In way to model and analyse systems with

In control engineering, a state space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. However, for systems with multiple inputs and outputs, description of such systems with differential equations are often time intense and burdensome. So, state space representation of the systems serves as alternative approach to alleviate the challenges. In addition, the state space representation of a system replace the higher-order differential equations with a single first-order matrix differential equation that  gives an expedient and concise way to model and analyse systems with multiple inputs and outputs. The state model is notably advantageous when applied to simulation. Hence, the state and output equations are given in 18 as:1.pring damper systems using SimElectronics A coupled mass spring damper system is modeled and simulated using SimElectronics toolbox in MATLAB software. In MATLAB software, SimElectronics is a components libraries and special simulation features for modeling and stimulating physical system in the Simulink environment. The distinct feature of SimElectronics is the use of physical network approach to model electronic and mechatronic systems which mimic the physical system. Therefore, the use of physical connection permits a bidirectional flow of energy between components. The SimElectronics permit the use of Simulink library in modeling in which Simulink-PS-converter block converts the Simulink signal to physical system signal and PS-Simulink converter block does the reverse19.Simulink is a block diagram environment embedded in the MATLAB that allows model, simulate and analyse multi-domain dynamics systems. For modeling, Simulink provides a graphical user interface (GUI) for building models as block diagram. In the light of this, it provides detailed function of each block that represent the mathematical model of the dynamic system and such model is often reduced to first order differential equation to simulate the dynamic accurately. It is dominant among other softwares in engineering field because it enables rapid design, simulation, verification, testing and debugging of virtual prototypes of a model prior to real time implementation. As a result of flexibility and efficient in use, it permits conversion of MATLAB code to other source codes such as C, C++  for real time implementation especially in embedded systems and robotic. Simulink model of a coupled mass spring damper system is prepared with mathematical model presented through equations (21) and (22). PD controller is implemented to control the masses position,