IMC based Smith Predictor Design with PI+CI Structure: Control of Delayed MIMO Systems

MATEC Web of Conferences 4 2 , 0 1 0 1 1 (2016 ) DOI: 10.1051/ m atecconf/ 2016 4 2 0 1 0 1 1  C Owned by the authors, published by EDP Sciences, 2016 IMC based Smith Predictor Design with PI+CI Structure: Control of Delayed MIMO Systems 1,a 2 3 Ali Dokht Shakibjoo , Nastaran Vasegh and Hassan HosseinNia 1, 2 3 Departement of Electrical Engineering, Shahid Rajaee Teacher Training university, Tehran, Iran Departement of Precision and Microsystems Engineering, Delft University of Technology, The Netherlands Abstract. In this study a novel structure for time-delay MIMO systems controller design is introduced. In this method decoupled Smith predictor (SP) controller is designed using Internal Model Control structure (IMC). In order to approximate decoupled system, step response model approximation is employed and simulated on MIMO multiple time-delay system. Moreover, to improve system performance from overshoot and rise time perspective, Smith predictor controller is combined with PI+CI structure. Furthermore, to increase system robustness, a low pass filter is designed. Afterwards, the proposed structure is applied to the model of a time-delay MIMO distillation tower system and obtained results are compared to those of a PID controller. Finally, performance of different design methods is evaluated using Integral error criterion (Integral Square Error criterion). 1 Introduction Time delay is common in most of industrial processes. It basically results from information, mass and energy transfer phenomena which are known as groups of time delays in simple connected dynamic systems. Probing the impacts of disturbance is time consuming; thus, processes with significant time delay are difficult to be controlled by standard feedback controllers. A considerable amount of recent research works have focused on time delay as it is the most crucial factor affecting control quality. The first instance of time-delay compensator for classic control systems was introduced by Smith in 1957 called Smith predictor. Smith predictor aims to remove time delay from control loop. As a result a time-delay free section is achieved for which an ideal controller can be designed [1,2]. The PI+CI controller consists of two parallel PI and CI controllers [3]. Clegg Integral (CI) is the simplest structure for reset control which increases the phase of system and its stability. Reset action occurs when the input signal is set to zero. Additionally, CI is able to overcome limitations of LTI control system. It was firstly introduced by Clegg in 1985 [4]. To design PI+CI structure PI controller is designed in first step so that the most speed and overshoot could be achieved. Then, nonlinear reset mechanism is added to reduce overshoot. Changing reset coefficient which is between [0, 1], the best output, from performance indices perspective, might be derived. To date, most of the processes which have a been studied using Smith predictor were single input single output systems. Recently, PI+CI structure with Smith predictor control is designed for time-delay first order system [5]. However, this method is not simulated for MIMO systems. In this paper, Smith predictor controller is designed using internal model control structure. This structure is applied to a distillation tower system. To improve output response PI+CI controller is added. Finally, comparing simulation results to PID controller, the potential of this hybrid structure for improving performance indices of MIMO systems is discovered. After PI+CI structure and Smith predictor controller are introduced, the Smith predictor controller with Internal Model Control is designed in section 3. Afterwards, adjustment of PI+CI structure is discussed to improve system performance. Then, this structure is applied to a MIMO distillation tower system model. Also, results of desired system are compared to PID controller. At the end, the results are validated using Integral error criterion (Integral Square Error criterion). The final section concludes the paper. 2 Equivalent structure for Smith predictor controller with Internal Model Control In this study an equivalent structure of Internal Model Control together with a Smith predictor compensator are utilized. The structure is depicted in figure 1. Corresponding author: This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits    distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.matec-conferences.org or http://dx.doi.org/10.1051/matecconf/20164201011 MATEC Web of Conferences  g1m ( s )    g 2m ( s )       g mm ( s )   g 11( s ) g12 ( s )   g ( s ) g 22 ( s ) G( s )   21    g (s) g (s) m2  m1 According to the structure demonstrated in figure 1, Gnc ( s ) is Internal Model controller, Gc ( s ) is Smith predictor controller, G( s ) is the actual system, Gm ( s ) is system model, Gm0 ( s ) is the system model ignoring time Figure 1. Controller scheme It is a combination of both Internal Model Control structure (figure 2) and Smith predictor structure (figure 3) and takes advantage of these two structures simultaneously. delay and GF ( s ) is the filter. Initially, using the structure of Internal Model control Gnc ( s ) is designed. Subsequently, Smith predictor controller is derived from Internal Model Controller. Considering figure 1 we have: Gnc ( s )  Gc ( s ) 1 Gc ( s )G( s )  And consequently one may write: Gc ( s )  Gnc ( s ) 1  Gnc ( s )G( s )  To adjust parameters of Gc ( s ) controller, a first order time-delay system is assumed as follows: Figure 2. MIC scheme Ĝ( s )  Kes Ts 1  It could be separated as shown below: Ĝ( s )  Ĝ ( s )Ĝ ( s )  Ĝ ( s )  e s  Ĝ ( s )  Figure 3. Smith predictor scheme In the Internal Model Control structure disadvantages such as open loop system, sensitivity to modelling errors and lack of disturbance rejection ability are eliminated. In case of perfect matching between model and process, as well as no disturbance, the system operates as an open loop system which may achieve precise and rapid tracking; whereas, in presence of either mismatch between model and process, or disturbance entrance into the system, it operates as a closed loop system which is able to remove disturbance effects. In our research, the system is a time-delay one; therefore, equivalent structure of Smith predictor together with Internal Model Controller are exploited [6, 7]. K Ts 1  Ĝ ( s ) Includes all time delays and right half plane zeros. Modelling errors must be minimized in internal model controller. Notice that difference between model and process behaviour happens in high frequencies at the end of frequency response. Hence, a series low pass filter is utilized with Internal Model Controller to attenuate mismatch impact. F ( s ) is the simplest type of low pass fi (...truncated)