Time delay compensation for the secondary processes in a multivariable carbon isotope separation unit
Highlights
► A novel control strategy for multivariable time delay processes is proposed. ► Control strategy suitable for a general class of chemical processes. ► Proposed control strategy is compared with the “in house” EPSAC controller. ► Robustness test for significant time delay uncertainties.
Introduction
Time delays are frequently encountered in process control loops (Normey-Rico and Camacho, 2008), especially in chemical processing units such as distillation plants, oil fractionators, reactors or isotope separation plants (Stephanopoulos, 1984, Wang et al., 2000). Variable time delays in feedback control loops are challenging for the purpose of optimum process operation, since they limit the degree of freedom for the control action. Additionally, most industrial plants have a nonlinear and multivariable nature. Hence, control algorithms designed for such plants must cope with a manifold of dynamic challenges and constraints.
A commonly applied solution for the time delay compensation problem for SISO processes has been firstly mentioned by Smith (1957). The proposed control structure has the great advantage of removing the delay from the closed-loop characteristic equation, with significant improvement of the setpoint tracking response performance. An extension of the SISO Smith predictor to multivariable systems has been proposed firstly for MIMO systems with single delay (Alevisakis and Seborg, 1973) and then for multiple delays (Ogunnaike and Ray, 1979). Improvements have been made to the overall performance of the MIMO Smith predictor (Jerome and Ray, 1986). A key element in all these MIMO Smith predictors is the decoupling of the process. Different strategies have been used for the design of the decoupling matrix. A modified form of the MIMO Smith predictor for processes with multiple time delays has been used by Wang et al., (2000), in which the design of the decoupling matrix is based on a frequency domain approach. Later, the internal model control (IMC) method has been used for the same decoupling matrix (Wang et al., 2002). Seshagiri and Chidambaram (2006) extend the MIMO Smith predictor structures to nonsquare processes represented by first order transfer functions and time delays. The decoupling is done only in steady state by using the pseudo-inverse of the steady-state gain matrix; the final controller, consisting of a matrix of PI's, is then computed using the Davison method (Davison, 1976). Robustness issues are usually tackled by filter design methods. Chen et al. (2011) start from the previously designed MIMO Smith predictor for the same type of nonsquare processes, but claim that an IMC approach smoothes the design burden for the final PI matrix of controllers and also leads to better robustness.
In this paper, we propose an improved variant of the method of Chen et al. (2011). The original method is altered by using the designed decoupling matrix as a pre-compensator. The designed IMC controller can then be directly used as a final controller, rather than as a means to compute the final PI controller matrix. The proposed method offers in this way a simplified and straightforward approach to the design of the controller. Also, the method is extended for a more general class of processes, rather than the simple first order transfer function tackled by both (Chen et al., 2011, Seshagiri and Chidambaram, 2006). For comparison, we introduce an alternative approach to time delay compensation using a model based predictive control (MPC) algorithm (Allgöwer and Zheng, 2000, Camacho and Bordons, 2004). The MPC controller implemented on the plant is the EPSAC—Extended Prediction Self-Adaptive Controller (De Keyser and Van Cauwenberghe, 1981, De Keyser, 2003). The choice for the predictive controller relies upon its inherent time delay compensation properties, as well as to the adaptive characteristics that usually trigger an increased closed loop robustness to time delay uncertainties.
The paper is organized as follows: In Section 2, the method proposed in this paper is described, as compared to the original one (Chen et al., 2011). Section 3 presents the process under study in this paper, a carbon isotope separation pilot plant. Section 4 presents the design using the IMC-Smith predictor structure for the carbon isotope separation process, while Section 5 presents the EPSAC–MPC approach. Section 6 presents comparative results using the IMC controller and the EPSAC controller. The final part contains the conclusions and some discussions.
Section snippets
Original dead time compensation method for MIMO first order time delay systems: PI controller matrix
Since in this paper the multivariable time delay process is a square one, the original mathematical formulae (Chen et al., 2011) are modified for controlling these types of processes (Stephanopoulos, 1984, Wang et al., 2008). Nevertheless, the approach for non-square systems will be tackled in a subsequent section of the paper.
For a general square process with ‘m’ inputs and ‘m’ outputs, the transfer function matrix is given as (Chen et al., 2011, Seshagiri and Chidambaram, 2006):
The carbon isotope separation process
The majority of chemical elements that exist in the universe have two or more isotopes. Among these, carbon represents the fourth most abundant chemical element, having two stable isotopes. The least abundant of the carbon stable isotopes, 13C has a natural amount fraction of approximately 1.1%; however, it is also the most used in a wide variety of industrial fields and especially medicine (Dulf et al., 2008, Dulf et al., 2009b. Carbon isotopes can nowadays be separated using many methods, one
Design of the proposed control structure—application example
In this section, the delay compensator described in Section 2.2 is derived for the secondary processes in the carbon isotope separation column, described by the transfer function matrix given in (15′).
The steady state gain matrix of the process in (15′) iswith its inverse being equal to
The decoupled process is represented bywith
Alternative control algorithm for dead time processes: the EPSAC–MPC approach
To compare the results obtained using the decoupling technique in Section 4, we design a predictive control strategy based on the in-house EPSAC–MPC methodology (De Keyser and Van Cauwenberghe, 1981, De Keyser, 2003). The choice of the predictive controller is based on its inherent dead-time compensation, thus making it a suitable choice for the control of multivariable dead-time processes (Allgöwer and Zheng, 2000, Camacho and Bordons, 2004, Normey-Rico and Camacho, 2008). The different
Results
The considered scenarios include reference tracking for nominal case, disturbance rejection and a ‘worst case’ scenario for reference tracking in which the time delays are varied ±50%.
The first scenario, for nominal case reference tracking, in which the y2 reference is changed at 100 min simulation time, is given in Fig. 10.
The two control strategies offer similar results in terms of overshoot and settling time. The IMC method and decoupling strategy works well in decoupling the y3 output from
Conclusions
The control method described in this paper is based on the Smith predictor for MIMO systems, using a primary controller designed according to the IMC tuning rules. The decoupling matrix used in the IMC strategy is considered as a pre-compensator, rather than part of the controller, while the IMC controllers are used directly in the closed loop scheme, rather than as a method to compute the PI controller matrix. The main advantage of the method, as compared to the similar method (Chen et al.,
Nomenclature
- Gp(s)
process transfer function matrix
- Gm(s)
model of the process transfer function matrix
- gij
single input single output transfer functions
- τ
time delay
delay free model of the process
- Gm(s=0)
steady state gain matrix of the process
inverse of the steady state gain matrix
- GD(s)
decoupled process transfer function matrix
diagonal terms in GD(s)
approximations of the diagonal terms in GD(s)
- IMC
internal model controller
IMC filter time constant
- PI
proportional integrative controller
- t
time
- s
Acknowledgment
C.M. Ionescu is a postdoctoral fellow of the Flanders Research Foundation (Belgium). This work was supported by UEFISCDI, project PN-II-PT-PCCA-201-3.2-0591.
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