Continuous versus discrete sliding mode control as applied to a pneumatic positioning system

Presented in this thesis is the development of a practical set of design guidelines to improve the performance of pneumatic positioning systems by appropriate sizing of the valve and the cylinder, and by careful choice of the tuning parameters for Continuous Sliding Mode (CSLM) and Discrete Sliding Mode (DSLM) controllers. CSLM and DSLM were selected because of their robustness in the presence of nonlinearities such as those found in a pneumatic positioning system.; Pneumatic systems exhibit parameter variations along the length of the stroke due to air compressibility. The size ratio (area to stroke) of the cylinder was found to dictate the limitations on the sampling time for adequate performance with a linear controller. A technique to identify the ultimate gain is presented, in order to illustrate how system stability varies with piston position and cylinder size ratio. Finally, the effect of the cylinder size ratio, valve port area and valve configuration on system performance with a linear Proportional-Velocity-Acceleration (PVA) controller is documented.; The first nonlinear controller investigated was CSLM. Techniques for the design of the sliding surface, the selection of the boundary layer thickness and sliding gain, as well as the effect of the equivalent gain, were investigated and a comprehensive design procedure was developed. With CSLM, the sliding surface design can be linked to familiar time domain performance parameters, but its performance is limited to relatively small sampling times. The robustness of CSLM in the context of its ability to maintain specified overshoot and settling time was tested by changing the payload mass.; The second nonlinear controller investigated was DSLM which is intended for discrete implementation and consequently takes explicit account of the sampling time. Techniques for the design of the controller are presented that are based on a compilation of existing methods, but with new features added for sliding surface design and controller tuning. The main contributions are: (1) the design approach for the sliding surface, where a link to time domain performance is established, and (2) the switching elements of DSLM which are selected by means of a classical linear controls approach. Finally, an original set of comprehensive design guidelines for DSLM are documented.; Following a set of experimental tests to validate the system model, a series of additional robustness tests were performed in simulation. These tests were designed to further verify the performance of the linear PVA and the nonlinear CSLM and DSLM controllers in the presence of model errors such as incorrect bore size and incorrect stroke length. In conclusion, DSLM was found to be the more robust of the three controllers for large sampling times. On the other hand, CSLM was competitive with DSLM for small sampling times.