Intelligent Control of the inverted pendulum
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Date
2011-07-14
Authors
Ng'oma, Anthony
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Abstract
Artificial Intelligence (AI) based control techniques are becoming more popular for their applicability to complex control systems. In this research, an Intelligent Controller is designed for a non-linear process with complex dynamics - the Inverted Pendulum. The controller is designed
to interact with other controllers in the process. That is, the Intelligent Controller is designed to control the Inverted Pendulum for part of the state space and afterwards transfers control to other existing controllers. This arrangement is referred to as Operation-Space (OS) based control. The
Intelligent Controller is designed to steer the Inverted Pendulum from the downward resting position or state, to a state controllable by an existing OS based controller. Control knowledge for this swing up operation is generated by applying a multi-stage decision process called Differential Dynamic Programming (DDP).
A DDP algorithm is developed by solving a set of partial differential equations. The Inverted Pendulum is represented as a discretised fourth order process model. The discretised model is based on the corrected van Luenen continuous time model. The van Luenen model has an error which I discovered using step response simulations. After a series of trials, two cost objective functions J, and J2 were chosen for the DDP algorithm. This was the most difficult part of the design process. The DDP equations were implemented in a computer algorithm to compute optimal control data in the form of process states and control signals. The downward resting position was the initial state , x(0) while the final state x ( N ) , was a state controllable by the OS based controller. The resulting two sets of control data constituted the training data for the Neural Network (N-Net) structure. An N-Net structure was designed and trained on the generated control data. Its simulation results showed excellent performance. Sensitivity analysis to variations of model parameters was performed. The N-Net was then implemented as a controller on the laboratory setup. Hardware
constraints on the laboratory setup and the transputer system, made it difficult to test the controller's full capabilities. However, results obtained indicated that the N-Net controller was able to reproduce the control trajectories in real time.In addition to the design of the N-Net controller, an integrated PD swing up controller was
designed and implemented on the laboratory setup. The PD controllers, assisted by saturation effects, successfully steer the Inverted Pendulum from the downward resting position to join the OS based control cycle. The controller demonstrates compatibility with the existing OS based controller, which the N-Net was designed to have.
An N-Net structure was designed and trained on the generated control data. Its simulation results showed excellent performance. Sensitivity analysis to variations of model parameters was
performed. The N-Net was then implemented as a controller on the laboratory setup. Hardware constraints on the laboratory setup and the transputer system, made it difficult to test the controller's full capabilities. However, results obtained indicated that the N-Net controller was able to reproduce the control trajectories in real time.
In addition to the design of the N-Net controller, an integrated PD swing up controller was designed and implemented on the laboratory setup. The PD controllers, assisted by saturation effects, successfully steer the Inverted Pendulum from the downward resting position to join the
OS based control cycle. The controller demonstrates compatibility with the existing OS based controller, which the N-Net was designed to have.
Description
Keywords
Pendulum , Rotational motion