## 1 Introduction  
Proportional-Derivative-Integral (PID) control is the most popular and typically the default controller of choice by most practitioners for most industrial processes. This is especially true for Single-Input, Single-Output (SISO) processes. As such, advanced control schemes, such as MPC, are generally reserved for large Multi-Input Multi-Output (MIMO) systems. To justify the default adoption of PID control, there is often the argument that PID's popularity is due to its simplicity and ability to regulate most processes with a decent performance. However, some studies have shown that many industrial loops controlled using PID operate far from optimally [1, 2]. This observation could be due to practitioners' default choice of PID, even on non-suitable processes. Therefore, we believe that advanced control could benefit low-performing loops if applied to suitable processes, even in the SISO case. Model predictive control (MPC) is the most successful industrial advanced control scheme. The success of MPC has been attributed to factors, such as its inherent ability to deal with constraints, handle process interaction and accommodate dead time. Therefore, MPC is a good replacement when PID fails to give good performance. Much work has been done to propose MPC as a replacement for PID control [3, 4, 5, 6]. Moreover, MPC has demonstrated improved performance for a certain class of SISO systems, such as dead-time dominant systems [7, 8, 9]. A significant of processes can be approximated using second-order models. Hence, the behavior of the Second Order Plus Deadtime (SOPDT) system models is crucial in studying control systems performance. In the control of SOPDT systems, two parameters affecting system response and performance are the process dead time and the damping ratio. Therefore, studying the effects of varying these two parameters with different control techniques could give insight into which control scheme is more suitable for specific parameter values. Earlier works have focused on studying the relative performance of PID and MPC due to a single process parameter. For example, [7], PID and MPC are compared for different dead-time to time-constant ratio values. The study demonstrated that MPC outperformed PID in dead-time dominant systems, even in the SISO, non-constrained case. Similarly, it was demonstrated in [8] that, even for small dead-times when the process model was well defined, using a complex controller, such as MPC, was justifiable. However, it was argued that PID equipped with anti-windup for robust implementations provided comparable or superior performance. [PERSON] [10] tuned PID controllers for five different systems (first, second, third, fourth and fifth order) using Bacterial Foraging Optimization (BFO) and compared them with results obtained using MPC. The work demonstrated improved performance with MPC in all the considered case studies. However, the results could not be generalized for any of the class of systems considered as the case studies used do not capture the entire spectrum of system model parameters. In [11], the relative performance of MPC and PID in Continuous Stirred Tank Reactor (CSTR) process control was studied. In this application, MPC improved in maintaining the reactor temperature at a predefined setpoint. The success of MPC was attributed to its anticipatory capability of MPC due to its inherent prediction capabilities. Despite the recent adoption of MPC in diverse fields of application, it is still more prevalent in the process and industries. An area where MPC is finding more applications is the field of robotics and biomedical engineering. In [12], the performance of PID and MPC to control upper limb rehabilitation robots was studied. The results demonstrated comparable results for the two controllers. However, PID outperformed MPC with the introduction of disturbances. But the PID controller suffered some setbacks due to noise, which was effectively handled by the MPC using Kalman filter.