Inverted Pendulum Control - Report Example

Table of Contents Table of Contents 1 Control of an Inverted Pendulum 2 Introduction 2 Theory 2 Lab VIEW schematics & Procedure 4 Results and Discussion 6 Conclusion 9 References 10 Table of Figur Figure 1: 2-D version of the inverted pendulum 3 Figure 2: Frontal Panel 4 Figure 3: Swing-Up control showing the pendulum angle/energy 5 Figure 4: Successfully inverted Pendulum 6 Figure 5: Resulting angle/energy and voltage vs time graphs 7 Figure 6: Block Diagram 8 Control of an Inverted Pendulum Introduction This report outlines how to build a model size inverted pendulum. It is a classical control system problem that requires simulation and modelling. Simulation in this case would help to develop numerical solutions and mathematically represents the control system for the inverted pendulum. Closed form solutions to the problem can then be generated, and help to ascertain the authenticity of a linear version of the model. The main objective of the exercise was to develop a control system that can be used to balance an inverted pendulum. A cost effective means of conducting the test was to use a software that was designed economically and used in tandem with the mechanical and hardware systems. The results of the exercise should be system that has the ability to balance an inverted pendulum which in itself is an inherently unstable system. The ability of the control system to stabilize an unstable system is a measure of its success and for this case it was. LabVIEW software was used to analyse the system and it proved a convenient way of simulating the system. Theory The entire experiment is based on a premise of developing stability loops with the ability to stabilize unsteady state values. The pendulum problem can be solved using several methods, all of which need to be checked for efficiency before determining whether or not to use them. For this case, a 2-D model of an inverted pendulum with a DC motor got considered. The pendulum was constrained so as to only move about the y-axis as show in figure 1 below. The control input for the system is the external force, and has the ability to move the pendulum cart horizontally. The outputs for the system is the angular position of the pendulum, and the position of the pendulum cart in the horizontal plane. Essentially, the inverted pendulum problem is an intriguing system to those studying control systems since it offers a means to understand system control using simulation loops. It is added to the control process as it increases the accuracy of the results obtained during the process. In a simulation loop, the process is repeated until the simulation final time is reached or the process is stopped by a halt command. It is relevant in this case since the pendulum is a continuous process aimed at achieving stability. Figure 1: 2-D version of the inverted pendulum By selecting the block diagram and scrolling to the right parameters on the functions palette, the simulation loop can be added to the system. The pendulum experiment is planned to operate in an up-swing mode with the below 250, i.e. at a value between 20 and 250, the generator motor does not receive any form of power. The balancing process is initiated whenever the angle is below 200. System parameters such as the type of signal, frequency, reaction offset and amplitude, are recorded using the signal generator. It is therefore important to note that when the when stability is achieved, the system response is recorded in the re-arm angle and output of energy is recorded in the blue pendulum angle of the LabVIEW panel. Lab VIEW schematics & Procedure The process was commenced by launching the LabVIEW software on the computer system. With each VI having 2 windows, i.e. the Frontal Panel that includes indicators and controls. The input section is represented by the controls while the output was represented by the indicators. The Frontal Panel (Fig. 2) contains a control palette and input-output, controls in this case refer to virtual buttons, knobs and appliances (Quintero, 2014). A block diagram was developed in the input controls such that the entered graphical code, allows the data to travel from the input controls via functions and to the indicators. The block diagram (Fig. 6) execute the data and outputs the graphs as shown below. LabVIEW provides outputs in the form of graphs, tables and optimal design data that can be used to design system controllers. Figure 2: Frontal Panel Figure 3: Swing-Up control showing the pendulum angle/energy The successful control of the inverted pendulum was the sole aim of the experiment. Undertaking the process as described above activated the motors that enable effective balancing of the pendulum for a specific time. (Kleinigger & Craig, 2007). The energy of the pendulum was contained in the swing-up practice, the swing-up performance on the other hand determined the required number of swings to attain a balanced status. (Kleinigger & Craig, 2007). The motor is pushed by an amplifier controlled by the input variables when restrained. The stability of the pendulum link is run by the DC motor. A block diagram is contained in the functions palette and allows for the execution of the simulation loop to achieve system control. It also assisted in planning and designing a suitable controller for the inverted pendulum. Figure 4: Successfully inverted Pendulum Results and Discussion In the case of this experiment, the technique used to ensure accuracy in the pendulum arm was the swing-up method. This technique involves calculating the overall system output that controls the voltage to the motor and thus its productivity. As stated before, signal generators help to record the electrical energy contained in the pendulum during motion. In case the pendulum fails to achieve effective control, the swing-up ought to be initiated. The virtual model created in LabVIEW assists in regulating unprecedented reactions by the pendulum. It therefore means that the balance control is guaranteed and that the pendulum will eventually balance. Unlike the suspended pendulum that in an anti-clockwise manner, the inverted pendulum moves in a circular manner. Among the components applied in running the experimental exercise were the pendulum, the DC-motor and the arm encoder. Apart from powering the system, the motor system provides support to the hollow vertical pendulum arm that in turn forms the L-shaped hub. The pendulum arm is associated to the shaft of the motor such that the angle between them is within 1800. The pendulum angle is measured using the encoder that immediately performs this task once it is connected to the system in the circuit board (Quanser, 2016). As a consequence of the output voltage and the flow of energy being balanced efficiently, a successful simulation could be performed resulting in the experimental objective being achieved. Essential apparatus that created the motion, recorded measurements and created system control were used in this case. Figure 5: Resulting angle/energy and voltage vs time graphs Figure 6: Block Diagram Conclusion The aforementioned objectives of the experiment, i.e. to balance the inverted pendulum using a virtual model in LabVIEW was achieved successfully. The inverted pendulum’s rod was balanced about the tip of a rotating arm powered by a DC motor. The chances of a successful control of the experiment was improved through taking care to use the right VI window when undertaking control and simulation. Furthermore, success was guaranteed by following the anticipated formula and models. Notably, the swing-up played a vital role in the stabilization and achieving effective control of the inverted pendulum as it drives it to its upright position. Interfacing of PID controllers could be done to design the inverted pendulum and the angle & energy calculation. The inverted pendulum has several applications mostly in robotics. References Kleinigger, M. & Craig, K., 2007. System Control Implementation Using LabVIEW 8.0. LabView Control Implementation Tutorial Doc, pp. 1-21. Quanser, 2016. Rotary Pendulum (ROTPEN) User Manual. QNET ROTPEN (Quanser Ni-Elvis Trainer (QNET) Series, pp. 1-10. Quintero, A. P. S., 2014. Controlling the Inverted Pendulum. pdf report, pp. 1-5. Read More