Cascade controllers design based on model matching in frequency domain for stable and integrating processes with time delay

Abstract

Purpose This paper aims to present an efficient and simplified proportional-integral/proportional-integral and derivative controller design method for the higher-order stable and integrating processes with time delay in the cascade control structure (CCS). Design/methodology/approach Two approaches based on model matching in the frequency domain have been proposed for tuning the controllers of the CCS. The first approach is based on achieving the desired load disturbance rejection performance, whereas the second approach is proposed to achieve the desired setpoint performance. In both the approaches, matching between the desired model and the closed-loop system with the controller is done at a low-frequency point. Model matching at low-frequency points yields a linear algebraic equation and the solution to these equations yields the controller parameters. Findings Simulations have been conducted on several examples covering high order stable, integrating, double integrating processes with time delay and nonlinear continuous stirred tank reactor. The performance of the proposed scheme has been compared with recently reported work having modified cascade control configurations, sliding mode control, model predictive control and fractional order control. The performance of both the proposed schemes is either better or comparable with the recently reported methods. However, the proposed method based on desired load disturbance rejection performance outperforms among all these schemes. Originality/value The main advantages of the proposed approaches are that they are directly applicable to any order processes, as they are free from time delay approximation and plant order reduction. In addition to this, the proposed schemes are capable of handling a wide range of different dynamical processes in a unified way.

Improved control of integrating cascade processes with time delays using fractional-order internal model controller with the Smith predictor

“…A series plant, G p1 (s) = e À0:7s =s 2 and G p2 (s) = e À0:3s =(s + 1) was studied by C xakırog˘lu et al 14 and Siddiqui et al 16 In C xakırog˘lu et al, 14 the output decomposition method is presented with two outer-loop controllers, G c1a (s) = 0:833 and G c1b (s) = 0:333, and inner controller as G c2 (s) = 3:33s + 1=s. Whereas in Siddiqui et al, 16 G c2 = 3:74 + 7:95=s and G c1 = 0:16 + 0:02=s + 0:56s were suggested. After adopting the proposed controller, l = 1:28 and b = 1:02 are obtained from the chosen g m = 2:5 and f m = 52:288.…”

“…One can see From Figure 17, it can be inferred that the maximum permitted perturbation is 70% because any additional rise in perturbation causes output from the system to become excessively oscillatory. When we tested the methods under the measurement noise with variance = 0.001, Siddiqui et al's 16 method obtained large variations in a control signal. The noise test also proved the proposed scheme's robustness as per Figures 18 and 19.…”

“…Recent works presented by Siddiqui et al, 16,37 Raja and Ali, 15 Çakıroğlu et al, 14 Jeng, 13 Padhan and Majhi, 11 and Uma et al 10 were considered for comparative analysis. The response parameters such as rise time ( t r ) , settling time ( t s , s), and integral of time-weighted squared error (ITSE) are calculated to demonstrate performances.…”

“…A modified cascade controller is based on the method of moments and the Routh stability criterion developed in Raja and Ali. 15 Recently, a frequency domain method with model matching was discussed for cascade controllers 16 in a nonlinear continuous stirred tank reactor.…”

“…Figure 19. Control responses with measurement noise for Example 2: (a) proposed, (b) proposed with f s , (c) C xakırog˘lu et al, 14 and (d) Siddiqui et al-2 16. …”