engineering

PID Controller Tuner

Automatic PID tuning using Ziegler-Nichols (open-loop and closed-loop) and Cohen-Coon methods with step response comparison chart

Reviewed by Christopher FloiedPublished March 31, 2026Updated May 21, 2026

This free online pid controller tuner provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Supports both metric (SI) and imperial units with built-in unit selection dropdowns on every input field, so you can work in whatever units your problem provides. Designed for engineering students and professionals working through coursework, design projects, or quick reference calculations.

PID Controller Tuner

Automatic PID tuning using Ziegler-Nichols and Cohen-Coon methods. Plant: FOPDT G(s) = K/(Ts+1).

Plant Gain K

Dead Time L (s)

Time Constant T (s)

3.6000

Ki (1/Ti)

1.0000

1.0000 s

Kd (Td)

0.2500

Step response comparison (1st-order plant simulation)

Step Response Data Table

t (s)	Open-loop y	With PID y
0.000	0.00667	0.19073
0.010	0.01331	0.17785
0.020	0.01993	0.19931
0.030	0.02653	0.21452
0.040	0.03311	0.23040
0.050	0.03967	0.24579
0.060	0.04620	0.26089
0.070	0.05272	0.27567
0.080	0.05921	0.29015
0.090	0.06568	0.30434
0.100	0.07212	0.31823
0.110	0.07855	0.33183
0.120	0.08495	0.34516
0.130	0.09134	0.35821
0.140	0.09770	0.37100
0.150	0.10404	0.38352
0.160	0.11036	0.39578
0.170	0.11666	0.40779
0.180	0.12294	0.41956
0.190	0.12919	0.43108
0.200	0.13543	0.44237
0.210	0.14165	0.45342
0.220	0.14784	0.46425
0.230	0.15401	0.47486
0.240	0.16017	0.48524
0.250	0.16630	0.49542
0.260	0.17241	0.50538
0.270	0.17850	0.51514
0.280	0.18458	0.52470
0.290	0.19063	0.53407
0.300	0.19666	0.54324
0.310	0.20267	0.55222
0.320	0.20866	0.56102
0.330	0.21463	0.56964
0.340	0.22058	0.57808
0.350	0.22651	0.58635
0.360	0.23243	0.59445
0.370	0.23832	0.60238
0.380	0.24419	0.61015
0.390	0.25004	0.61776
0.400	0.25588	0.62522
0.410	0.26169	0.63252
0.420	0.26748	0.63967
0.430	0.27326	0.64668
0.440	0.27902	0.65354
0.450	0.28475	0.66027
0.460	0.29047	0.66685
0.470	0.29617	0.67330
0.480	0.30185	0.67962
0.490	0.30751	0.68580
0.500	0.31315	0.69187
0.510	0.31877	0.69780
0.520	0.32438	0.70362
0.530	0.32996	0.70932
0.540	0.33553	0.71490
0.550	0.34108	0.72036
0.560	0.34661	0.72572
0.570	0.35212	0.73096
0.580	0.35761	0.73610
0.590	0.36309	0.74114
0.600	0.36854	0.74607
0.610	0.37398	0.75090
0.620	0.37940	0.75563
0.630	0.38480	0.76026
0.640	0.39019	0.76480
0.650	0.39555	0.76925
0.660	0.40090	0.77360
0.670	0.40623	0.77787
0.680	0.41154	0.78205
0.690	0.41684	0.78615
0.700	0.42212	0.79016
0.710	0.42737	0.79409
0.720	0.43262	0.79794
0.730	0.43784	0.80171
0.740	0.44305	0.80541
0.750	0.44824	0.80903
0.760	0.45341	0.81257
0.770	0.45857	0.81605
0.780	0.46370	0.81945
0.790	0.46883	0.82278
0.800	0.47393	0.82605
0.810	0.47902	0.82925
0.820	0.48409	0.83238
0.830	0.48914	0.83545
0.840	0.49418	0.83846
0.850	0.49919	0.84141
0.860	0.50420	0.84430
0.870	0.50918	0.84713
0.880	0.51415	0.84990
0.890	0.51911	0.85261
0.900	0.52404	0.85528
0.910	0.52896	0.85788
0.920	0.53387	0.86044
0.930	0.53875	0.86294
0.940	0.54362	0.86539
0.950	0.54848	0.86779
0.960	0.55332	0.87014
0.970	0.55814	0.87245
0.980	0.56294	0.87471
0.990	0.56774	0.87692
1.000	0.57251	0.87909
1.010	0.57727	0.88122
1.020	0.58201	0.88330
1.030	0.58674	0.88534
