cmac PP.pdf

A NEUROCONTROL SCHEME OF A 2-DOF

MANIPULATOR USING CMAC.

Leal Ascencio Raúl*

rleal@iteso.mx

Depto. de Electrónica, Sistemas e

Informática

Instituto Tecnológico de Estudios Superiores

de Occidente, ITESO,

Tlaquepaque Jal., 45090, México

*Corresponding author

Perez Cisneros Marco

marcop@cucs.udg.mx

Depto. de Electrónica, Sistemas e

Informática

Instituto Tecnológico de Estudios Superiores

de Occidente, ITESO,

Tlaquepaque Jal., 45090, México

ABSTRACT.

Artificial Neural Networks (ANN) are an emerging technology, yet, in continuous dynamic

behavior, much work has been done to attempt to generate a formal method to design a controller

based on this technology. Based on this fact we are starting to work towards contributing to the

generation of a formal method of the application of neurocontrol and thus present several control

schemes using multilayer perceptrons and also Albus' Cerebellar Model Articulation Controller

(CMAC). The control schemes are presented and explained. The direct inverse neurocontroller

model is used as the system controller without a linear controller. Results from two neurocontrollers

are presented in a comparative way versus linear system using a 2-DOF plant.

I NTRODUCTION .

Artificial Neural Networks (ANN) are an emerging technology, yet, in continuous

dynamic behavior, much work has been done to attempt to generate a formal method to

design a controller based on this technology. Based on this fact we are starting to work

towards contributing to the generation of this formal method of the application of

neurocontrol and thus present several control schemes using multilayer perceptrons and

also Albus' Cerebellar Model Articulation Controller (CMAC) [1].

ANN applications in control are characterized by operating in an ill-defined, time-varying

environment, adapting to changes in the plant's dynamics as well as the environmental

effects, learning significant information in a stable manner and placing few restrictions on

the plant's behavior. It is hoped that increased adaptation will result in improved system

performance, increasing the quality of the solution and reducing the design cost. Neural

algorithms have much to offer to the control engineer given the above characteristics [4].

A key feature of neurocontrol is that the non-linear activation functions of neurons lend

themselves naturally to the control of systems whose dynamics are highly nonlinear and

unknown or uncertain. The inverted pendulum and double inverted pendulum systems are

bechmark nonlinear dynamic systems which are inherently unstable and thus attractive for

testing control schemes. One objective of this project is to investigate the use of the neural

network schemes for the control of the simple inverted pendulum system for the

preliminary experiments and a double inverted pendulum system as the final objective.

D ESCRIPTION OF THE CONTROL SCHEME .

Towards fulfilling the above objective, system identification for the simple pendulum and

double pendulum models are first carried out. A neurocontroller (fig. 1) is then designed

using neural network model for the pendulum. We show that the controller is found to be

stable in the presence of sensor and actuator noise and parametric uncertainty (i.e.

modeling errors).

The simple inverted pendulum neurocontroller is trained with a linear controller made via

the 'Pole Placement Design' method. A direct inverse control scheme is used as the control

element [5][6][7]. Fig. 1 shows the neurocontrol block diagram using a direct inverse

scheme. The input to the model receives signals from states of the plant and its output is a

control signal directed towards the inverted pendulum. The direct inverse model is used as

the system controller without a linear controller [3].

Linear Controller

Linear Model.

Plant´s inverse

model.

Learn.

Fig. 1 Direct inverse-model of the plant.

The double inverted pendulum is modeled through the dynamics of the plant using a

direct inverse model. This neural model will be used as a reference model in a direct

adaptive control scheme [2]. This scheme is presented in fig. 2 and it serves to train a

neurocontroller. In this scheme, the target output is defined through the output of the

reference model, which allows adjusting the control signal in a stable manner so that the

plant´s output asymptotically tracks the output of the reference model [4]. The

performance of this algorithm depends on the choice of a suitable reference model and the

derivation of an appropriate learning mechanism.

