Automation and Robotics Part 9 potx

3.1 The fuzzy algorithm proposal Figure 3 shows the control block diagram used for the pneumatic actuator system, taking the θ angle as the mechanical system output.. Table 5 shows the

3 The fuzzy algorithm

The Thermo-Mechanical Model has the next control inputs: the valve effective area air flow,

eq (1)

Where A1, A2 and A3, are the valve area of cylinder side, rod side, and air return,

respectively However the value of A1 and A2 are the same

3.1 The fuzzy algorithm proposal

Figure 3 shows the control block diagram used for the pneumatic actuator system, taking

the θ angle as the mechanical system output

Fig 2 The fuzzy controller proposal for pneumatic position

Equation (2), shows the error equation; the eqs (3) and (4) shows the proportional valve

open level, obtained with a fuzzy logic method, where θp is the reference and θ is the actual

position of the arm

Next, the fuzzy rules used to solve the problem are presented

3.2 The fuzzy rules

Before the rule settings, both inputs and outputs variables were specified, and are showed in

table 1

Input Output Reference, θp Valve 1, A1

Angle, θ Valve 2, A3

Error, e

Table 1 Fuzzy rules, inputs and outputs

The membership functions used in the fuzzy process are showed in figures 3 to 5 The used

membership functions for the input variables, called reference and angle are the same; and

the membership functions for the output variables called valve open A1 and A2, are the

same

Pneumatic Fuzzy Controller Simulation vs Practical Results for Flexible Manipulator 195

0.2 0.4 0.6 0.8 1

Reference Memberships for ERROR

ANGLE NEG1 ZERO POS1

0.2 0.4 0.6 0.8 1

Reference Memberships for ANGLE

0.4 0.6 0.8 1

Reference Memberships for A2

ANGLE ZERO FEW HALF ALL

(a) (b) Fig 5 Membership functions for the valve values (a) Valve 1 (b) Valve 2

These membership functions are used to control the pneumatic actuator on the manipulator

system In the fuzzy process, the control needs 26 rules, and those rules are distributed

depending of the interval of each variable Table 5 shows the fuzzy rules used to control the

pneumatic actuator position The values for A1 and A3 are normalized, that is, a value of 1.0

represents a 100% open valve (completely open); a 0.5 represents a 50% open valve and 0%

means the valve is completely closed

INPUT OUTPUT

LOW LOW NEG1 FEW ZERO

LOW LOW ZERO ZERO ZERO

LOW LOW POS1 FEW ZERO

LOW LOW POS2 FEW FEW

HALF HALF ZERO ZERO ZERO

HALF HALF POS1 FEW FEW

HALF HALF POS2 FEW FEW

Table 2 Set of fuzzy rules used in the control process

3.3 Experimental description

Figure 6 shows a functionally block diagram of the system The ADC is a 12-bit ADS7841

device, with a synchronous serial interface communication, 4-channel and up to 200 KHz

conversion rate The DAC is a 12-bit DAC7624 device, with quad voltage output, parallel

input data and 10 µs of settling time Both DAC and ADC are manufactured by Texas

Instruments The DAC is used to control the proportional valve, and the ADC is used to

read the flexible arm position with a 10KΩ resistive sensor, which output value has an

interval of 0 to 2 V Finally, an FPGA is used to implement the digital interfaces with the

personal computer, and the PD FPGA based controller

Pneumatic Fuzzy Controller Simulation vs Practical Results for Flexible Manipulator 197

Fig 6 Control block diagram for single-link flexible manipulator with pneumatic actuator Figure 7 shows a block diagram of hardware description to be implemented into FPGA, such as DAC driver, ADC driver, 50 ms sample time generator, communication protocol controller (RS232 driver), a register to load the DAC input (Register) and the finite state machine to synchronize each module (FSM control)

Fig 7 Hardware description for FPGA block diagram

The FPGA is used to implement the digital interface to control the flexible manipulator robot prototype that is shown in figure 8 Figure 9 shows the hardware used to control the flexible manipulator development

Fig 8 Flexible manipulator robot prototype (a) General view (b) Impulse mechanism (c) Position sensor

