Controlling of Water Flowrate in Pipe With Optimal Control
Eko Sarwono and Hendro Priyatman
Departement of Mechanical Engineering, Muhammadiyah University Pontianak Departement of Electrical Engineering, Tanjungpura University
ABSTRACT
Optimal control application gives more roles for performance improvement. One of control object is water flowrate in pipe with turbulence flow. This water flow kind could disturb process, measurement equipment, and so information from measuring not exactly measurable and observable. According that reason, control system the water flowrate are needed to decrease error from steady state condition. Comparing simulation result from system no control and with optimal control, can be concluded that optimal controller design could improve system performance, with decrease error, because all information about state could be measured and observed. Optimal controller design by simulation is better use with high speed Personal Computer (PC) and capability to process information. PC’s delay effect from low speed PC for data processing which represented by graphic could give unsatisfaction simulation result.
Keywords: Flowrate, Optimal Control.
INTRODUCTION
Source of drinking water process for subscriber handled (PDAM) Kotamadya Pontianak took from of Kapuas River (with Long River 1.143 km) and then processed became drinking water then distributed to special reservoir. In drinking water fluids distribution most get trouble so that influence water need level in reservoir.
The obstacle is often damaged by leakage in primary distribution pipe at the location and usually very difficult to detected by drinking water company (because of the primary distribution pipe located in underground), so that it take to long repair this obstacle, and it cause water debit to reservoir will low rate. While flow rate it must be kept constant in order to subscriber consumption not influenced.
this paper took data as we need and then some analysis and simulation to find a better system.
In this paper set to design a optimal controller system for controlling water flow rate which drought straight pipe rounded crossection, fix diameter using of regulator and observer so that it will be found design system with deviation as small as possible from steady state condition. The system design result will be simulated and analyzed.
This paper represents design of optimal controller and makes it software by simulation. From this research, we will obtain optimal controller and use the optimal controller to analysis fluid of water flow rate in pipe problem and their application.
OPTIMAL CONTROL
Optimal control theory have state variable system equation is describe system dynamic. For continuous system, state variable equation in form first order differential:
x f(x,u,t) ; t[t0,t1] (1)
where :
x(t) = state vector nx1.
u(t) = input vector, px1. (Ogata Katsuhiko, 1997) The systems may be represented by equation of the type:
) ( ) ( )
(t Axt But
x
(2)
y = Cx (3)
Where
x = state vector (n-vector) U = control vector (r-vector) A = n x n constant matrix B = n x r constant matrix
In the following, we consider the problem of determining the optimal control vector u(t). The block diagram showing the optimal configuration is shown in figure 2. (Gopal M, 1987)
Figure 2. Optimal Control System
u(t) = -Kx(t) (4)
PHYSIC AND MATHEMATICS MODEL OF PLANT
In the steady state, the velocity of flow in a pipe varies with pressure drop
Cq = flow coefficient G = gravity,m/s2
Equation (6) is plant transfer function. Data of the plant is,
(L) = 1000m
Flow coefficient in steady state is
p
Then we can get plant transfer function
1
Valve transfer function is,
1
A = diaphragm area = 0,0254m2 K = Hookes spring constant = 49N/m
C = friction coefficient between stem and valve body = 2,744 Kg = flow rate constant between spring move = 1920
Kv = Kg.A/K = 0,988 ;p= C/K = 0,056, (Stephanopoulos George, 1984)
9 , 17
64 . 17
1 056 , 0
988 , 0 ) (
s s s
valve
G (9)
DISCUSSION OF SIMULATION RESULT AND ANALYSIS
The simulation has been done to know open loop system performance and designed system with controller based on design specification, as we desired. (Ogata Katsuhiko, 1994).
Plant simulation result
Figure 4. Plant Response. Figure 5. Output Response of Open Loop System
Figure 5 and 6. if plant and system given disturbance so that system will back to initial condition or if the system is bounded input bounded output (BIBO), system will be stable base on given response test signal.
Figure 6. White Noise Input Response
Figure 7 show process disturbance curve and measurement for open loop system , closed loop and optimal regulator. We will find the influence in system caused by noise. After given noise and in measuring for every system condition, and how is the design system change with controller whether still in steady state based on designed system specification or not.
Figure 7. Output Response Disturbance
Figure 8. Output Response Optimal Controller Designed About Disturbance Water Flow Turbulence.
Figure 9 show out response from closed loop system after given white noise disturbance signal. Deviation from steady state can be minimized (as design specification) compared with condition system without controller. In designed system specification hoped system flow rate in interval 10% from input flow rate, 0,00443 m3/s from steady state condition but there is noise in the response so that we need a filter in system, namely observer in order to measure and observe the resulted information of system.
CONCLUSION
From the simulation and analysis we could make conclusions:
1. Optimal control theory using designed linear quadratic regulator method, observer could improve system performance based on curve at simulation result, with error deviation, and noise of open loop can be minimized as desired system specification so that state information of system can be measured and observed. 2. Weight to Q and R matrices will minimize index performance as small as
possible; its means the system will use energy as small as possible to decrease error deviation system as design specification. In this case we give weight to R and Q by trial and error method.
REFERENCE
1. Benedict, Robert P, “Fundamentals of Pipe Flow”, First Edition, John Wiley & Sons, pp 23-344, 1980.
2. Gopal, M, “Modern Control System Theory”, John Wiley & Sons, pp 22-70, 1987.
3. Ogata Katsuhiko, “Solving Control Engineering Problems with Matlab”,
Prentice Hall International, pp 41-90, 1994.
4. Ogata Katsuhiko, “Modern Control Engineering”, Third Edition, Prentice Hall, Inc. pp 786-798, 1997.
