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ABSTRACTIMC-PID controllers provide good set point tracking but sluggish disturbance rejection, because of introduction of slow process pole by the conventional filter. In many industrial applications disturbance rejection is important than set point tracking. In this paper PID controller with Internal model control tuning method (IMC-PID) with an improved IMC filter is presented for effective disturbance rejection and robust operation of first order process with time delay (FOPTD). The suggested filter eliminates the slow dominant pole. The present study illustrates that the suggested IMC filter provides good disturbance rejection irrespective of where the disturbance enters the process and provides good robustness to model mismatch in terms of sensitivity in comparison with other methods cited in the literature. Simulation study was performed on processes with different θ/τ ratios to show the effectiveness of suggested method by calculating the controller parameters to have same robustness in terms of maximum sensitivity. The closed loop performance was tested using integral error criteria Viz. IAE, ISE, ITAE. The suggested IMC filter provides good disturbance rejection response for process having θ/τ< 1.

Robust MPC is an advanced control strategy to optimize control performance subject to the constraints of the system inputs/outputs and in the presence of bounded disturbance. Several alternative approaches of online robust MPC design based on LMI formulation are formulated. The proposed alternative approaches are based on existing approaches. Suitable properties of these approaches are adopted to reduce the conservativeness of the quadratic stability condition, to reduce the conservativeness of control inputs constraints evaluation, and to minimize a computational effort. Therefore, these alternative robust MPC methods may be considered as a tool for overcoming some of the robust MPC design obstacles. Simulation case studies are proposed to demonstrate the effectiveness of the proposed strategies.

Software MUP represents an efficient and user-friendly MATLAB-based toolbox for online robust MPC design in LMI-framework. The toolbox enables designing robust MPC using an all-in-one MATLAB/Simulink block. The advanced users may benefit from designing robust MPC using MATLAB Command-Line-Interface. One of the most valuable features is an advanced feasibility check, i.e., when the optimization problem is found infeasible, then we suggest to the user how to modify the robust MPC design problem to make it feasible. The MUP is dependent on the YALMIP toolbox that reformulates the optimization problem and delegates it to an external SDP solver, e.g., MOSEK or SeDuMi. An illustrative case study of robust MPC design for a real process is proposed to demonstrate the effectiveness of the MUP toolbox.

The LMI-based robust MPC design exercises are oriented on the implementation of simple robust MPC for the uncertain system with input and state constraints. Two approaches are considered, i.e., manual implementation and implementation using the MUP toolbox. The manual implementation aims to point out the key ideas of robust MPC design. On the other hand, MUP-based implementation demonstrates the efficacy of the software and enables the user to focus the attention on the robust MPC tuning to improve the closed-loop control performance. This task includes also some hints on how to solve the considered robust MPC design problem.

Chapters 2 and 3 discussed wide classes of process control problems that can be formulated using linear matrix inequalities. Chapter 7 considered State-Feedback Synthesis for the systems in the continuous-time domain.

System states have to converge into the origin in each control step. This paper considered the robust MPC design subject to the required value of states convergence just for the nominal system, i.e., system vertices were forced to converge without preset value.

Extension of Cao et al. (2005). The robust MPC design tuning parameter was introduced to set the weight of the constrained and non-constrained control action. It enabled to compute more aggressive control action when the control input is not constrained.

AbstractThe performance of the Proportional Integral Derivative (PID) controllers commonly used in process control industries depends upon the controller tuning parameters. In this paper an Internal Model Control (IMC) based PID controller is proposed to estimate controller tuning parameters in terms of single parameter, known as closed-loop time constant which provides improved performance and robustness to control system. An IMC based controller is designed and presented here for a coupled tank level control system which is of non-interacting type. The transfer function of the system is obtained from the equipment specifications. The obtained transfer function is approximated into first order plus delay time (FOPDT) model for the estimation of the IMC-PID controller tuning parameters in terms closed-loop time constant. The process is simulated in MATLAB/Simulink to record the closed-loop performance with IMC-PID based tuning parameters. The result are compared with the Ziegler-Nichols, Cohen-Coon and Tyreus-Luyben tuning methods in terms of time response characteristics and various performance Indices like Integral of Absolute Error (IAE), Integral Squared Error (ISE) and Integral Time Absolute Error (ITAE). The robustness is checked by incorporating uncertainties in the process. The results indicate PID controller tuned with IMC has better performance and robustness as compared to other tuning techniques.