Fig 9 Hardware used for flexible manipulator control

VEA252 power board must be supplied with 24 V dc and the control signal should have

ground isolation For that, an HCNR200 device, manufactured by Hewlett Packard, is used

4 Results

To test the behavior of the system, a set points vector was used, as shows the eq (2)

Figure 10 shows the fuzzy control simulation results, in comparison with practical results

The values for open valve are small, due to the air pressure; if the valve open are high, the

actuator goes up too fast and arrive to the top in less than one second; in simulation way,

the maximum value for the valves was established in 10% This result was compared with

practical results of the Fuzzy control

Fig 10 Fuzzy control behavior of the flexible arm

The pneumatic actuator is used to generate a flexible manipulator arm displacement in

radial way To control the air flow through the cylinder, a fuzzy logic algorithm was

implemented In figure 10, the system response at the end of cylinder, must be improved

That behaviour is due to the gravity influence on the arm, the valves response and

mechanical structure The behaviour of figure 10 shows several step responses, and speed

profile must be developed to obtain better results

Pneumatic Fuzzy Controller Simulation vs Practical Results for Flexible Manipulator 199

5 Conclusions and future work

The pneumatic actuator is used for the arm position, and to control the air flow through the cylinder, a fuzzy logic algorithm was tested in simulation and practical process, with satisfactory results The Fuzzy control works only with the percent of valve open, to limit the air flow from the compressor trough the cylinder chambers The values for A1 and A2 are the same, but different for A3 Actually A3 must be small than A1 to get a better system response In this case, we can see that a single Fuzzy Logic control is not enough to get a soft behaviour of the system, and a PID algorithm must be used

The system has been tested using several step functions, but a speed profile developing is necessary to improve the system response

The innovation of this work is the application of artificial intelligence control for one-link flexible arm position, with pneumatic cylinder, instead of electrical or hydraulic actuator The contribution is the base of the knowledge about flexible manipulators with pneumatic actuator and fuzzy logic application

As future work, is considering the use of reference frame, neuronal networks and maybe a combination of those controllers By other hand, a speed profile should be developed

9 References

Moore P y J Pu; Progression of servo pneumatics toward advanced applications; Fluid

Power Circuit, Component and System Design; K Edge and C Burrows, Eds Boldock, U K.: Research Studies Press; pages 347 to 365; 1993

Ramos, J.M.; Gorrostieta, E.; Vargas, E.; Pedraza, J.C.; Romero, R.J.; Piñeiro, B Pneumatic

cylinder control for a flexible manipulator robot 12th IEEE International Conference on Methods and Model in Automation and Robotics, Miedzyzdroje, Poland, 28 – 31 August 2006a; ISBN 978-83-60140-88-8

Ramos, J.M.; Vargas, E.; Gorrostieta, E.; Romero, R.J.; Pedraza, J.C Pneumatic Cylinder

Control PID for Manipulator Robot; 2006 International Conference on Dynamics, Instrumentation and Control; Queretaro, México, August 13-16 2006b

Suarez, L.; Luis, S Estrategias de Control Adaptable para el posicionamiento continuo de

Cilindros Neumáticos XI Convencion Informatica 2005; La Habana, Cuba; ISBN 959-7164-87-6; 2005

Wang, J.; Wang, J D Identification of Pneumatic Cylinder Friction Parameters using Genetic

Algorithms IEEE Transactions on Mechatronics; vol 9, no 1; pages 100 to 107;

2004

Jozsef, K.; Claude, J Dynamics Modelling and Simulation of Constrained Robotic System

EEE/ASME Transactions on Mechatronics; vol 8, no 2; pages 165 to 177; 2003 Henri, P.; Hollerbach, J.M An Analytical and Experimental Investigation of a Jet Pipe

controlled electro-pneumatic Actuator IEEE Transactions on Robotics and Automation; vol 14, no 4; pages 601 to 611; 1998

Feliu, V.; García, A.; Somolinos, J.A Gauge-Based Tip Position Control of a New Three –

