pso 粒子群算法 在时滞方面的应用
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Keywords-PID controller; Time delay; Pade approximation;
Particle swarm optimization
I. INTRODUCTION
Many industrial process control systems, such as the paper manufacturing process, the chemical reactor and rectification column, can be presented using models with large dead time. According to (Barve et aI., 2004), more than 90% of physical systems in process control can be approximated by FOPDT(first order plus time delay) (about 60%) and SOPDT(second order plus time delay) (about 30%) models with acceptable accuracy. A typical feature of these processes is that they usually have large time delay, which is also the focus of many controller designing methods. Proportional-integral-derivative (PID) controllers are still widely used in industrial systems because of their simplicity and satisfactory performances for a wide range of processes.
II． PROPOSED METHOD
G(s) =
1/ τ i + k p s +τ d s2 (as2 + bs) + (1/ τ i + k p s + τ d s2 ) 1 − 0.5Ls 1 + 0.5Ls
(5)
=
where
N (s) D( s)
N ( s ) = 1/ τ i + (k p + 0.5 L / τ i ) s + (τ d + 0.5 Lk p ) s 2 + 0.5 Lτ d s 3
2. Department ofAutomation, Tsinghua University, Beijing 100084, PR China For systems with long time delay, several methods for
Abstract-A novel method is proposed to design PID
D ( s ) = 1/ τ i + (b + k p - 0.5 L / τ i ) s + (0.5bL + τ d - 0.5 Lk p + a ) s 2 + (0.5aL - 0.5 Lτ d ) s 3
(1)
(6)
ቤተ መጻሕፍቲ ባይዱ
A. First order Plus Time Delay Process Consider a FOPTD process described by
s in the numerator and those in the denominator of the closed
loop transfer function for FOPTD processes. Such relationship between these coefficients is searched using particle swarm optimization (PSO) algorithm. Then, the approach is applied to high order systems by approximating them to FOPDT models. The proposed method originates from processes with small time delay; however, it is still effective even if the time delay is quite large. Simulation results show that the proposed method gives significantly better dynamic performances than IMC-PID method and the formula proposed by Smith, C.A. et al.
1-4244-2386-6/08/$20.00 ©2008 IEEE
Chidambaram and Padma Sree (2003) and PSO algorithm (J. Kennedy and R. Eberhart, 1995). The proposed method originates from processes with small time delay; however, it is still effective even if the time delay is quite large. This paper is organized as follows. The method is presented in section 2. Simulation examples will follow in section 3 to demonstrate the performance of the proposed method. Finally, conclusions will be drawn in section 4.
A New PSO-PID Tuning Method for Time-delay Processes
YANG Bo 1, LI Wan-zhou2 , YANG Feng2
1. Automation Business Unit ofCISDI Engineering Co., Ltd., Chongqing 400013, China
controllers for stable first order and high order systems with time delay. Using a first-order Pade approximation for the transport delay, this method is based on developing a certain relationship between the coefficients of corresponding powers of
(7)
G p (s) =
1 e − Ls as + b
It seems that if the corresponding coefficients of s, s2 and s3 of the numerator in Eq. (5) are equal to that of the denominator (Chidambaram et al., 2003), the output signal will quickly follow the input signal since G (s) becomes a constant 1. However, equation (5) is just an approximation of the closed-loop transfer function; the error will be very big using first-order Padé approximation in case of large L.
determining PID controller parameters have been developed over the past 60 years. Ziegler and Nichols (1942) give a method of tuning PI controllers empirically, however it gives very poor performance in the case of large dead time. The Smith predictor is well known to give a good performance for a stable process with long time delay (Smith et aI., 1959). However, the strategy is affected by the accuracy of the plant model and very sensitive to modeling errors. Imprecise parameters will result in bad dynamic performances or instability of systems. There are also some robust PID tuning methods for plants with long time delay, such as method proposed by Smith, C.A. et aI. (1997) and IMC-PID method proposed by Rivera et aI. (1986). Nevertheless their dynamic performances are not good enough. Particle swarm optimization (PSO) algorithm is an evolutionary computation technique developed by Kennedy and Eberhart (1995). PSO and other improved PSO algorithms are combined with PID controllers to optimize PID parameters by Z. L. Gaing (2004) and other authors. These methods always directly select PID parameters to compose a particle. Because PID parameters may range from zero to positive infinity, it is not easy to find the global optimum solution. Padma Sree et aI. (2003, 2004 and 2005) have proposed a simple and robust method of tuning PID controllers, which was originally applied to integrator/dead-time processes. They extended it to stable and unstable FOPTD systems in the year of 2004. However, they can only give some empirical formulas for FOPTD systems with quite short time delay, which is no bigger than 1 second. A novel PID tuning method for stable processes with time delay is proposed in this paper based on the scheme of
Particle swarm optimization
I. INTRODUCTION
Many industrial process control systems, such as the paper manufacturing process, the chemical reactor and rectification column, can be presented using models with large dead time. According to (Barve et aI., 2004), more than 90% of physical systems in process control can be approximated by FOPDT(first order plus time delay) (about 60%) and SOPDT(second order plus time delay) (about 30%) models with acceptable accuracy. A typical feature of these processes is that they usually have large time delay, which is also the focus of many controller designing methods. Proportional-integral-derivative (PID) controllers are still widely used in industrial systems because of their simplicity and satisfactory performances for a wide range of processes.
