Parallel-type Double Inverted Pendulum Research Articles

A novel tensor product model transformation-based adaptive variable universe of discourse controller

In this paper, a tensor product (TP) model transformation-based variable universe of discourse (VUD) controller is presented for a class of under-actuated nonlinear systems. First, the under-actuated nonlinear system is transformed into a parameter-varying weighted polytopic system by TP model transformation. Next, the VUD approach is extended to the TP model case; in this model, the gains of the error and error derivative in the VUD are calculated by linear matrix inequalities rather than traditional linear methods, such as the linear quadratic regulator or the Lyapunov equation. The TP model transformation-based VUD (TPVUD) is augmented with a σ-adaptive strategy to improve the controller׳s performance. To demonstrate the advantages of the developed control method, numerical simulations are carried out on a parallel-type double inverted pendulum and an aeroelastic wing system. Moreover, experimental results are employed to test the effectiveness of TPVUD on a laboratory-scale three-dimensional (3-D) crane system.

Instance-based Policy Learning by Real-coded Genetic Algorithms and Its Application to Control of Nonholonomic Systems

The stabilization control of nonholonomic systems have been extensively studied because it is essential for nonholonomic robot control problems. The difficulty in this problem is that the theoretical derivation of control policy is not necessarily guaranteed achievable. In this paper, we present a reinforcement learning (RL) method with instance-based policy (IBP) representation, in which control policies for this class are optimized with respect to user-defined cost functions. Direct policy search (DPS) is an approach for RL; the policy is represented by parametric models and the model parameters are directly searched by optimization techniques including genetic algorithms (GAs). In IBP representation an instance consists of a state and an action pair; a policy consists of a set of instances. Several DPSs with IBP have been previously proposed. In these methods, sometimes fail to obtain optimal control policies when state-action variables are continuous. In this paper, we present a real-coded GA for DPSs with IBP. Our method is specifically designed for continuous domains. Optimization of IBP has three difficulties; high-dimensionality, epistasis, and multi-modality. Our solution is designed for overcoming these difficulties. The policy search with IBP representation appears to be high-dimensional optimization; however, instances which can improve the fitness are often limited to active instances (instances used for the evaluation). In fact, the number of active instances is small. Therefore, we treat the search problem as a low dimensional problem by restricting search variables only to active instances. It has been commonly known that functions with epistasis can be efficiently optimized with crossovers which satisfy the inheritance of statistics. For efficient search of IBP, we propose extended crossover-like mutation (extended XLM) which generates a new instance around an instance with satisfying the inheritance of statistics. For overcoming multi-modality, we propose extended CCM for selection. Extended CCM always chooses the child for next generation among children and a parent which generates the children. By doing so, the diversity of the population is expected to be well maintained. Our proposals, FLIP (Functionally sophisticated Learner for IBP), consist of extended XLM and extended CCM. The effectiveness of FLIP is shown by experiments with nonholonomic control problems, a space robot, a car-like robot, and a parallel-type double inverted pendulum.

A new fuzzy controller for stabilization of parallel-type double inverted pendulum system

A new fuzzy controller with 6 input items and 1 output item for stabilizing a parallel-type double inverted pendulum system is presented based on the single input rule modules (SIRMs) dynamically connected fuzzy inference model. Each input item is assigned with a SIRM and a dynamic importance degree. The SIRMs and the dynamic importance degrees are designed such that the angular control of the longer pendulum takes the highest priority over the angular control of the shorter pendulum and the position control of the cart when the angle of the longer pendulum is big. By using the SIRMs and the dynamic importance degrees, the priority orders of the three controls are automatically adjusted according to control situations. The proposed fuzzy controller has a simple and intuitively understandable structure, and executes the three controls entirely in parallel. Simulation results show that the proposed fuzzy controller can stabilize completely a parallel-type double inverted pendulum system within 10.0 s for a wide range of the initial angles of the two pendulums. This is the first result for a fuzzy controller to achieve successfully complete stabilization control of a parallel-type double inverted pendulum system.

PC-based sliding-mode control applied to parallel-type double inverted pendulum system

This paper presents a ‘sliding-link’ condition for the discrete sliding mode control. Besides, by using the ‘sliding-link’ condition, the PC-based sliding-mode controller is introduced. The usefulness of the proposed controller is demonstrated by the control of a parallel-type double inverted pendulum system.

Swing-Up Control of a Inverted Pendulum Using Chaotic Motion.

The dynamics of an inverted pendulum system is generally described by nonlinear ordinary equations including trigonometric functions. Therefore, under certain conditions in the periodic motion of a cart, the pendulum exhibits chaotic motions. In this paper, we propose a new swing up control method for a parallel type double inverted pendulum using the chaotic motions that appear inherently in its dynamiCS. We calculate the bifurcation diagram in the control parameter plane, then design the swing up controllers based on this diagram. One chosen pendulum or two pendulums can be swung up from lowest position to upper positiom The experimental results demonstrate the effectiveness of this controller. We also compute the basins of attraction to understand the reason of effectiveness clearly.