Smith Predictor Based Neural Fuzzy Controller Applied in a Water Gas Heater that Presents a Large Time-Delay and Load Disturbances José Vieira and Alexandre Mota
Abstract--This paper presents a work in progress concerning the use of neuro-fuzzy based non-linear Smith predictor for control a real system with a large and variant time delay and load disturbances. The main objective is to control the output water temperature of one domestic water gas heater that presents a large time-delay and water flow, cold water temperature and wanted output temperature changes. It is presented a detailed description of the water gas heater in terms of non-linearity, time constants and time delay. The steps taken to arrive at the direct and inverse models using a neuro-fuzzy technique are described. The two control strategies, non-linear Smith predictor controller and an improved non-linear Smith predictor controller, were implemented in the 89C51RD PHILIPS micro-controller and the real time results are presented. The improved non-linear Smith predictor controller consists in a fuzzy compensation of the steady-state errors and a compensation for small variations of the time-delay. Index terms-- Fuzzy Hybrid Systems, Applied NeuroFuzzy Control, Model Based Control, Prediction, Time-Delay Compensation, Real Time Control and Water Temperature Control.
domestic water gas heater. This system presents a large time-delay, non-linearity, load disturbances and measurement noise. The control structure should be able to handle with the characteristics of the system, water flow changes, cold water temperature changes and setpoint changes (desired hot water temperature). To succeed in this mission, one improved neuro-fuzzy based non-linear Smith predictor controller (INFSPC) was implemented. This paper starts, in section II, with a full description of the implemented system to control the water gas heater, including a detailed description of the heater allowing the reader to have a comprehension of the control problems that will be explained in later sections. Section III reports the architecture used to identify the direct and inverse models of the system. Section IV focuses the control structures used: neuro-fuzzy based non-linear Smith predictor controller (NFSPC) and in particularly on the improved neuro-fuzzy based non-linear Smith predictor controller (INFSPC). Section V reports the real time results achieved with the two control strategies implemented with the 89C51RD PHILIPS micro-controller. At last, section VI presents the conclusions and gives some of the future works.
I. INTRODUCTION II. THE WATER GAS HEATER CONTROL SYSTEM Many industrial processes contain time-delays. When time-delay is larger than or equal to the time constant of the process, the close loop control of the system is difficult. In this case, one of the alternatives to handle the large timedelay is to use prediction technique to compensate for the influence of the time delay. Smith predictor control (SPC) is one of the simplest and most often used strategies to compensate large time-delay in industries. Usually, the Smith predictor is applied to linear systems. As many industrial systems involve not only time-delay but also nonlinearity, developing of a non-linear Smith predictor is necessary. Nahas [5], and Tan [9], present different approaches for these kinds of problems. The main objective of this work is to develop a control structure to control the output water temperature on a J. Vieira is with the Departamento de Eng. Electrotécnica, Escola Superior de Tecnologia de Castelo Branco, Instituto Politécnico de Castelo Branco, 6000 Castelo Branco, Portugal (email:
[email protected]). A. Mota is with the Departamento de Electrónica e Telecomunicações, Universidade de Aveiro, 3810 Aveiro, Portugal (email:
[email protected]).
The overall system can be divided in to two main blocks: the water gas heater and the micro-controller board (figure 1). The personal computer is used just to monitor the system. PC
Water Gas Heater RS232C connection Receive data
Monitor the control of the water gas heater
Controls the all system
Micro-controller board with 89C51RD
Fig. 1. The system main blocks.
A. The Water Gas Heater The water gas heater is a multiple input single output (MISO) system. The input variables are, the cold water
temperature (cwt(k)), the water flow (wf(k)) and the gas flow applied into the burner (gf(k)). The output variable is the hot water temperature (hwt(k)). The hot water temperature is a variable that depends of the cold water temperature, water flow, gas flow and the water gas heater dynamics. The water gas heater is physically composed by a gas burner, a permutation chamber, a ventilator, two gas valves and several sensors used for control and security as is shown on figure 2. The gas burner can burn natural or propane gas. This burner heats the copper permutation chamber where the cold water enters from bellow and circulates. The amount of power applied to the permutation chamber is controlled by one “proportional-type” gas valve driven by a pulse-width modulated (PWM) signal. The cold and hot water temperature sensors are inexpensive negative coefficient resistors (NTC). The water flow sensor is an optical linear sensor. Overheat, ionisation and ventilation sensors are all binary-type sensors. Exaution Sensor Over Heat Sensor
Water Gas Heater Surface
Hot Water Temperature (ºC) 100,0
80,0
60,0
100,0
40,0
80,0 60,0
Gas Flow (%)
20,0
40,0 20,0 14,5 12,7
10,9
9,0
7,2
5,3 3,5
Water Flow (l/min)
Fig. 3. Characterisation of the water gas heater for a specific cold water temperature of 18ºC.
