Quantized Feedback Control Software Synthesis from System Level Formal Specifications

Many Embedded Systems are indeed Software Based Control Systems (SBCSs), that is control systems whose controller consists of control software running on a microcontroller device. This motivates investigation on Formal Model Based Design approaches for automatic synthesis of SBCS control software. In previous works we presented an algorithm, along with a tool QKS implementing it, that from a formal model (as a Discrete Time Linear Hybrid System, DTLHS) of the controlled system (plant), implementation specifications (that is, number of bits in the Analog-to-Digital, AD, conversion) and System Level Formal Specifications (that is, safety and liveness requirements for the closed loop system) returns correct-by-construction control software that has a Worst Case Execution Time (WCET) linear in the number of AD bits and meets the given specifications. In this technical report we present full experimental results on using it to synthesize control software for two versions of buck DC-DC converters (single-input and multi-input), a widely used mixed-mode analog circuit. 1 ar X iv :1 10 5. 56 40 v5 [ cs .S Y ] 2 0 Ju n 20 12 1. Every T seconds (sampling time) do 2. Read AD conversion x̂ of plant sensor outputs x 3. If (x̂ is not in the Controllable_Region) 4. Then // Exception (Fault Detected): 5. Start Fault Isolation and Recovery (FDIR) 6. Else // Nominal case: 7. Compute (Control_Law) command û from x̂ 8. Send DA conversion u of û to plant actuators Figure 1: A typical control loop skeleton