Degree-Freedom Flexible Robot The International Journal of Robotics Research; vol 20, no 8; pp 660-675; August 2001

Mirro, J.; Automatic Feedback Control of a Vibrating Flexible Beam; MS Thesis, Department

of Mechanical Engineering, Massachussets Institute of Technology, August 1972

Whitney, D.E.; Book, W.J.; Lynch, P.M Design and Control Considerations for Industrial

and Space Manipulators; Proceedings of the Joint Automatic Control Conference,

June, 1974

Burrows, C.R.; Webb C.R Simulation of an On – Off Pneumatic Servomechanism;

Automatic Control Group, 1968

Quiles, E.; Morant, F.; García, E.; Blasco, R.; Correcher, A Control Adaptivo de un Sistema

de Control Neumatico 3ra Conferencia Iberoamericana en Sistemas, Cibernetica e

Informatica CISCI, Julio 2004

Burbano, J.C.; Bacca, G.; Hoyos, M Control de Posicion y Presion para Manipulador

Neumatico a traves de PC Scientia Et Tecnica, UTP; vol 21, pp 71-76; 2003

Pérez, J Analisis Dinamico de Mecanismos Accionados Neumaticamente Ph.D Thesis;

Facultad de Ingeniería Mecanica, Electrica y Electronica, FIMEE; Salamanca, Gto.;

March 2003

Kiyama, F.; Vargas, J Modelo Termo-Mecanico para un Manipulador tipo Dielectrico

Informacion Tecnologica; vol 15; no 5; pages 23 to 31; 2004; ISSN 0716-8756

Feliu, V.; Garcia, A Gauge-Based tip Position Control of a New Three Degree of Freedom

Flexible Robot The International Journal of Robotics Research; vol 20, no 8; pp

660-675; 2001

Ramos, J.M.; Vargas, J.E.; Gorrostieta, E.; Pedraza, J.C Nuevo Modelo Polinomial del

Comportamiento de un Cilindro Neumatico Revista Internacional Informacion

Tecnologica; vol 17, no 3; ISSN 0716-8756; 2006

12

Nonlinear Control Strategies for Bioprocesses: Sliding Mode Control versus Vibrational Control

Dan Selişteanu, Emil Petre, Dorin Popescu and Eugen Bobaşu

Department of Automation and Mechatronics, University of Craiova

Romania

1 Introduction

Nowadays, the domain of biotechnology is characterized by rapid changes in terms of novelty and by highly complex processes that require advanced procedures for design, operation and control From the engineering point of view, the control of bioprocesses poses

a number of challenging problems These problems arise from the presence of living organisms, the high complexity of the interactions between the micro-organisms, as well as the high complexity of the metabolic reactions Moreover, for monitoring and control applications, only a few measurements are available, either because the measuring devices

do not exist or are too expensive, or because the available devices do not give reliable measurements Therefore, we can deduce that the main difficulties arising in the control of bioprocesses arrive from two main sources: the process complexity and the difficulty to have reliable measurements of bioprocess variables (Bastin & Dochain, 1990; Selişteanu et al., 2007a)

In order to overcome these difficulties several strategies for the control of bioprocesses were developed, such as adaptive approach (Bastin & Dochain, 1990; Mailleret et al., 2004), vibrational control (Selişteanu & Petre, 2001; Selişteanu et al., 2007a), sliding mode control (Selişteanu et al., 2007a; Selişteanu et al., 2007b), fuzzy and neural strategies etc

Sliding mode control (SMC) has been widely accepted as an efficient method for control of uncertain nonlinear systems (Utkin, 1992; Slotine & Li, 1991; Edwards & Spurgeon, 1998) The classical applications of SMC (such as robotics, electrical machines etc.) were extended

to SMC of chemical processes (Sira-Ramirez & Llanes-Santiago, 1994) and to SMC of bioprocesses (Selişteanu et al., 2007a; Selişteanu et al., 2007b) The well-known advantages of the SMC are the robustness, controller order reduction, disturbance rejection, and insensitivity to parameter variations The main disadvantage of the SMC strategies used in real applications remains the chattering phenomenon, even if some techniques of chattering reduction were developed (Slotine & Li, 1991; Edwards & Spurgeon, 1998)

