The dynamic controller and the dynamic model can be built within the Matlab environment. The model is built in SimMechanics while the controller is built in Simulink. SimMechanics disposes of a library from which different bodies, constraints, joints, drivers, force elements, actuators, and sensors can be selected and used to synthesize models of multi-body system. The ground block defines the ground and the world coordinates. The coordinates of the center of gravity (COG) can be provided in each body block. In this way bodies can be placed within the 3-D space. Bodies are connected to each other by means of joints, force elements or constraints/drivers. It is possible to obtain different properties such as positions and speeds and plot the results with respect to the time, or actuate bodies with e.g. torques. Joints can be actuated and their position can be obtained. The model is described by a right- handed orthogonal set of axes and the coordinates and angles are defined. It is essentials to note that blocks in SimMechanics do not model mathematical functions directly; instead they have specified physical meaning.
The SimMechanics toolbox can be used both to calculate the forces that are required to realize specified movement and to calculate the movement that is the result of forces applied. The type of analysis must be chosen for selecting what to calculate. SimMechanics provides four modes for analyzing mechanical systems:
• Forward dynamics calculates the motion of the mechanism resulting from the applied torques or forces and constraints;
• Inverse dynamics finds the torques or forces necessary to produce a specified motion for open loop systems;
• Kinematics does the same for closed loop systems including the extra internal invisible constraints arising from those structures;
• Trimming searches for equilibrium or steady states of a system’s motion with the Simulink trim command. It is used mostly to find a starting point for linearization analysis.
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