PID Controllers are extensively employed in process control industries because of their relatively simple structure and design. Tuning technique is adopted for determining the proportional, integral and derivative constants of these controllers which depend upon the dynamic response of the plants. Ziegler-Nichols and Cohen-Coon [1-3] tuning methods are the most popular methods used in process control to determine the parameters of a PID controller. Although these methods are very old, they are still widely used because of their capability to achieve desired optimal performance for specific inputs with less tolerance to plant variations. PID controller tuned with these methods shows less robust results. A controller is said to be robust if it is insensitive to small changes in process or to inaccuracies in process model. Robustness can be defined as amount of Uncertainty in process parameters or inaccuracy in Process model that can be tolerated by controller before the closed-loop system becomes

unstable [4-5]. In reality a, model is never perfect, so controllers must be designed to be robust (to remain stable even when the true plant characteristics are different from the model). Internal model control (IMC) based PID controller has gained attention because of its robustness and single tuning parameter selection [6-7].

Maintaining the level at a desired state is an important and common task in all process industries. IMC based PID controller is developed in this paper to control the liquid level in the coupled tank system. Among the other tuning methods, IMC based PID controllers tuning methods has gained widespread acceptance in the process industries because of its easy in design and simple in understand, robustness and fast in real time applications.

Internal Model Control (IMC) has been presented by Garcia and Morari [6] which is developed upon Internal Model principle to combine the process model and external signal dynamics. The IMC controller is a model based procedure, where a process model is embedded in the controller, and is considered to be robust. Mathematically, robust means that the controller must perform to specification, not just for one model but also for a set of models [4]. The IMC controller design philosophy adheres to this robustness by considering all process model errors as bounded and stable. IMC Theory states that a perfect control can be achieved only if the control system encapsulates, either implicitly or explicitly, some representation of the process to be controlled.

The IMC basic structure is shown in Fig.3 is characterized by a controller Gc(s), actual process or plant Gp(s) and predictive model of the plant Gp(s). d(s) is an unknown disturbance affecting the system. The manipulated input U(s) is introduced to both the process and its model. The process output is Y(s). d*(s) is the difference between the output of the actual process Gp(s) and process model Gp(s)which is the result of model mismatch and the disturbances; this is used by the internal model controller.

The design procedure of IMC involves factorization of the plant model Gp(s) as invertible Gp (s) and non- invertibleGp + (s) parts as shown in Eq. (1) by simple factorization or all pass factorization. Ideal IMC controller Gc(s) is the inverse of the invertible portion Gp (s) of the process model Gp(s).

]In IMC based PID design procedure Gc(s) is made semi proper or even improper to give the resulting PID controller derivative action. A first or second order pade approximation is used if a process model has a time delay. The standard PID

The robustness testing of IMC tuned PID Controller was evaluated by incorporating uncertainty in the actual process by a factor of 20% and 25% in gain(), delay time() and time constant().Results in Table 4-9 and simulation responses Fig.11-16 were presented to show the robustness of IMC tuned PID Controller in comparison with other tuning techniques.

Coon and Tyreus-Luyben are considered for PID Controller and are comparatively analyzed based on performance and robustness. From Table 3 it is evident that IMC based PID tuning provides better time response characteristics i.e. optimum settling time and reduced overshoot as compared to other tuning methods. Table 3 and Fig.6-8 also shows that IMC based PID tuning exhibits minimum Integral error criterias i.e. ISE, IAE and ITAE compared to other tuning methods. Simulation responses in Fig.9 and Fig.10 shows that IMC-PID tuning has better set-point tracking and disturbance rejection capability than other tuning methods. The Robustness of IMC tuned PID Controller was tested by incorporating uncertainty in the actual process by a factor of 20% and 25% in gain(), delay time() and time constant().Results in Table 4-9 and simulation responses in Fig.11-16 indicates that IMC based PID tuning shows robust performance in Comparison with other tuning techniques. It is evident from the robustness analysis that Gain Margin is related to the amount of gain uncertainty that can be tolerated, and the Phase Margin is related to the amount of delay time uncertainty that can be tolerated. Therefore we can say that Gain and Phase Margin indicates the Robustness of the Controller. The result can be found from Table 3 that as we increase the value of the Gain and Phase Margin values increases which indicates Robustness increases. Decreasing the value of makes the closed-loop response fast whereas increasing its value makes the closed-loop system more robust. Hence, the IMC based PID controller tuning has the advantage of using only a single tuning parameter () whose value is adjusted to achieve a clear trade-off between the closed loop performance and robustness. 2b1af7f3a8