Tomohiro Henmi

Swing-up Control of the Acrobot Using a New Partial Linearization Controller Based on the Lyapunov Theorem

In this paper, a design of swing-up controller of an Acrobot is proposed. The Acrobot is a model of a horizontal bar gymnast, it has only one actuator at the joint of both links and is a typical example of a nonlinear underactuated system. Since the robot has a large range of motion, the Acrobot has a highly nonlinear characteristic and swing-up control of the Acrobot is a difficult problem. The Acrobot has a simple structure and its control objective is clear, hence it is used as a controlled object of not only the nonlinear underactuated control problem but also a remote network control problem recently. For swing-up control of the Acrobot, this paper proposes a controller, which uses pumping energy of the first link. In the controller, a newly proposed partial linearization is used. The nonlinear feedback is constructed based on the Lyapunov theorem. The new feature of the proposed partial linearization method is to guarantee that the linearized sub-systems track the time-variant reference function, which is not guaranteed in previous methods. Numerical simulation is performed to show the effectiveness of the proposed method

Adaptive control of a two-link planar manipulator using nonlinear Model predictive control

A Model predictive control (MPC) calculates a control input for tracking the system output to a reference trajectory which is an ideal trajectory for the system output to converge on a desired value. In MPC, the parameters of controlled systems are needed for calculating of the control input, and these parameters are treated as well-known and invariable parameters. However, the parameters of system are variable in real system and that is a cause of deterioration in the control performance. Then, in this paper, an adaptive controller for a two-link planar manipulator on the horizontal space via nonlinear model predictive control (NMPC) is proposed. In proposed method, systems parameters are estimated by using past states of systems and control inputs, and the estimated parameters are used in calculating of control inputs. In order to show the effectiveness of the proposed NMPC controller, numerical simulations comparing between the proposed method and the previous method are performed.

Swing-up controller for the Acrobot using skill of human movements

In this paper, a control method to swing up the Acrobot, which is a model of horizontal bar gymnast, is proposed. In order to materialise the movement of the Acrobot as same as movement of human, the swing-up controller of the Acrobot with considering limitation of joint which is model of human hip is proposed. And from an analysis of the gymnastic technique called tap swing forward (TSF), the proposed swing-up controller can make the two links of the Acrobot do a human-like movement. That is, the desired value of angle of the second link is decided based on the movement of TSF technique, where the controller is based on the partial linearisation method. Numerical simulation and experimental result to swing up of the Acrobot are given to show the effectiveness of the proposed method.

Swing-up and stabilizing control system design for an Acrobot

This paper proposes a control system design for an Acrobot. The proposed control system consists of two controllers, namely, swing-up controller and stabilizing controller. In the swing-up, the two links are swinging at the top simultaneously. After the swing-up, the controller also stabilizes both of the two links. Numerical simulation is given to show the effectiveness of the proposed scheme.

Nonlinear control of the underactuated two-link manipulator using the sliding-mode type partial linearisation method

In this paper, a control method for an underactuated two-link manipulator is proposed. This manipulator is a two-degree-of-freedom system with single actuator at the joint of two links. In the proposed method, using the sliding-mode type partial linearisation method which has a robustness for input disturbance, sub-controllers for two state variables based on angle of each link are designed. The control input is consisted of two sub-inputs by regarding each sub-input as input disturbances for each other. Numerical simulation is performed to show the effectiveness of the proposed method.

Tracking control of the two-link manipulator using nonlinear model predictive control

Model predictive control(MPC) an optimization-based approach that decides a control input by the optimal computation as the system output tracks the reference trajectory which is the ideal trajectory while the system output converges on the desired value. In this paper, a tracking controller for the two-link manipulator on the horizontal space via nonlinear model predictive control (NMPC) is proposed. In order to guarantee a tracking performance, the time constant of reference trajectory in proposed controller, it is set as the fixed constant value in common, changes based on error signal between controlled variable and time-variant desired values. For decision of the control inputs, we use the inverse system with assuming angular acceleration is constant in interval of one step and realize the system to track for the reference trajectory in next step. In order to show the effectiveness of proposed NMPC controller, numerical simulations comparing between proposed method and previous method are performed.

Non-linear controller for stabilisation control of a cart-type inverted pendulum system

This paper discusses a stabilisation control of a cart-type inverted pendulum system (CIPS). In general, a state feedback controller with linear approximation of the pendulum around its equilibrium point is used for this control and it can not guarantee stability and needs large amounts of a control input in case a control is started at system’s states away from the equilibrium point. Then, in this paper, a new non-linear controller which guarantees stabilising for widespread states of the systems is proposed. In the proposed controller, at first, we designed a reference function for the angular position of the pendulum by analysing a necessary movement of the cart to keep any angle of the pendulum (Step 1). And, a tracking controller which can track pendulum to the reference angular position decided in Step 1 is designed by partial linearisation method (Step 2). Simulation results are given to show the effectiveness of the proposed controller.

A mathematical expression of an index function in FRIT

FRIT(Fictitious Reference Iterative Tuning) is a model free designing method and a practically useful method. But in the method, there are some drawbacks, That is, the optimal controllers parameters are obtained to minimize a performance index. That is, for each set of parameter candidates, a response of the inverse system of the controller at every sampling time is required to be calculated. Hence, the drawbacks are (1) A large amount of calculation is required. (2) Since the method searches a minimal point of a performance index as the desired design parameters, the optimal point is unknown until the search ends to the optimal point. (3) Sometimes the design parameter values are changed from the optimal values according to practical reasons, as a result, how the index deteriorates is unknown. If a mathematical expression of the index function is obtained, then the index is calculated by just substituting the parameter values and these drawbacks will dissolve. Then this paper proposes a method to give the mathematical expression of the performance index. An example of designing a PID controller is given and the comparison of the necessary computing times of the original FRIT method and the proposed method is shown. Also simulation results are given.

Nonlinear Control of Two-Link Planar Manipulator Using Unstable Property of Zerodynamics

In this paper, a control method for an underactuated two-link planar manipulator using a partial linearization method, which is a one of the nonlinear control method based on structure theory, is proposed. In proposed method, for controlling of 2nd link, sliding-mode type partial linearization method is used, and for 1st link, the unstable property of Zerodynamics(it is dynamics of 1st link) is used, respectively. By analyzing a relationship between behavior of Zerodynamics and desired value of 2nd link, we find the property of Zerodynamics is changing by desired value of 2nd link. Therefore, the control of both links is able to achieve by single control input by deciding the desired value of 2nd link based on behavior of Zerodynamics. Finally, numerical simulations are performed to show the effectiveness of the proposed method.

PRACTICAL SWING-UP CONTROLLER DESIGN FOR A CART-TYPE SINGLE INVERTED PENDULUM HAVING A SERIAL SECOND PENDULUM AS PARASITIC DYNAMICS

Abstract This paper proposes a swing-up control scheme for a cart-type single pendulum having a serial second pendulum as a parasitic part. The proposed control scheme swings up the first pendulum with controlling the motion of a cart and being robust to the parasitic part. In the swing-up, the second pendulum is swinging at the top of the first pendulum and the motion of the second pendulum works as strong disturbance to the control of the first pendulum. Hence the control scheme is required to be strongly robust to the disturbance, and this paper uses sliding mode control law as the controller, which is strongly robust to disturbance. After the swing-up, the controller also stabilizes both angles of the pendulums and cart position. Numerical simulations are given to show the effectiveness of the proposed scheme.