1.040	0.59145	0.88734
1.050	0.59614	0.88930
1.060	0.60082	0.89122
1.070	0.60549	0.89310
1.080	0.61013	0.89494
1.090	0.61477	0.89675
1.100	0.61938	0.89852
1.110	0.62399	0.90025
1.120	0.62857	0.90195
1.130	0.63315	0.90361
1.140	0.63770	0.90525
1.150	0.64224	0.90685
1.160	0.64677	0.90841
1.170	0.65128	0.90995
1.180	0.65577	0.91145
1.190	0.66026	0.91293
1.200	0.66472	0.91437
1.210	0.66917	0.91579
1.220	0.67361	0.91718
1.230	0.67803	0.91854
1.240	0.68244	0.91987
1.250	0.68683	0.92118
1.260	0.69121	0.92246
1.270	0.69557	0.92371
1.280	0.69992	0.92494
1.290	0.70425	0.92615
1.300	0.70857	0.92733
1.310	0.71287	0.92849
1.320	0.71716	0.92962
1.330	0.72144	0.93074
1.340	0.72570	0.93183
1.350	0.72995	0.93290
1.360	0.73418	0.93394
1.370	0.73840	0.93497
1.380	0.74261	0.93598
1.390	0.74680	0.93697
1.400	0.75098	0.93793
1.410	0.75514	0.93888
1.420	0.75929	0.93981
1.430	0.76343	0.94072
1.440	0.76755	0.94162
1.450	0.77166	0.94249
1.460	0.77575	0.94335
1.470	0.77983	0.94419
1.480	0.78390	0.94502
1.490	0.78795	0.94583
1.500	0.79199	0.94662
1.510	0.79602	0.94740
1.520	0.80003	0.94816
1.530	0.80403	0.94891
1.540	0.80802	0.94965
1.550	0.81199	0.95037
1.560	0.81595	0.95107
1.570	0.81990	0.95176
1.580	0.82383	0.95244
1.590	0.82775	0.95311
1.600	0.83166	0.95376
1.610	0.83555	0.95440
1.620	0.83944	0.95502
1.630	0.84330	0.95564
1.640	0.84716	0.95624
1.650	0.85100	0.95683
1.660	0.85483	0.95742
1.670	0.85865	0.95798
1.680	0.86245	0.95854
1.690	0.86625	0.95909
1.700	0.87003	0.95963
1.710	0.87379	0.96015
1.720	0.87755	0.96067
1.730	0.88129	0.96118
1.740	0.88502	0.96168
1.750	0.88873	0.96216
1.760	0.89244	0.96264
1.770	0.89613	0.96311
1.780	0.89981	0.96357
1.790	0.90348	0.96403
1.800	0.90713	0.96447
1.810	0.91077	0.96490
1.820	0.91440	0.96533
1.830	0.91802	0.96575
1.840	0.92163	0.96616
1.850	0.92522	0.96657
1.860	0.92881	0.96696
1.870	0.93238	0.96735
1.880	0.93594	0.96773
1.890	0.93948	0.96811
1.900	0.94302	0.96847
1.910	0.94654	0.96883
1.920	0.95005	0.96919
1.930	0.95355	0.96954
1.940	0.95704	0.96988
1.950	0.96052	0.97021
1.960	0.96398	0.97054
1.970	0.96744	0.97086
1.980	0.97088	0.97118
1.990	0.97431	0.97149
2.000	0.97773	0.97180
2.010	0.98114	0.97210
2.020	0.98453	0.97239
2.030	0.98792	0.97268
2.040	0.99129	0.97296
2.050	0.99465	0.97324
2.060	0.99800	0.97352
2.070	1.00134	0.97379
2.080	1.00467	0.97405
2.090	1.00799	0.97431
2.100	1.01130	0.97457
2.110	1.01459	0.97482
2.120	1.01788	0.97506
2.130	1.02115	0.97530
2.140	1.02441	0.97554
2.150	1.02767	0.97577
2.160	1.03091	0.97600
2.170	1.03414	0.97623
2.180	1.03736	0.97645
2.190	1.04057	0.97667
2.200	1.04376	0.97688
2.210	1.04695	0.97709
2.220	1.05013	0.97730
2.230	1.05329	0.97750
2.240	1.05645	0.97770
2.250	1.05959	0.97790
2.260	1.06273	0.97809
2.270	1.06585	0.97828
2.280	1.06897	0.97847
2.290	1.07207	0.97865
2.300	1.07516	0.97883
2.310	1.07825	0.97901
2.320	1.08132	0.97918
2.330	1.08438	0.97935
2.340	1.08743	0.97952
2.350	1.09048	0.97969
2.360	1.09351	0.97985
2.370	1.09653	0.98001
2.380	1.09954	0.98017
2.390	1.10254	0.98032
2.400	1.10553	0.98048
2.410	1.10852	0.98063
2.420	1.11149	0.98077
2.430	1.11445	0.98092
2.440	1.11740	0.98106
2.450	1.12034	0.98120
2.460	1.12327	0.98134
2.470	1.12620	0.98148
2.480	1.12911	0.98161
2.490	1.13201	0.98174
2.500	1.13491	0.98187
2.510	1.13779	0.98200
2.520	1.14066	0.98213
2.530	1.14353	0.98225
2.540	1.14638	0.98238
2.550	1.14923	0.98250
2.560	1.15206	0.98262
2.570	1.15489	0.98273
2.580	1.15771	0.98285
2.590	1.16052	0.98296
2.600	1.16331	0.98307
2.610	1.16610	0.98318
2.620	1.16888	0.98329
2.630	1.17165	0.98340
2.640	1.17441	0.98350
2.650	1.17717	0.98361
2.660	1.17991	0.98371
2.670	1.18264	0.98381
2.680	1.18537	0.98391
2.690	1.18808	0.98401
2.700	1.19079	0.98411
2.710	1.19349	0.98420
2.720	1.19617	0.98430
2.730	1.19885	0.98439
2.740	1.20152	0.98448
2.750	1.20419	0.98457
2.760	1.20684	0.98466
2.770	1.20948	0.98475
2.780	1.21212	0.98483
2.790	1.21474	0.98492
2.800	1.21736	0.98500
2.810	1.21997	0.98509
2.820	1.22257	0.98517
2.830	1.22516	0.98525
2.840	1.22774	0.98533
2.850	1.23032	0.98541
2.860	1.23288	0.98549
2.870	1.23544	0.98556
2.880	1.23799	0.98564
2.890	1.24053	0.98571
2.900	1.24306	0.98579
2.910	1.24558	0.98586
2.920	1.24810	0.98593
2.930	1.25061	0.98600
2.940	1.25310	0.98607
2.950	1.25559	0.98614
2.960	1.25807	0.98621
2.970	1.26055	0.98628
2.980	1.26301	0.98635
2.990	1.26547	0.98641
3.000	1.26792	0.98648
3.010	1.27036	0.98655
3.020	1.27279	0.98661
3.030	1.27521	0.98667
3.040	1.27763	0.98674
3.050	1.28004	0.98680
3.060	1.28244	0.98686
3.070	1.28483	0.98692
3.080	1.28721	0.98698
3.090	1.28959	0.98704
3.100	1.29196	0.98710
3.110	1.29432	0.98715
3.120	1.29667	0.98721
3.130	1.29901	0.98727
3.140	1.30135	0.98732
3.150	1.30368	0.98738
3.160	1.30600	0.98744
3.170	1.30831	0.98749
3.180	1.31062	0.98754
3.190	1.31292	0.98760
3.200	1.31521	0.98765
3.210	1.31749	0.98770
3.220	1.31977	0.98775
3.230	1.32203	0.98780
3.240	1.32429	0.98785
3.250	1.32655	0.98791
3.260	1.32879	0.98795
3.270	1.33103	0.98800
3.280	1.33326	0.98805
3.290	1.33548	0.98810
3.300	1.33770	0.98815
3.310	1.33990	0.98820
3.320	1.34210	0.98824
3.330	1.34430	0.98829
3.340	1.34648	0.98834
3.350	1.34866	0.98838
3.360	1.35083	0.98843
3.370	1.35300	0.98847
3.380	1.35515	0.98852
3.390	1.35730	0.98856
3.400	1.35944	0.98860
3.410	1.36158	0.98865
3.420	1.36371	0.98869
3.430	1.36583	0.98873
3.440	1.36794	0.98878
3.450	1.37005	0.98882
3.460	1.37215	0.98886
3.470	1.37424	0.98890
3.480	1.37633	0.98894
3.490	1.37841	0.98898
3.500	1.38048	0.98902
3.510	1.38254	0.98906
3.520	1.38460	0.98910
3.530	1.38665	0.98914
3.540	1.38870	0.98918
3.550	1.39073	0.98922
3.560	1.39277	0.98926
3.570	1.39479	0.98930
3.580	1.39681	0.98933
3.590	1.39882	0.98937
3.600	1.40082	0.98941
3.610	1.40282	0.98945
3.620	1.40481	0.98948
3.630	1.40679	0.98952
3.640	1.40877	0.98956
3.650	1.41074	0.98959
3.660	1.41271	0.98963
3.670	1.41466	0.98966
3.680	1.41661	0.98970
3.690	1.41856	0.98973
3.700	1.42050	0.98977
3.710	1.42243	0.98980
3.720	1.42435	0.98984
3.730	1.42627	0.98987
3.740	1.42819	0.98990
3.750	1.43009	0.98994
3.760	1.43199	0.98997
3.770	1.43388	0.99001
3.780	1.43577	0.99004
3.790	1.43765	0.99007
3.800	1.43953	0.99010
3.810	1.44140	0.99014
3.820	1.44326	0.99017
3.830	1.44511	0.99020
3.840	1.44696	0.99023
3.850	1.44881	0.99026
3.860	1.45064	0.99030
3.870	1.45247	0.99033
3.880	1.45430	0.99036
3.890	1.45612	0.99039
3.900	1.45793	0.99042
3.910	1.45974	0.99045
3.920	1.46154	0.99048
3.930	1.46333	0.99051
3.940	1.46512	0.99054
3.950	1.46691	0.99057
3.960	1.46868	0.99060
3.970	1.47045	0.99063
3.980	1.47222	0.99066
3.990	1.47398	0.99069
4.000	1.47573	0.99072
4.010	1.47748	0.99075
4.020	1.47922	0.99078
4.030	1.48096	0.99081
4.040	1.48269	0.99083
4.050	1.48441	0.99086
4.060	1.48613	0.99089
4.070	1.48784	0.99092
4.080	1.48955	0.99095
4.090	1.49125	0.99097
4.100	1.49295	0.99100
4.110	1.49464	0.99103
4.120	1.49632	0.99106
4.130	1.49800	0.99108
4.140	1.49967	0.99111
4.150	1.50134	0.99114
4.160	1.50300	0.99117
4.170	1.50466	0.99119
4.180	1.50631	0.99122
4.190	1.50796	0.99125
4.200	1.50960	0.99127
4.210	1.51123	0.99130
4.220	1.51286	0.99132
4.230	1.51449	0.99135
4.240	1.51610	0.99138
4.250	1.51772	0.99140
4.260	1.51932	0.99143
4.270	1.52093	0.99145
4.280	1.52252	0.99148
4.290	1.52412	0.99150
4.300	1.52570	0.99153
4.310	1.52728	0.99156
4.320	1.52886	0.99158
4.330	1.53043	0.99161
4.340	1.53199	0.99163
4.350	1.53355	0.99166
4.360	1.53511	0.99168
4.370	1.53666	0.99170
4.380	1.53820	0.99173
4.390	1.53974	0.99175
4.400	1.54128	0.99178
4.410	1.54281	0.99180
4.420	1.54433	0.99183
4.430	1.54585	0.99185
4.440	1.54736	0.99187
4.450	1.54887	0.99190
4.460	1.55038	0.99192
4.470	1.55187	0.99194
4.480	1.55337	0.99197
4.490	1.55486	0.99199
4.500	1.55634	0.99201
4.510	1.55782	0.99204
4.520	1.55929	0.99206
4.530	1.56076	0.99208
4.540	1.56223	0.99211
4.550	1.56369	0.99213
4.560	1.56514	0.99215
4.570	1.56659	0.99218
4.580	1.56803	0.99220
4.590	1.56947	0.99222
4.600	1.57091	0.99224
4.610	1.57234	0.99227
4.620	1.57376	0.99229
4.630	1.57519	0.99231
4.640	1.57660	0.99233
4.650	1.57801	0.99235
4.660	1.57942	0.99238
4.670	1.58082	0.99240
4.680	1.58222	0.99242
4.690	1.58361	0.99244
4.700	1.58500	0.99246
4.710	1.58638	0.99248
4.720	1.58776	0.99251
4.730	1.58914	0.99253
4.740	1.59051	0.99255
4.750	1.59187	0.99257
4.760	1.59323	0.99259
4.770	1.59459	0.99261
4.780	1.59594	0.99263
4.790	1.59728	0.99265
4.800	1.59863	0.99268
4.810	1.59996	0.99270
4.820	1.60130	0.99272
4.830	1.60263	0.99274
4.840	1.60395	0.99276
4.850	1.60527	0.99278
4.860	1.60659	0.99280
4.870	1.60790	0.99282
4.880	1.60921	0.99284
4.890	1.61051	0.99286
4.900	1.61181	0.99288
4.910	1.61310	0.99290
4.920	1.61439	0.99292
4.930	1.61568	0.99294
4.940	1.61696	0.99296
4.950	1.61823	0.99298
4.960	1.61951	0.99300
4.970	1.62078	0.99302
4.980	1.62204	0.99304
4.990	1.62330	0.99306
5.000	1.62455	0.99308
5.010	1.62581	0.99310
5.020	1.62705	0.99312
5.030	1.62830	0.99314
5.040	1.62954	0.99316
5.050	1.63077	0.99318
5.060	1.63200	0.99320
5.070	1.63323	0.99321
5.080	1.63445	0.99323
5.090	1.63567	0.99325
5.100	1.63688	0.99327
5.110	1.63809	0.99329
5.120	1.63930	0.99331
5.130	1.64050	0.99333
5.140	1.64170	0.99335
5.150	1.64290	0.99337
5.160	1.64409	0.99338
5.170	1.64527	0.99340
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6.000	1.73113	0.99476
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10.500	1.94016	0.99849
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10.520	1.94056	0.99850
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10.540	1.94095	0.99851
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10.570	1.94154	0.99852
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10.590	1.94193	0.99853
10.600	1.94212	0.99853
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10.640	1.94289	0.99855
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10.690	1.94384	0.99857
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10.790	1.94568	0.99861
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15.830	1.98990	0.99965
15.840	1.98994	0.99965
15.850	1.98997	0.99965
15.860	1.99001	0.99966
15.870	1.99004	0.99966
15.880	1.99007	0.99966
15.890	1.99010	0.99966
15.900	1.99014	0.99966
15.910	1.99017	0.99966
15.920	1.99020	0.99966
15.930	1.99024	0.99966
15.940	1.99027	0.99966
15.950	1.99030	0.99966
15.960	1.99033	0.99967
15.970	1.99037	0.99967
15.980	1.99040	0.99967
15.990	1.99043	0.99967
16.000	1.99046	0.99967
16.010	1.99049	0.99967
16.020	1.99053	0.99967
16.030	1.99056	0.99967
16.040	1.99059	0.99967
16.050	1.99062	0.99967
16.060	1.99065	0.99967
16.070	1.99068	0.99968
16.080	1.99071	0.99968
16.090	1.99074	0.99968
16.100	1.99077	0.99968
16.110	1.99081	0.99968
16.120	1.99084	0.99968
16.130	1.99087	0.99968
16.140	1.99090	0.99968
16.150	1.99093	0.99968
16.160	1.99096	0.99968
16.170	1.99099	0.99968
16.180	1.99102	0.99969
16.190	1.99105	0.99969
16.200	1.99108	0.99969
16.210	1.99111	0.99969
16.220	1.99114	0.99969
16.230	1.99117	0.99969
16.240	1.99120	0.99969
16.250	1.99123	0.99969
16.260	1.99125	0.99969
16.270	1.99128	0.99969
16.280	1.99131	0.99969
16.290	1.99134	0.99969
16.300	1.99137	0.99970
16.310	1.99140	0.99970
16.320	1.99143	0.99970
16.330	1.99146	0.99970
16.340	1.99149	0.99970
16.350	1.99151	0.99970
16.360	1.99154	0.99970
16.370	1.99157	0.99970
16.380	1.99160	0.99970
16.390	1.99163	0.99970
16.400	1.99165	0.99970
16.410	1.99168	0.99970
16.420	1.99171	0.99971
16.430	1.99174	0.99971
16.440	1.99176	0.99971
16.450	1.99179	0.99971
16.460	1.99182	0.99971
16.470	1.99185	0.99971
16.480	1.99187	0.99971
16.490	1.99190	0.99971
16.500	1.99193	0.99971
16.510	1.99196	0.99971
16.520	1.99198	0.99971
16.530	1.99201	0.99971
16.540	1.99204	0.99971
16.550	1.99206	0.99972
16.560	1.99209	0.99972
16.570	1.99211	0.99972
16.580	1.99214	0.99972
16.590	1.99217	0.99972
16.600	1.99219	0.99972
16.610	1.99222	0.99972
16.620	1.99225	0.99972
16.630	1.99227	0.99972
16.640	1.99230	0.99972
16.650	1.99232	0.99972
16.660	1.99235	0.99972
16.670	1.99237	0.99972
16.680	1.99240	0.99973
16.690	1.99242	0.99973
16.700	1.99245	0.99973
16.710	1.99247	0.99973
16.720	1.99250	0.99973
16.730	1.99252	0.99973
16.740	1.99255	0.99973
16.750	1.99257	0.99973
16.760	1.99260	0.99973
16.770	1.99262	0.99973
16.780	1.99265	0.99973
16.790	1.99267	0.99973
16.800	1.99270	0.99973
16.810	1.99272	0.99974
16.820	1.99275	0.99974
16.830	1.99277	0.99974
16.840	1.99279	0.99974
16.850	1.99282	0.99974
16.860	1.99284	0.99974
16.870	1.99287	0.99974
16.880	1.99289	0.99974
16.890	1.99291	0.99974
16.900	1.99294	0.99974
16.910	1.99296	0.99974
16.920	1.99298	0.99974
16.930	1.99301	0.99974
16.940	1.99303	0.99974
16.950	1.99305	0.99975
16.960	1.99308	0.99975
16.970	1.99310	0.99975
16.980	1.99312	0.99975
16.990	1.99315	0.99975
17.000	1.99317	0.99975
17.010	1.99319	0.99975
17.020	1.99321	0.99975
17.030	1.99324	0.99975
17.040	1.99326	0.99975
17.050	1.99328	0.99975
17.060	1.99330	0.99975
17.070	1.99333	0.99975
17.080	1.99335	0.99975
17.090	1.99337	0.99975
17.100	1.99339	0.99976
17.110	1.99342	0.99976
17.120	1.99344	0.99976
17.130	1.99346	0.99976
17.140	1.99348	0.99976
17.150	1.99350	0.99976
17.160	1.99352	0.99976
17.170	1.99355	0.99976
17.180	1.99357	0.99976
