity, and it can be studied with several control theories and methods, such as PID (proportional-integral-derivative) control, adaptive control, state feedback control, neural network control, fuzzy control, and so on. When a brand new control method is announced that cannot be proven on a theoretical level, its correctness and physical applicability can be verified with the inverted pendulum.
Optimal robust tracking by state feedback: infinite horizon
Published in International Journal of Control, 2022
The model of an inverted pendulum is encountered in many control engineering applications, including missile control systems, dynamic stabilisation systems of civil engineering structures, walking robots, personal transport vehicles, and others. We consider the control of the following inverted pendulum (Bian et al., 2014): Here, , and are constant parameters; their nominal values are , , , and they are subject to uncertainty ranges of about , so that , , and . The input amplitude bound of Σ is K = 1, and the state amplitude bound of Σ is A = 0.5. The initial state can be any member of , i.e. .
Control of rotary double inverted pendulum system using LQR sliding surface based sliding mode controller
Published in Journal of Control and Decision, 2022
Sondarangallage D.A. Sanjeewa, Manukid Parnichkun
Underactuated systems have attracted a lot of interest from researchers in the control engineering field because of the challenges of controlling these systems. Some examples of the underactuated system can be found in robotics systems, for example, flying robots, aerospace vehicles, etc. Inverted Pendulum system is a well-known underactuated system that has less number of actuators than the control parameters. Balancing control of the inverted pendulum system is considered one of the challenging research topics in control engineering due to its nonlinearity and instability. It is a benchmark apparatus that can be used to evaluate the performance of diverse controllers. Several types of inverted pendulum systems can be seen in the literature. The inverted pendulum systems can be classified into two groups, that is, moving-cart type and rotary type. Chih-Chen Yih (2013) proposed only one sliding mode control scheme to swing up and stabilize a single inverted pendulum on a moving cart. Sukontanakarn and Parnichkun (2009) have applied an energy-based algorithm to swing up and LQR to balance a rotary single inverted pendulum. In order to increase the complexity of the inverted pendulum system, double inverted pendulum systems which consist of two serially or parallel connected pendulums have been introduced and developed. Serial type double inverted pendulum systems have been developed by Delibasi et al. (2007) and Graichen et al. (2007) and applied feed-forward and feedback control and a robust PID like state-feedback control via LMI approach controller respectively. A parallel type double inverted pendulum system has been implemented by Deng et al. (2008). A weighted energy-based controller and a pole assignment control scheme were proposed by them for swing up process and cart position control, respectively.
Relative Stability Analysis of Perturbed Cart Inverted Pendulum: An Experimental Approach
Published in IETE Technical Review, 2018
Sandeep Hanwate, Yogesh V. Hote
Recently in [8], it is shown that classical PID controller can be designed for inverted pendulum system using linear quadratic regulator (LQR) approach. This work has also referred by various authors [9–11]. Although authors of [8] have been studied robustness by calculating gain margin, phase margin, delay margin, and sensitivity. However, in [8] parameter variations have not been considered. This is important in real-time applications. The variation in cart mass is an important element in CIPS. For example, in guided missile system, the mass of the system changes due to the consumption of fuel. It may be possible that the controller which stabilizes the inverted pendulum for some specific cart mass but may be unstable if some additional load is applied. Furthermore, variation of length of the pendulum and force applied are also important. Therefore, in this paper, mathematical conditions have been developed for LQR-based PID controller and stability boundary locus (SBL) based PID controller for stabilization of CIPS. This approach is based on well-known Krishnamurthi's corollary [12] on Routh stability criterion [1]. The proposed condition gives the information about the additional load (mass) either minimum or maximum which can bear by the CIPS. The proposed condition has been verified in simulation and also in real-time environment. It is shown that SBL-based PID controller can be helpful in carrying more additional cart mass in comparison to LQR-based PID controller. Furthermore, the effectiveness of both the controllers in the presence of increase in pendulum length and applied force is carried out. Here, effect of increase in pendulum length is shown in hardware and increase of applied force is shown in simulation. Finally, practical issues have been discussed by comparing simulation and real-time results on a hardware set-up.