![]() A Nichols plot is a transfer function’s gain plotted versus its phase. This paper illustrates a methodology for ensuring the stability of a flight con- trol system by performin g a formal analysis of a Nic hols plot using the MetiT arski automated theorem prover. The output of MetiTarski is a complete proof that contains alge- braic simplification and decision procedure calls that can be verified using other tools. It works by a combi- nation of resolution inference and algebraic simplification, invoking a decision procedure (QEPCAD) to prove polynomial inequalities over the real closed filed (RCF). MetiTarski is an automatic theorem prover for real-valued analytical func- tions, including trigonometric and exponential functions. This is one major hurdle that has limited the application of formal methods to the physical portion of aeronautical models. The tools and methods available for the formal verification of continuous and hybrid-systems cannot handle systems at the same level of complexity. ![]() Systems of large orders of magnitude can now be verified. There have been several breakthroughs in formal analysis of discrete systems. Unlike simulation, a formal proof is valid regardless of the input test cases. Formal verification is a method where logical reasoning can be used to prove that the implementation of a system correctly matches its design specification. It is therefore quite important to investigate methods that will reduce the effort and cost of the verification process while ensuring the reliability of the results. Secon d, to achie ve the F AA’s fail ure rate a complex m ulti-domain, labour intensive and costly process must be undertaken. There will always be the possibility of a catast rophic failure d ue to design errors. The first issue with this conclusion is that with simulation alone it is not possible to give 100% safety assurance due to the great number of variations of the model components and parameters. We present a case study of the proposed approach applied to the lateral autopilot of a Model 24 Learjet.Įven though there are over 78,000 flights without incident per day, we cannot assume that the current verification methods are perfectly sound. MetiTarski is then used to prove that the exclusion region is never entered. Next, using the conditions for a stable dynamical system, an exclusion region of the Nichols Plot is defined. ![]() First the transfer function for the flight control system is extracted from a Matlab/Simulink design. To leverage the safety verification problem, we present in this paper a method for per- forming a formal Nichols Plot analysis using the MetiTarski automated theorem prover. However, to guarantee stability within a certain margin of uncer- tainty requires an informal visual inspection of many plots. A Nichols plot is a tech- nique that can be used to conclusively determine if a control system is stable. ![]() Current aircraft control systems verification methodologies are based on conducting extensive simulations in an attempt to cover all worst-case scenarios. To ensure that an aircraft is safe to fly, a complex, lengthy and costly process must be undertaken. ![]()
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