Feedforward networks have been used with the Levenberg-Marquardt optimization

algorithm for training for both system identification and controller training phases which

results in superior learning as compared to regular backpropagation or backpropagation

with momentum and adaptive learning rate. On implementing the CMAC technique, one

appealing feature is its efficient realization in software in terms of training time and real-

time operation. Modelling and training of CMAC are presented also through its

application to the simulations of the plant.

REFERENCE

MODEL

LEARNING

SIGNAL.

LEARN

TARGET

OUTPUT

TRAINED

CONTROLLER

CONTROL

SIGNAL

PLANT

OUTPUT

FEEDBACK

Fig. 2 Model reference control arquitecture.

T HE PLANT ´ S MODEL .

The inverted pendulum system is a typical benchmark dynamic non-linear system. Two such

systems are shown on figure 3. For this initial experiments, the simple inverted pendulum (fig. 3a)

is being used as the plant and we will move on to control the double-inverted pendulum in the as a

next step. A state-space approach is used to generate a plant model. Then a controller is designed

using the pole placement design technique. The design is formulated in terms of obtaining a

closed-loop system with specific pole locations. The controller generates a control signal

that is going to be applied to the inverted pendulum in order to control the arm in a

vertical position.

Fig. 3 Two possible plants. a) the simple pendulum. b) the double inverted pendulum.

The inverted pendulum’s model expressions are:

•

0 Ml

•

Using an Ackerman´s solution for pole placement, with: m 1 =-2+j3.464, m 2 =-2-j3.464, m 3 =-

10, m 4 =10, we find a controlled system expression:

•

277

549

997

163

099

394

•

148

5845

3485

5495

697

with a control force equal to:

u= -Kx = 298.15 x 1 + 60.697 x 2 + 163.099 x 3 + 73.394 x 4

T HE SECOND PLANT

In this paper we describe the Pendubot TM [9], a mechatronic device for use in control

engineering education and for research in non-linear control and robotics. This device is a

two-link planar robot with an actuator at the shoulder but no actuator at the elbow. With

this system, a number of fundamental concepts in non-linear dynamics and control theory

may be illustrated. The pendubot complements previous mechatronic systems, such as the

inverted pendulum. We will discuss the design, and control of the Pendubot TM , a two-

link, underactuated robotic mechanism that we are using for research in non-linear

control and to teach students in various concepts in non-linear dynamics, robotics, and

control system design. The Pendubot TM consists of two rigid aluminium links of lengths 9

in and 6 in, respectively. Link 1 is directly coupled to the shaft of a 90V permanent

magnet DC motor mounted to the end of a table. The motor mount and bearings are then

the support for the entire system. Link 1 also includes the bearing housing for joint two.

Needle roller bearings riding on a ground shaft were used to construct the revolving joint

for link 2. The shaft extends out both directions of the housing allowing coupling to the

second link and to an optical encoder mounted on link one. The design gives both links

full 360º of rotational motion. Link 2 is constructed of a 1/4 inch (0.635 cm) thick length

of aluminium with a coupling that attaches to the shaft of joint two.

All of our control computations are performed on a Pentium PC with a D/A card and an

encoder interface card. Using the standard software library routines supplied with these

interface cards we are able to program control algorithms directly in C.

T HE SECOND PLANT ´ S MODEL .

Figure 4 shows a drawing of the Pendubot TM . Since our device is a two link robot (with

only one actuator) its dynamic equations can be found in numerous robotics textbooks as:

•

(5)

•

(6)

Lc1

Lc2

Fig. 4 Front perspective drawing of the Pendubot.

where q 1 , q 2 are the joint angles and t is the input torque. The important distinction then

between the equation 5, equation 6 and a standard two-link robot is, of course, the absence

of a control input torque to equation 6. Underactuated mechanical systems generally have

equilibria which depend on both their kinematic and dynamic parameters. If the

Pendubot TM is mounted so that the joint axes are perpendicular to gravity, then there will

be a continuum of equilibrium configurations. These equilibria are characterized by the

second link vertical for any position of the first link.

T HE NEURO - CONTROLLER BASED ON A LINEAR MODEL USING A MLP AND CMAC

ARCHITECTURE .

The direct-inverse architecture described above is the one being used. In fig. 5 we show

the graphical representation of the direct-inverse neurocontroller.

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: