C. Agees Kumar et. al. / International Journal of Engineering Science and Technology Vol. 2(7), 2010, 3179-3184
MULTI-OBJECTIVE PID CONTROLLER BASED ON ADAPTIVE WEIGHTED PSO WITH APPLICATION TO STEAM TEMPERATURE CONTROL IN BOILERS C.AGEES KUMAR1 1
Department of Electronics& Instrumentation Engineering, Noorul Islam College of Engineering, Kumara coil, TamilNadu,India (
[email protected])
N.KESAVAN NAIR2, 2
Department of Electrical & Electronics Engineering, Noorul Islam College of Engineering, Kumara coil, TamilNadu, India
Abstract- PID controller is widely used for main steam temperature control of boiler unit in thermal power plant. To avoid the drawback of current PID design methods, this paper presents a new design method for multi-objective PID controller to synthetically consider system requirement in reliability and robustness. Adaptive weighted PSO (AWPSO) technique is applied to the parameter optimization design. The optimization problem considered is highly nonlinear, complex, with multiple objectives and constraints. The simulation results on an actual main steam temperature control system indicate that, the multi-objective PID controller designed by presented method, can improve the dynamic performance of main steam temperature control system, with good robustness ability. Keywords: boiler; main steam temperature control; multi-objective PID controller; AW-PSO algorithm; Pareto-optimal solutions I. INTRODUCTION Many real world control problems track several objectives simultaneously. The objectives under consideration conflict with each other and optimizing a particular solution with respect to single objective will result in unacceptable results with respect to other objective. The main steam temperature control system of boiler in largescale thermal power plant is to improve the economic profit and to ensure the operation safety for thermal units [1].As the achievements of control theory and computer technology, the control strategy of main steam temperature system has been unceasingly developed[2-3]. But the most widely used, is still typical PID control systems, mainly due to its structure simplicity and universality. The performance quality of the PID controller depends on its setting of parameters. Frequency domain design method [4] aims to meet reasonable gain margin and phase margin for good robustness; time-domain design method is to satisfy the requirement of some performance indices (such as ISE and ITAE, etc.)[5] or its weighted value for good output response. However, when the system has to satisfy concrete requirement for speediness, stability and robustness in same time, the PID design methods mentioned above often face obvious co-ordination bottleneck due to the blindness in weight setting for the indices, difficult to get optimal PID parameters to meet practical requirements.
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C. Agees Kumar et. al. / International Journal of Engineering Science and Technology Vol. 2(7), 2010, 3179-3184 To avoid the drawback of current PID design methods, this paper presents a new design method, In this study multi-objective particle swarm optimization (MOPSO) is used for tuning of non-linear PID controller parameters for steam temperature control of boiler unit in thermal power plant.. Unlike classical methods such as Ziegler-Nichols and Cohen-Coon and single objective optimization methods such as GA [6] and PSO [7], multi-objective optimization can minimize some important aspect of a system such as overshoot/undershoot and settling time simultaneously, so that various solutions with different overshoot/undershoot and settling time are obtained. The multi-objective PID controller designed by presented method, can improve the dynamic performance of main steam temperature control system, with good robustness ability. II. MULTI-OBJECTIVE PID CONTROLLER IN MAIN STEAM TEMPERATURE CONTROL Main steam temperature control system has to possess stronger restrain ability for inner-disturbance from spraywater d1 (t) and faster correction speed for outer-disturbance from the change rate of fuel d2 (t). For cascade PID controller in main steam temperature control system, the main loop adopts PID controller, the by-loop, P controller, the block diagram shown in Figure 1.G1(s) and G2(s) are transfer functions for outer loop and inner loop respectively. In order to simplify the realization complexity of the control system, sufficiently take the advantage of overcoming inner-disturbance from cascade control, so combine the by-loop of cascade control and inner loop into a generalized controlled object, refer the part in dotted line block in Figure 1.
r (t)
+
+
e(t) PID
+
+
P
+
+
-
-
G1(s)
y (t)
G2(s)
Fig. 1 Structure of PID cascade control for main steam temperature system.
The dynamic characteristics of main steam temperature system are closely related to operating conditions of entire unit, when the load changes, the object feature of the units will cause significant change. The transfer function of main steam temperature due to spray-water disturbance under typical loads, for the over-heater of a 600MW once-through boiler with supercritical pressure is shown as Table 1,where D, the main steam flow. Table I. Transfer Function of Main Steam Temperature Due To Spray-Water Disturbance under Typical Loads
Load
G1(s)
G2(s)
50%(D=242.2kg/s) 75%(D=347.9kg/s) 100%(D=527.8kg/s)
3.067/(1+25s)2 1.657/(1+20s)2 0.815/(1+18s)2
1.119/(1+42.1s)7 1.202/(1+27.1s)7 1.276/(1+18.4s)6
For cascade PID control of main steam temperature system, the controller parameters of PID main loop Kop, Toi, Tod and the controller parameters of P by-loop control Kip are all edited by real number code. Using AW-PSO algorithm for optimization search, the actual cascade PID parameter satisfied actual requirement can be obtained. For above system example, the search ranges of Kop, Toi and Tod are [0.001, 1.5] [0.001, 400] [0.001, 100] and [5, 30] respectively. Gmin and Pmin are 2 and 600. III. THE MULTI-OBJECTIVE PID CONTROLLER BASED ON THE AW-PSO ALGORITHM PID regulator makes proportional, integral and differential operation by means of feedback signals, and uses its weighted sum to form the control signal. Consider the structure of a typical PID controller:
G PID (s) kp(1
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1 Td s ) Ti s
(1)
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C. Agees Kumar et. al. / International Journal of Engineering Science and Technology Vol. 2(7), 2010, 3179-3184 Where, kp, Ti and Td present proportional coefficient, integral time constant and differential time constant respectively. The particle swarm optimization algorithm is a population based search algorithm based on the simulation of the social behavior of birds within a flock. In PSO, individuals referred to as particles, are flown through hyper dimensional search space. Changes to the position of particles within the search space are based on the social psychological tendency of individuals to emulate the success of other individuals. The changes to a particle within the swarm are therefore influenced by the experience, or knowledge, of its neighbors. The search behavior of a particle is thus affected by that of other particles within the swarm (PSO is therefore a kind of symbiotic cooperative algorithm). The consequence of modeling this social behavior is that the search process is such that particles stochastically return toward previously successful region in the search space [7]. A swarm consists of a set of particles, where each particle represents a potential solution. Particles are then flown through the hyperspace, where the position of each particle is changed according to its own experience and that of its neighbors. Let xi (t) denotes the position of particle Pi in hyperspace, at time step t. The position of Pi is then changed by adding a velocity vii(t) to the current position as:
x i (t ) xi (t 1) vi (t )
(2)
The velocity vector drives the optimization process and reflects the socially exchange information. Velocity update equation is as follows:
vi (t ) wvi (t 1) c1r1 (Pbi xi (t 1)) c2r2 (Pg xi (t 1)) (3) where w is the inertia weight, c1 and c2 are positive constants and r1 and r2 are random numbers obtained from a uniform random distribution function in the interval [0, 1]. The parameters Pbi and Pg represent the best previous position of the i-th particle and position of the best particle among all particles in the population respectively [8]. The inertia weight controls the influence of previous velocities on the new velocity. Large inertia weights cause larger exploration of the search space while smaller inertia weights focus the search on a smaller region. Typically, PSO started with a large inertia weight, which is decreased over time. Shi and Eberhart proposed a ‘fuzzy adaptation’ of the inertia weight [8] due to the fact that a linearly-decreasing weight would not be adequate to improve the performance of the PSO due to its nonlinear nature. In this paper we use the following formula to change the inertia weight at each generation: w w0 r (1 w0 ) (4) where w0 is the initial positive constant in the interval [0, 1] and r is random number obtained from a uniform random distribution function in the interval [0, 1]. The suggest range for w0 is [0, 0.5], which make the weight w randomly varying between w0 and 1. To improve the performance of the PSO for multi-objective optimization problems, Mahfouf [11] proposed an Adaptive Weighted PSO (AWPSO) algorithm, in which the velocity in Eq. (3) is modified as follows:
(5)
vi (t) wvi (t 1) c1r1(Pbi xi (t 1))c2r2(Pg xi (t 1))