Ventilator Temperature Sensor of Hot Water NTC
Permutation Chamber
Ionization Sensor
Burner
Water Flow Sensor
Spark
Controlled gas valve
Temperature Sensor of Cold Water NTC
Cold Water
relation between water flow and the hot water temperature is not linear for a specific gas flow.
hwt =
On-Off gas valve
Gas
Hot Water
Fig. 2. Schematic of water gas heater with its sensors and actuators.
The operating range of the hot water temperature is limited between 30ºC and 60ºC. Operating range of the cold water temperature, is between 5ºC and 25ºC, this range depends on the climatic conditions of the region and the season of the year. The operating range of the water flow is between 3 and 15 liters/minute. There are water gas heaters with several maximum powers, like 125, 225, 325 and 400 Kcal/min. The maximum power depends on the physic characteristics of the water gas heater (the burner and the permutation chamber). The maximum power (MaxP) of a water gas heater is given by the equation 1. MaxP = (hwt − cwt) × wf hwt − cwt = MaxP wf º C
This non-linearity is already expected because of the power characteristics of the water gas heater presented in equation 1. One other important variable that changes the working point is the cold water temperature. However, the effect of this variable is more predictive because it is governed by the maximum power equation 1. The effect of a variation of the cold water temperature in the hot water temperature is showed in equation 2.
Kcal/min (1)
In our case, it will be used a water gas heater of 325 Kcal/min of maximum power. As can be seen in figure 3 there are two main variables that affect directly the hot water temperature (working point), which are the gas flow and the water flow. The relation between gas flow and the hot water temperature is almost linear for a specific water flow. However, the
MaxP − cwt wf
(2)
As can be seen from equation 2 the relation between water flow and the hot water temperature is not linear. The effect of the cold water temperature is a positive or negative shift in the surface of figure 3, depending of the cold water temperature is lower or higher than 18ºC (cold water temperature at the time of the acquisition signals). In order to get good models we need to study and define the following parameters: Sampling time Dead time Order of the system (space lag) To calculate the sampling time several step signals were applied in the gas valve for different water flows and the rise and fall times of the hot water temperature were measured. The step responses in figure 4, showed that the water gas heater presents time-delay between the gas flow and the hot water temperature. Table I summarises the measurements. It can be seen from table I that the rise and fall times are equal for fixed water flow but they increase with the decrease of the water flow. To define the sampling time h it was used equation 3 [1].
Time-Delay hwt (ºC) with 3.5 l/min 800
% of PWM Gas Control Flow taq Signal Controlled Burner Gas Valve
hwt(ºC) with 5.5 l/min 700
gf (%) and hwt (ºC)
gf Step 20% to 80% 600
Water Flow Dead Time = 1 seg. Non Linear
Permutation Chamber
Hot Water Temperature Linear
Almost Linear
Dead Time = 1 seg.
hwt(ºC) with 7.7 l/min
Dead Time +-
4.0 seg.
500
hwt (ºC) with 10.8 l/min
Cold Water Temperature
Fig. 5. Block diagram of the water gas heater.
400 hwt (ºC) with 13.1 l/min
B. The Micro-Controller Board 300
5
7
10
15
20
25
Time(sec)
Fig. 4. Step gas flow response of the water gas heater in five specific water flows.
TABLE I STEP GAS FLOW RESPONSES ( SAMPLED WITH 0.25 S).
Water Flow(l/m) Time-Delay (sec) Rise Time (sec) Fall Time (sec)
3,5 4.50 17.25 17.25
5,5 4.25 11.00 11.00
h = sampling time