17.190	1.99359	0.99976
17.200	1.99361	0.99976
17.210	1.99363	0.99976
17.220	1.99365	0.99976
17.230	1.99367	0.99976
17.240	1.99370	0.99976
17.250	1.99372	0.99977
17.260	1.99374	0.99977
17.270	1.99376	0.99977
17.280	1.99378	0.99977
17.290	1.99380	0.99977
17.300	1.99382	0.99977
17.310	1.99384	0.99977
17.320	1.99386	0.99977
17.330	1.99388	0.99977
17.340	1.99390	0.99977
17.350	1.99392	0.99977
17.360	1.99394	0.99977
17.370	1.99396	0.99977
17.380	1.99398	0.99977
17.390	1.99400	0.99977
17.400	1.99402	0.99978
17.410	1.99404	0.99978
17.420	1.99406	0.99978
17.430	1.99408	0.99978
17.440	1.99410	0.99978
17.450	1.99412	0.99978
17.460	1.99414	0.99978
17.470	1.99416	0.99978
17.480	1.99418	0.99978
17.490	1.99420	0.99978
17.500	1.99422	0.99978
17.510	1.99424	0.99978
17.520	1.99426	0.99978
17.530	1.99428	0.99978
17.540	1.99430	0.99978
17.550	1.99432	0.99978
17.560	1.99433	0.99978
17.570	1.99435	0.99979
17.580	1.99437	0.99979
17.590	1.99439	0.99979
17.600	1.99441	0.99979
17.610	1.99443	0.99979
17.620	1.99445	0.99979
17.630	1.99447	0.99979
17.640	1.99448	0.99979
17.650	1.99450	0.99979
17.660	1.99452	0.99979
17.670	1.99454	0.99979
17.680	1.99456	0.99979
17.690	1.99457	0.99979
17.700	1.99459	0.99979
17.710	1.99461	0.99979
17.720	1.99463	0.99979
17.730	1.99465	0.99979
17.740	1.99466	0.99980
17.750	1.99468	0.99980
17.760	1.99470	0.99980
17.770	1.99472	0.99980
17.780	1.99474	0.99980
17.790	1.99475	0.99980
17.800	1.99477	0.99980
17.810	1.99479	0.99980
17.820	1.99481	0.99980
17.830	1.99482	0.99980
17.840	1.99484	0.99980
17.850	1.99486	0.99980
17.860	1.99487	0.99980
17.870	1.99489	0.99980
17.880	1.99491	0.99980
17.890	1.99493	0.99980
17.900	1.99494	0.99980
17.910	1.99496	0.99980
17.920	1.99498	0.99981
17.930	1.99499	0.99981
17.940	1.99501	0.99981
17.950	1.99503	0.99981
17.960	1.99504	0.99981
17.970	1.99506	0.99981
17.980	1.99508	0.99981
17.990	1.99509	0.99981
18.000	1.99511	0.99981
18.010	1.99512	0.99981
18.020	1.99514	0.99981
18.030	1.99516	0.99981
18.040	1.99517	0.99981
18.050	1.99519	0.99981
18.060	1.99521	0.99981
18.070	1.99522	0.99981
18.080	1.99524	0.99981
18.090	1.99525	0.99981
18.100	1.99527	0.99981
18.110	1.99528	0.99982
18.120	1.99530	0.99982
18.130	1.99532	0.99982
18.140	1.99533	0.99982
18.150	1.99535	0.99982
18.160	1.99536	0.99982
18.170	1.99538	0.99982
18.180	1.99539	0.99982
18.190	1.99541	0.99982
18.200	1.99542	0.99982
18.210	1.99544	0.99982
18.220	1.99545	0.99982
18.230	1.99547	0.99982
18.240	1.99548	0.99982
18.250	1.99550	0.99982
18.260	1.99552	0.99982
18.270	1.99553	0.99982
18.280	1.99554	0.99982
18.290	1.99556	0.99982
18.300	1.99557	0.99982
18.310	1.99559	0.99983
18.320	1.99560	0.99983
18.330	1.99562	0.99983
18.340	1.99563	0.99983
18.350	1.99565	0.99983
18.360	1.99566	0.99983
18.370	1.99568	0.99983
18.380	1.99569	0.99983
18.390	1.99571	0.99983
18.400	1.99572	0.99983
18.410	1.99573	0.99983
18.420	1.99575	0.99983
18.430	1.99576	0.99983
18.440	1.99578	0.99983
18.450	1.99579	0.99983
18.460	1.99580	0.99983
18.470	1.99582	0.99983
18.480	1.99583	0.99983
18.490	1.99585	0.99983
18.500	1.99586	0.99983
18.510	1.99587	0.99983
18.520	1.99589	0.99983
18.530	1.99590	0.99984
18.540	1.99592	0.99984
18.550	1.99593	0.99984
18.560	1.99594	0.99984
18.570	1.99596	0.99984
18.580	1.99597	0.99984
18.590	1.99598	0.99984
