A cart inverted pendulum is an under actuated system that highly unstable and nonlinear. Therefore, it makes a good problem example which attracts control engineers to validate the developed control algorithms. In this paper, an augmented PID control algorithm is proposed to stabilise a cart inverted pendulum at the desired state. The derivation of a mathematical model of the cart inverted pendulum using Lagrange's equation is discussed in detail. The system dynamics is illustrated to understand better the behaviour of the system. A simulation program has been developed to verify the performance of the proposed control algorithm. The system dynamic behaviours with respect to the variation of the controller parameters are analysed and discussed. Controllers parameters are expressed into two PID gain sets which associated with 2 dynamic states: the cart position (ϰ) and the pendulum angle (θ). It can be concluded from the simulation result that the proposed control algorithm can perform well where acceptable steady errors can be achieved. The best response from the cart inverted pendulum system has been obtained with the value of kPX 190, kDX 50, kIX 5, kPθ 140, kDθ 5, and kIθ 25.
A Cart Inverted Pendulum System is an unstable, nonlinear and underactuated system. This makes a cart inverted pendulum system used as a benchmark for testing many control method. A cart must occupy the desired position and the angle of the pendulum must be in an equilibrium point. System modeling of a cart inverted pendulum is important for controlling this system, but modeling using assumptions from state-feedback control is not completely valid. To minimize unmeasured state variables, state estimators need to be designed. In this paper, the state estimator is designed to complete the state-feedback control to control the cart inverted pendulum system. The mathematical model of the cart inverted pendulum system is obtained by using the Lagrange equation which is then changed in the state space form. Mathematical models of motors and mechanical transmissions are also included in the cart inverted pendulum system modeling so that it can reduce errors in a real-time application. The state gain control parameter is obtained by selecting the weighting matrix in the Linear Quadratic Regulator (LQR) method, then added with the Leuenberger observer gain that obtained by the pole placement method on the state estimator. Simulation is done to determine the system performance. The simulation results show that the proposed method can stabilize the cart inverted pendulum system on the cart position and the desired pendulum angle.
The condition of community-managed forest areas varies according to biophysics characteristics and management activities. This study aims to investigate the condition of vegetation and soil carbon stocks of various types of forest management by the community in Karang Sidemen Village, Lombok, Indonesia. In the study area, it was found 4 types of landuse management, namely; dense forest-like vegetation (Tp1), moderate vegetation with intensive (Tp2) and less intensive (Tp3) under-stand cultivation, and sparse vegetation resembling dryland agriculture (Tp4). Vegetation condition was analyzed based on satellite derived NDVI index and field observation. Sentinel satellite images for 2015 and 2019, with a resolution of 10x10 m was used. Field data collection was carried out in August 2019. It was made 5 sample plots of 20x20 m for each management type. Vegetation data with diameter (D) ≥ 20 cm, 10 cm ≤D< 20 cm, 2 cm ≤D< 10 cm and D< 2 cm were collected from plots of 20x20 m, subplots 10x10 m, 5x5 m and 2x2 m, respectively. Soil samples were taken diagonally on a 20x20 m plot, at a depth of 0-5 cm, 5-10 cm, 10-20 cm and 20-30 cm. The results showed that the NDVI derived vegetation index for 2015 and 2019 images showed different patterns for the four types of management. The number of species for Tp1, Tp2, Tp3 and Tp4 were 9, 15, 9 and 8 species, respectively. The dominant species are generally from groups of plants providing economic benefits such as avocado (Persea americana), candlenut (Aleurites moluccana), cocoa (Theobroma cacao), coffee (Coffea canephora), jackfruit (Artocarpus heterophyllus), mangosteen (Garcinia mangostana) and guava (Psidium guajava). Soil carbon stocks of the four types of management at a depth of 0-5 cm, 5-10 cm, 10-20 cm and 20-30 cm were18.61-21.04 tons C/ha, 16.56-20.80 tons C/ha, 29.66-34.48 tons C/ha and 27.54 - 33.66 tons C/ha, respectively. The soil carbon stock of denser vegetation is higher than that of medium and sparse vegetation. Therefore, forest management with the community needs to maintain forest-like vegetation.
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