Design of RTDA controller for industrial process using SOPDT model with minimum or non-minimum zero
Introduction
Most of the Industrial complex processes are non-linear and higher order in nature which can be approximated either by First order plus dead time (FOPDT) or Second order plus dead time (SOPDT) model structure [1], [2], [3], [4], [5]. In order to control the FOPDT or SOPDT model structures, the different control strategies are available in the literature. Among these, Proportional plus Integral plus Derivative (PID) and Model Predictive Control (MPC) controller are the popularly used in process industries. The main advantage of PID controller is simplicity, but unfortunately the tunable parameters are not directly related to performance attributes like robustness, disturbance rejection, set point tracking and overall aggressiveness of the controller [6], [7]. Similarly the performance of PID controller is not satisfactory especially on dead-time dominant, inverse response, non-linear and high order processes. On the other hand the Model predictive controller scheme is one of the popular control schemes for industrial processes [8], [9], [10], [11], [12]. It gives satisfactory performance in solving complex industrial problems due to its model predicting capabilities, but it requires solving an optimizing algorithm at every step, complex tuning procedures, etc. Due to the above-mentioned reasons it can be implemented in process industries as supervisory level mode only and the performance of the MPC directly depends on regulatory level PID controller performance. Even though many researchers are successful in reducing the computational complexity of MPC algorithm which is suitable for online control for a relatively fast system [13]. But still MPC is used in supervisory level in process industries due to the absence of flexibility in tuning parameter selection. Similarly, adaptive control, intelligent control, robust control and state feedback control are other popular control schemes alternative to PID control scheme [14], [15], [16], [17], [18]. The main problem of these controllers is the difficulty to tune like classical PID controller. Recently many research works are developed in the extension of PID control scheme into non-linear domain using multi-model approach [19], [20], [21]. But the main problem is the selection of scheduling variable and the switching of controller or control parameters when it changes from one operating point to another operating point.
Due to the above reasons, it leads to the invention of next generation alternative controller. Robustness, Set-point tracking, Disturbance rejection and Overall aggressiveness (RTDA) controller is considered as a next generation alternative controller which combines the features of MPC and PID controller. It retains simplicity of PID controller and superior performance like MPC controller [6], [7]. In the control law computation, RTDA controller incorporates model prediction control features. Ogunnaike is an innovator for RTDA control scheme [6]. He has demonstrated the design, implementation and performance of RTDA controller for First Order Plus Dead Time (FOPDT) process. Recently many researchers are working on the design of RTDA controller for different applications. Yelneedi et al. developed the RTDA and other advanced control schemes for regulation of hypnosis [22], [23]. They compared the designed RTDA control scheme with MPC and other conventional control schemes. Srinivasan et al. developed RTDA control scheme for FOPDT and SOPDT processes [24]. They have approximated the Second Order Plus Dead Time (SOPDT) process as a simplified FOPDT process and compared the performance of RTDA controller with MPC control scheme. Srinivasan and Anbarasan developed Fuzzy scheduled RTDA controller for pH neutralization process [25] in which a single controller is sufficient for the entire operating region. The gain and time constant variation at different operating regions are taken care by the variation of the robustness parameter which is adaptive in nature. In order to ensure bump less transfer, the different operating regions are combined using TS fuzzy gain interpolation techniques. Also they tested the applicability of proposed control scheme for different non-linear processes like conical tank and type I diabetic process.
Initially, MPC is designed based on FOPDT model and it is applied to different control applications [10], [15], [26]. This controller does not consider the effect of minimum or non-minimum zero and under damped characteristics of SOPDT models. Due to the above reason, this controller is not suitable for SOPDT model. Hence MPC algorithm is designed based on FOPDT model is modified, which is suitable for the SOPDT model is later proposed by Neshasteriz et al. [27]. In the same way, RTDA controller law proposed by Ogunaikae [6] is applicable only for process having FOPDT model structure.
All the research papers based on RTDA controller as stated above for different applications/concepts [6], [7], [22], [23], [24], [25] are based on the RTDA control law proposed by Ogunnaike [6]. This is applicable only for FOPDT model structure. As stated above, if the process is SOPDT or SOPDT with minimum or non-minimum zero, the RTDA controller designed based FOPDT model based control law cannot give satisfactory response.
Due to the above facts, we have attempted for the development of RTDA controller which is suitable for SOPDT model structure. In the development of RTDA controller design for SOPDT model which retains the advantage of RTDA controller proposed by Ogunnaike for FOPDT model structure like transparency and simplicity in tuning, all the tuning parameter values are normalized between 0 and 1 and independent tuning of servo and regulatory performance.
The main contributory features of this research paper are as follows: The design and development of process output prediction, model output prediction and model prediction update for different second order model structures like over-damped, under-damped and critically damped SOPDT process with minimum or non-minimum zero. The unique control law computation formula is developed for the above three processes. The closed loop equation and Block diagram for RTDA controller are developed. Theoretical stability derivation has been formulated and the design algorithm based on stability condition is developed. The performance of the RTDA controller design based on SOPDT model is compared with RTDA controller design based on FOPDT model. CSTR process is a highly dynamic non-linear process and is considered as one of the benchmark problems for control community to validate the control algorithm [27], [28], [29]. Finally the proposed RTDA control scheme is demonstrated on Industrial CSTR process and its performance is compared with DMC based MPC controller.
The paper is organized as follows. Section 2 describes the design and development of RTDA control scheme for SOPDT process and the validation of the proposed RTDA control scheme on different second order structures through simulation examples. The formulation of theoretical stability derivations for RTDA controller based on SOPDT process, the design algorithm based on stability considerations for implementation of RTDA control scheme, closed loop representation of RTDA controller and comparison of RTDA controller with Smith Predictor Controller (SPC) and Internal Model Controller (IMC) are reported in Section 3. Also the performance comparison of RTDA controller based on SOPDT model with DMC based MPC, PID, SPC and IMC controller is reported in the same Section 3. Section 4 focuses on the design of RTDA controller, DMC based MPC controller and PID controller for Industrial non-linear CSTR process. Conclusion of the proposed control scheme is discussed in Section 5.
Section snippets
SOPDT model with zero
The standard form of Second Order Plus Dead Time (SOPDT) process with process gain(K), pseudo time constant(τ) damping coefficient(ξ), dead time(td) and a minimum or non-minimum zero (c) is given bywhere y(s) is the process output and u(s) is the process input. Discretization [1] of Eq. (1) yieldsm=round (td/T) is the delay period and T is the sampling time. The coefficients l1, l2, r1 and r2 for the three categories of
Theoretical stability analysis
Theoretical stability analysis for RTDA control scheme based on SOPDT process transfer function is derived based on actual plant and nominal model. The mismatch occurs between true plant and nominal model due to non-linearity and other uncertainty during identification.
RTDA controller design for continuous stirred tank reactor (CSTR)
CSTR is considered as one of the benchmark setups for control community to validate control algorithm [27], [28], [29] and the dynamic behavior of CSTR process is underdamped in nature. The proposed RTDA control scheme performance is tested on dynamic non-linear CSTR process. The non-linear first principle model of the CSTR process is considered as true plant. State and sensor noise are added with the simulation of non-linear differential equation in order to reflect the real time process. The
Conclusion
In this paper, a simple and straight forward RTDA control law computation formula for second order plus dead time process with minimum or non-minimum zero is developed. Due to the simplicity in control law computation it can be implemented in regulatory level mode of Distributed Control System (DCS). The developed tuning formula is applicable to any standard SOPDT model structures and ARMA(2) discrete process models. Stability analysis for RTDA control scheme based on SOPDT process is
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