18.600	1.99600	0.99984
18.610	1.99601	0.99984
18.620	1.99602	0.99984
18.630	1.99604	0.99984
18.640	1.99605	0.99984
18.650	1.99606	0.99984
18.660	1.99608	0.99984
18.670	1.99609	0.99984
18.680	1.99610	0.99984
18.690	1.99611	0.99984
18.700	1.99613	0.99984
18.710	1.99614	0.99984
18.720	1.99615	0.99984
18.730	1.99617	0.99984
18.740	1.99618	0.99984
18.750	1.99619	0.99985
18.760	1.99620	0.99985
18.770	1.99622	0.99985
18.780	1.99623	0.99985
18.790	1.99624	0.99985
18.800	1.99625	0.99985
18.810	1.99627	0.99985
18.820	1.99628	0.99985
18.830	1.99629	0.99985
18.840	1.99630	0.99985
18.850	1.99632	0.99985
18.860	1.99633	0.99985
18.870	1.99634	0.99985
18.880	1.99635	0.99985
18.890	1.99637	0.99985
18.900	1.99638	0.99985
18.910	1.99639	0.99985
18.920	1.99640	0.99985
18.930	1.99641	0.99985
18.940	1.99643	0.99985
18.950	1.99644	0.99985
18.960	1.99645	0.99985
18.970	1.99646	0.99985
18.980	1.99647	0.99985
18.990	1.99649	0.99985
19.000	1.99650	0.99986
19.010	1.99651	0.99986
19.020	1.99652	0.99986
19.030	1.99653	0.99986
19.040	1.99654	0.99986
19.050	1.99655	0.99986
19.060	1.99657	0.99986
19.070	1.99658	0.99986
19.080	1.99659	0.99986
19.090	1.99660	0.99986
19.100	1.99661	0.99986
19.110	1.99662	0.99986
19.120	1.99663	0.99986
19.130	1.99665	0.99986
19.140	1.99666	0.99986
19.150	1.99667	0.99986
19.160	1.99668	0.99986
19.170	1.99669	0.99986
19.180	1.99670	0.99986
19.190	1.99671	0.99986
19.200	1.99672	0.99986
19.210	1.99673	0.99986
19.220	1.99674	0.99986
19.230	1.99676	0.99986
19.240	1.99677	0.99986
19.250	1.99678	0.99987
19.260	1.99679	0.99987
19.270	1.99680	0.99987
19.280	1.99681	0.99987
19.290	1.99682	0.99987
19.300	1.99683	0.99987
19.310	1.99684	0.99987
19.320	1.99685	0.99987
19.330	1.99686	0.99987
19.340	1.99687	0.99987
19.350	1.99688	0.99987
19.360	1.99689	0.99987
19.370	1.99690	0.99987
19.380	1.99691	0.99987
19.390	1.99692	0.99987
19.400	1.99693	0.99987
19.410	1.99695	0.99987
19.420	1.99696	0.99987
19.430	1.99697	0.99987
19.440	1.99698	0.99987
19.450	1.99699	0.99987
19.460	1.99700	0.99987
19.470	1.99701	0.99987
19.480	1.99702	0.99987
19.490	1.99703	0.99987
19.500	1.99704	0.99987
19.510	1.99705	0.99987
19.520	1.99706	0.99987
19.530	1.99707	0.99988
19.540	1.99707	0.99988
19.550	1.99708	0.99988
19.560	1.99709	0.99988
19.570	1.99710	0.99988
19.580	1.99711	0.99988
19.590	1.99712	0.99988
19.600	1.99713	0.99988
19.610	1.99714	0.99988
19.620	1.99715	0.99988
19.630	1.99716	0.99988
19.640	1.99717	0.99988
19.650	1.99718	0.99988
19.660	1.99719	0.99988
19.670	1.99720	0.99988
19.680	1.99721	0.99988
19.690	1.99722	0.99988
19.700	1.99723	0.99988
19.710	1.99724	0.99988
19.720	1.99725	0.99988
19.730	1.99725	0.99988
19.740	1.99726	0.99988
19.750	1.99727	0.99988
19.760	1.99728	0.99988
19.770	1.99729	0.99988
19.780	1.99730	0.99988
19.790	1.99731	0.99988
19.800	1.99732	0.99988
19.810	1.99733	0.99988
19.820	1.99734	0.99988
19.830	1.99734	0.99989
19.840	1.99735	0.99989
19.850	1.99736	0.99989
19.860	1.99737	0.99989
19.870	1.99738	0.99989
19.880	1.99739	0.99989
19.890	1.99740	0.99989
19.900	1.99741	0.99989
19.910	1.99741	0.99989
19.920	1.99742	0.99989
19.930	1.99743	0.99989
19.940	1.99744	0.99989
19.950	1.99745	0.99989
19.960	1.99746	0.99989
19.970	1.99747	0.99989
19.980	1.99747	0.99989
19.990	1.99748	0.99989
20.000	1.99749	0.99989