Vibrational control (VC) is a non-classical open-loop control method proposed by Bellman, Bentsman and Meerkov (Meerkov, 1980; Bellman et al., 1986a; Bellman et al., 1986b) Applications of the vibrational control theory can be found for: stabilization of plasma, lasers, chemical reactors, biotechnological processes (Selişteanu et al., 2007a) etc The VC technique is applied by oscillating an accessible system component at low amplitude and high frequency Therefore, this technique can be considered, like the SMC, a form of high-frequency control (obviously high-frequency relative to the natural frequency of the system)

But, unlike the SMC, the amplitude and the frequency of the control input are constants and

independent of the state of the system, so this technique is a form of open-loop control

In this chapter, which is an extended work of (Selişteanu et al., 2007a), two nonlinear control

strategies for bioprocesses are designed: a feedback SMC law and a vibrational control

strategy First, a class of bioprocesses is briefly analysed and a nonlinear prototype model is

presented in detail Then, the design of a feedback control law for a prototype bioprocess is

developed The design is based on a combination between exactly linearization, sliding

mode control, and generalized observability canonical forms In order to implement this

SMC law, asymptotic observers (Bastin & Dochain, 1990) will be used for the reconstruction

of unmeasured states The next paragraph deals with the presentation of most important

results of vibrational control theory Also, a VC strategy for a continuous bioprocess is

developed The existence and the choice of stabilizing vibrations, which ensure the desired

behaviour of the bioprocess are analysed Some simulations results, comparisons of the

proposed nonlinear control strategies, and final remarks are also presented

2 Nonlinear dynamical models of the bioprocesses

2.1 The dynamical model of a class of bioprocesses

In bioindustry, the bioprocesses take place in biological reactors, also called bioreactors A

bioreactor is a tank in which several biological reactions occur simultaneously in a liquid

medium (Bastin & Dochain, 1990) These reactions can be classified into two classes:

microbial growth reactions and enzyme-catalysed reactions The bioreactors can operate in

three modes: the continuous mode, the fed-batch mode and the batch mode For example, a

Fed-Batch Bioreactor (FBB) initially contains a small amount of substrates and

micro-organisms and is progressively filled with the influent substrates When the FBB is full the

content is harvested By contrast, in a Continuous Stirred Tank Bioreactor (CSTB) the

substrates are fed to the bioreactor continuously and an effluent stream is continuously

withdrawn from the reactor such that the culture volume is constant

In practice, the bioprocess control is often limited to regulation of the temperature and pH at

some constant values favourable to the microbial growth

There is however no doubt that the control of the biological state variables (biomass,

substrates, products) can help to increase the bioprocess performance In order to develop

and apply advanced control strategies for these biological variables, obviously is necessary

to obtain a useful dynamical model The modelling of bioprocesses is a difficult task;

however, using the mass balance of the components inside the bioreactor and obeying some

modelling rules, a dynamical state-space model can be obtained (Bastin & Dochain, 1990;

Bastin, 1991)

A process carried out in a bioreactor can be defined as a set of m biochemical reactions

involving n components (with n ≥m) The reaction scheme of a bioprocess (the reaction

network) contains n components and m reactions The concentrations of the physical

components will be denoted with the notations ξi,i=1,n The reaction rates will be

denoted as ϕj j=1,m The evolution of each component is described by the differential

equation (Bastin & Dochain, 1990):

( )

=ξ

Nonlinear Control Strategies for Bioprocesses: Sliding Mode Control versus Vibrational Control 203

where ξ is the time derivative of the concentration i ξ (g/l) and the notation i j~i indicates

that the sum is done in accordance with the reactions j that involve the component i The

positive and dimensionless constants k are yield coefficients The sign of the first term of ij

(1) is given by the type of the component ξ : plus (+) when the component is a reaction i

product and minus (-) otherwise D is the specific volumetric rate (h-1), usually called

dilution rate Fi represents the rate of supply of the component ξ (external substrate) to the i

bioreactor per unit of volume (g/lh) When this component is not an external substrate, then

