LQR, double-PID and pole placement stabilization and tracking control of single link inverted pendulum

Using real interpolation method for adaptive identification of nonlinear inverted pendulum system

“…Using above relation and from the nonlinear Equations (1) and (2) we obtained linearized equations of the proposed system as in (3) and (4). Note that U has been substituted for the input force F. To obtain the transfer functions of the linearized system equations, we must first take the Laplace transform of the system equation assuming zero initial conditions.…”

“…Moreover, inverted pendulum system is widely used in the field of robotics and aerospace field, and so has essential significance both in the field of the theoretical study research and practice [1]- [3]. There are a lot of researchers about most popular types inverted pendulums such as the rotational single arm pendulum, the cart inverted pendulum, and the double inverted investigated the inverted pendulum by switching two different control laws [3], and in [4] LQR, double-PID and pole placement control techniques are used to control a cart inverted pendulum system. Moreover, fractional order PID controllers are proposed in [5] and [6] for control of the inverted pendulum system.…”

Linear quadratic regulator and pole placement for stabilizing a cart inverted pendulum system

“…The nature of this inverted pendulum system makes the researchers make this system the choice of a test or benchmark tool for testing many control techniques since the 1973s to the present [1][2]. The PID control [3][4][5][6], fuzzy genetic algorithm [7][8][9][10], state-space control with pole placement methods [11][12][13], linear quadratic regulator (LQR) [14][15][16], linear quadratic gaussian (LQG) [17][18][19][20], observer [21][22][23], NCTL [24], flower pollination [25], and others have been used in this system.…”

Identificação e controle de sistemas dinâmicos com rede neural paraconsistente.

“…A resposta transitória aprimorada ou a estabilidade de um sistema naturalmente instável, pode ser alcançada pelo posicionamento de polos de malha fechada (pCL) na metade esquerda do plano do complexo s (SARKAR; DEWAN, 2017). Esse tipo de abordagem é chamado de realimentação de estado completo (full state feedback -FSF) ou controlador de posicionamento de polos (pole placement -PP) (SHEHU et al, 2016). A representação em espaço de estados de um sistema é dada pela equação (1).…”

“…Várias estratégias de controle têm sido estudadas com sistemas dinâmicos (AGUILAR-AVELAR; MORENO-VALENZUELA, 2016; HAMZA et al, 2019; PARK; KIM; LEE, 2011). O método de controle por alocação de polos (pole placement -PP), também chamado de retroalimentação de estado completo (full state feedback -FSF), é muito utilizado pois permite uma relação clara entre os parâmetros ajustados e o comportamento do controlador resultante (HALICIOĞLU; ÖKSÜZ, 2018; SARKAR;DEWAN, 2017a;SHEHU et al, 2016). Outra técnica poderosa é chamada de regulador quadrático linear (linear quadratic regulator -LQR), que busca valores ótimos de controlador para uma função de custo mínimo (KUMAR; JEROME, 2013) e que tem sido aplicado com sucesso ao pêndulo invertido (SUBRAMANIAN;ELUMALAI, 2016;HAMZA et al, 2019).…”