The second term in Eq. (9) can be viewed as an acceleration term which depends on distances between the current position xi (t) , the personal best PN and the global best Pg The acceleration factor α is defined as follows:
0
t T
(6)
where t is current generation, T denotes the number of generations and the suggest range for 0 is [0.5,1]. As can be seen from Equation (5), the acceleration term will increase as the number of iterations increases, which will enhance the global search ability at the end of run and help the algorithm to jump out of the local optimum, especially in the case of multi-modal problems. One of the simplest approaches to deal with multi-objective problems (MOPs) is to define an aggregate objective function as a weighted sum of the objectives. Single objective optimization algorithms can then be applied, without any changes to the algorithm, to find optimum solutions. We use an aggregation approach to construct the evaluation function Eval for multi-objective optimization (MOO) as follows [9]:
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C. Agees Kumar et. al. / International Journal of Engineering Science and Technology Vol. 2(7), 2010, 3179-3184
Eval (k ) wi f i (k ) where
w
i
1
(7)
where n is the number of objective functions and k denotes the k-th particle and the weights wi for each objective are changed and normalized as follows:
wi
i
; i , j U (0,1)
n
i 1
(8)
j
where μi and μj are random numbers obtained from uniform random distribution function in the interval [0,1] IV. RESULTS OF TUNING AND ITS COMPARISON Using AW-PSO algorithm for optimization of PID parameters of main steam temperature control system above mentioned, set the parameters of the controller parameters to be tuning at 75% load. For AW-PSO, actual running time reaches to 30, Pareto optimal solution has basically unchanged, with rapid convergence. Pareto solution set obtained from the AW-PSO algorithm in Figure 2 can satisfy the requirements of stability and robustness for different preferences. When the system needs low overshoot, can choose sample 3, or needs overshoot, solution 1 will be fine.. Therefore it provides an effective tool for trade-off analysis for speediness, stability and robustness and overcome the blindness in weight setting effectively.
Fig.2 Pareto Optimal front
The step response curves with different PID controllers shown as Fig. 3. It shows that the unbiased optimal solution from presented method is prior to the others.(y as output)
Fig. 3 Step response with different PID controllers.
Consider the unbiased optimal solution in 75% full load for analyzing the anti-disturbance ability of the multiobjective PID controller, add a step disturbance with d1 = 1 for spray-water in the by-loop and with d2 = 0.3 for the change of combustion rate in the main loop, in the cascade PID control system of main steam temperature
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C. Agees Kumar et. al. / International Journal of Engineering Science and Technology Vol. 2(7), 2010, 3179-3184 separately. And the disturbance is added on t = 800s during the stability condition of the system. The output response, given in Figure 4, shows that the control system behaves stronger anti-disturbance ability.
Fig. 4 Control system behaves as having stronger anti-disturbance ability.
The dynamic characteristics of main steam temperature vary with the change of load and operating conditions. So the controller designed must have strong robustness. Consider the unbiased optimal solution in 75% full load for analyzing the robustness of the multi-objective PID controller. Using the parameters above, the step response in 50% of full load can be obtained (Fig.5). The simulation shows that the control system still keeps good dynamic performance, good control quality and stronger robustness in the condition of different load of main steam system.
Fig. 5 Control system behaves as having robustness ability.
V.CONCLUSION According to the feature of main steam temperature control, a multi-objective design method of PID controller is presented. Using AW-PSO algorithm to tune control parameters, more Pareto solutions can be obtained from one time of operation. The multi-objective PID controller can coordinate various performance indices of the system, and provide an effective tool for trade-off analysis among speediness, stability and robustness. The decision-maker can choose the PID parameter needed from the Pareto solutions according to the requirement of actual system. The multi-objective PID controller using the design method presented has good control quality, which provides an effective approach for optimal design of PID controller and can be widely used for practical PID control.
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C. Agees Kumar et. al. / International Journal of Engineering Science and Technology Vol. 2(7), 2010, 3179-3184 REFERENCES [1]
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