0

Fi≡ Qi represents the rate of removal of the component ξ from the bioreactor in i

gazeous form per unit of volume (g/lh)

In order to obtain a dynamical state-space model of the entire bioprocess, we denote

n 2

ξ

=

ξ " , where ξ is the n-dimensional vector of the instantaneous

concentrations, also is the state of the model The vector of the reaction rates (the reaction

m 2

ϕ

=

ϕ " The reaction rate vector is m-dimensional

Usually, a reaction rate is represented by a non-negative rational function of the state ξ The

yield coefficients can be written as the (n ×m) – dimensional yield matrix K=[ ]Kij ,

1 "

n 2

Q

Q= " , where F is the vector of rates of supply and

Q is the vector of rates of removal of the components in gazeous form

From (1), with the above notations, the global dynamics can be represented by the

dynamical state-space model (Bastin & Dochain, 1990):

K⋅ϕξ − + −

=

This model describes in fact the behaviour of an entire class of biotechnological processes

and is referred to as the general dynamical state-space model of this class of bioprocesses

(Bastin & Dochain, 1990; Bastin, 1991) In (2), the term K⋅ϕ( )ξ is in fact the rate of

consumption and/or production of the components in the reactor, i.e the reaction kinetics

The term −D +F−Q represents the exchange with the environment, i.e the dynamics of

the component transportation through the bioreactor The strongly nonlinear character of

the model (2) is given by the reaction kinetics In many situations, the yield coefficients, the

structure and the parameters of the reaction rates are partially known or unknown

Remark 1 In a FBB, the termDξ represents the dilution of a component due to the increase i

in volume In this case D is the specific rate of volume increase (V =D⋅V, with V the liquid

volume in the FBB and V its time derivative) In a CSTB, Dξi represents the rate of

removal of a component in liquid form (in a CSTB, V = 0)

Often in practice, the bioprocess control goal is to regulate a scalar output y, which can be

defined as a linear combination of the state variables Usually, this control objective is

reached using as a control input one of the components of F, i.e a rate of supply of an

external substrate: u =Fi Consequently, the vector F can be written as F=b⋅u+F~, with

[ ]T

n 2

b

b= " ; bi= 1, bj=0, i ≠j; and [ ]T

n 2

F~

F~= " ; F~i=0, F~j=Fj j≠i Then, the model (2) can be rewritten as

=

⋅+ξ

=

⋅+

−+

−ξϕ

⋅

=ξhy

ubfubQF~

DK



(3)

2.2 The model prototype of a continuous bioprocess

A model prototype of a continuous bioprocess that takes place inside a CSTB is described by

the following nonlinear system (Bastin & Dochain, 1990; Dochain & Vanrolleghem, 2001):

influent substrate concentration, and D is the dilution rate (h-1) In (4), (5) μ is the specific

growth rate and k1 > 0 the yield coefficient

The bioprocess (4), (5) is in fact a fermentation process, which usually occurs in a bioreactor

A compact representation of (4), (5) is:

= the state vector

The equilibrium states of (4), (5) are of two types:

E1 Wash-out state, defined by:

in T

2 s 1 s

s= ξ ξ = 0 S

This equilibrium is a state when the bacterial life has disappeared; therefore, the wash-out

state has not practical interest

E2 Operational equilibrium states, implicitly defined by:

( ) ( )

⎩

⎨

⎧

=ξ+ξξξμ

=ξξμ

in 2 s 1 s 2 s 1 s 1 2 s 1 s

DSD

,k

D,

(8)

These equilibria can be attractive or repulsive depending on the particular form of μ(ξ1,ξ2)

Only these equilibria have a practical interest Let’s assume that the specific growth rate is of

the form:

( ) ( )

i 2 2 2 M

2 0

2 2

ξμ

=ξμ

=ξξ

This is the Haldane kinetic model of the specific growth rate (Bastin & Dochain, 1990),

where KM is the Michaelis-Menten constant, Ki the inhibition constant and μ the maxim 0

specific growth rate