II． PROPOSED METHOD
G(s) =
1/ τ i + k p s +τ d s2 (as2 + bs) + (1/ τ i + k p s + τ d s2 ) 1 − 0.5Ls 1 + 0.5Ls
(5)
=
where
N (s) D( s)
N ( s ) = 1/ τ i + (k p + 0.5 L / τ i ) s + (τ d + 0.5 Lk p ) s 2 + 0.5 Lτ d s 3
2. Department ofAutomation, Tsinghua University, Beijing 100084, PR China For systems with long time delay, several methods for
Abstract-A novel method is proposed to design PID
D ( s ) = 1/ τ i + (b + k p - 0.5 L / τ i ) s + (0.5bL + τ d - 0.5 Lk p + a ) s 2 + (0.5aL - 0.5 Lτ d ) s 3
(1)
(6)
ቤተ መጻሕፍቲ ባይዱ
A. First order Plus Time Delay Process Consider a FOPTD process described by
s in the numerator and those in the denominator of the closed
loop transfer function for FOPTD processes. Such relationship between these coefficients is searched using particle swarm optimization (PSO) algorithm. Then, the approach is applied to high order systems by approximating them to FOPDT models. The proposed method originates from processes with small time delay; however, it is still effective even if the time delay is quite large. Simulation results show that the proposed method gives significantly better dynamic performances than IMC-PID method and the formula proposed by Smith, C.A. et al.
1-4244-2386-6/08/$20.00 ©2008 IEEE
Chidambaram and Padma Sree (2003) and PSO algorithm (J. Kennedy and R. Eberhart, 1995). The proposed method originates from processes with small time delay; however, it is still effective even if the time delay is quite large. This paper is organized as follows. The method is presented in section 2. Simulation examples will follow in section 3 to demonstrate the performance of the proposed method. Finally, conclusions will be drawn in section 4.
A New PSO-PID Tuning Method for Time-delay Processes
YANG Bo 1, LI Wan-zhou2 , YANG Feng2
1. Automation Business Unit ofCISDI Engineering Co., Ltd., Chongqing 400013, China
controllers for stable first order and high order systems with time delay. Using a first-order Pade approximation for the transport delay, this method is based on developing a certain relationship between the coefficients of corresponding powers of
(7)
G p (s) =
1 e − Ls as + b
It seems that if the corresponding coefficients of s, s2 and s3 of the numerator in Eq. (5) are equal to that of the denominator (Chidambaram et al., 2003), the output signal will quickly follow the input signal since G (s) becomes a constant 1. However, equation (5) is just an approximation of the closed-loop transfer function; the error will be very big using first-order Padé approximation in case of large L.
determining PID controller parameters have been developed over the past 60 years. Ziegler and Nichols (1942) give a method of tuning PI controllers empirically, however it gives very poor performance in the case of large dead time. The Smith predictor is well known to give a good performance for a stable process with long time delay (Smith et aI., 1959). However, the strategy is affected by the accuracy of the plant model and very sensitive to modeling errors. Imprecise parameters will result in bad dynamic performances or instability of systems. There are also some robust PID tuning methods for plants with long time delay, such as method proposed by Smith, C.A. et aI. (1997) and IMC-PID method proposed by Rivera et aI. (1986). Nevertheless their dynamic performances are not good enough. Particle swarm optimization (PSO) algorithm is an evolutionary computation technique developed by Kennedy and Eberhart (1995). PSO and other improved PSO algorithms are combined with PID controllers to optimize PID parameters by Z. L. Gaing (2004) and other authors. These methods always directly select PID parameters to compose a particle. Because PID parameters may range from zero to positive infinity, it is not easy to find the global optimum solution. Padma Sree et aI. (2003, 2004 and 2005) have proposed a simple and robust method of tuning PID controllers, which was originally applied to integrator/dead-time processes. They extended it to stable and unstable FOPTD systems in the year of 2004. However, they can only give some empirical formulas for FOPTD systems with quite short time delay, which is no bigger than 1 second. A novel PID tuning method for stable processes with time delay is proposed in this paper based on the scheme of