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This study investigates the design of a field-programmable gate array-based custom computer architecture solution for implementing model predictive control (MPC). The solution employs a primal logarithmic-barrier interior-point algorithm in order to handle actuator constraints. The solution also incorporates practical aspects of a control algorithm including state observation and data sampling. The resulting circuit is profiled by application to a disturbance rejection control problem of a 14th-order lightly damped flexible beam structure with actuator constraints. This is achieved at 2 kHz sampling frequency and with 16-sample prediction horizon.