CVXGEN Case Study

CVXGEN is introduced by Mattingeley and Boyd in 2011 as a convex optimisation solver. It fulfil the requirements making embedded optimisation possible [39]. First and foremost, the user has to declare the QP problem in CVXGEN specification language. CVXGEN then will translate the QP problem and generate light weight custom C solver. Given its fast and small code size, the user can apply the solver in various kind of embedded system as CVXGEN targets small-sized problems [31], [39], [40].
CVXGEN is a custom code generation solver. Consequently, the QP problem needs to be specified in CVXGEN. Dimensions, variables and parameters are needed to state clearly in CVXGEN. The control objective of MPC is to control the actuator so it tracks the planned
DAQ system connects the hardware and the computer by converting sensor data into interpretable signals for the computer to process it. A National Instruments product, PCI-6221 DAQ system is used in this experiment. It has a maximum sampling rate of 250 kHz. It supports up to 16 analogue inputs and outputs, and 24 digital inputs and outputs.

There are several input signals which have been widely used by many other researchers. For example, Pseudo Random Binary Sequence (PRBS), sinusoidal, multi-sine, step, continuous step and etcetera. In this study, multi-sine, continuous step and PRBS are selected as input signals. A function of multi-sine with three different frequencies, 0.05Hz, 0.2Hz and 1Hz is used as the input signal. The equation is given and shows as below.

Since impulse signals are hard to generate and might cause problem to the control plant, PRBS is introduced to mimic the behaviour of impulse signal. PRBS is also used in the experiment for system identification. PRBS is a binary sequence and considered to be similar to truly random sequence within a range of frequencies. A RPBS contains full range of frequencies is known as Maximum Length Sequence (MLS), or in short, M-sequence