Sourced from 2 authoritative references including Wikipedia.See all references

How to Use This Calculator

Enter your input values

Fill in all required input fields for the PID Controller Tuner. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

Read the results

The PID Controller Tuner instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

PID Controller Tuner Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

•Use the PID Controller Tuner when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
•Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
•Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
•Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
•Use it in the field when a quick estimate is needed and a full engineering software package is not available.

About This Calculator

The PID Controller Tuner is a precision engineering calculation tool designed for students, engineers, and technical professionals. Automatic PID tuning using Ziegler-Nichols (open-loop and closed-loop) and Cohen-Coon methods with step response comparison chart All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.

The Theory Behind It

PID (Proportional-Integral-Derivative) controllers are the most widely used feedback control strategy in industrial applications, accounting for roughly 95% of process control loops. The PID control law is u(t) = K_p·e(t) + K_i·∫e(t)dt + K_d·de/dt, where e(t) is the error (setpoint − process variable), and K_p, K_i, K_d are the proportional, integral, and derivative gains respectively. The proportional term provides correction proportional to current error; the integral term eliminates steady-state error by accumulating past error; the derivative term provides damping by responding to error rate of change. PID tuning is the process of selecting appropriate gains for a specific process. The Ziegler-Nichols method (1942) is the classical approach: for open-loop tuning, step-test the process and identify delay L and time constant T, then use K_p = 1.2T/L, K_i = 2L, K_d = 0.5L for a PID controller. For closed-loop (ultimate) tuning: increase proportional gain until sustained oscillation occurs at gain K_u and period P_u, then use K_p = 0.6·K_u, K_i = P_u/2, K_d = P_u/8. The Cohen-Coon method is an alternative using the same open-loop step test with different formulas optimized for disturbance rejection. Modern methods include IMC (Internal Model Control), lambda tuning, and auto-tuning based on relay feedback tests. The calculator supports all three classical methods and provides guidance for further refinement.

Real-World Applications

•Temperature control: tune PID gains for process heaters, ovens, cryogenic chambers, and HVAC systems to achieve stable temperature control with minimum overshoot.
•Flow and level control: tune process flow controllers for pumps, control valves, and level control in tanks and reservoirs.
•Motor speed and position control: tune servo motors for machine tools, robotics, and automation equipment.
•Autopilot and flight control: aircraft autopilots use PID controllers for altitude, heading, and attitude hold with gains scheduled for different flight conditions.
•Electronic circuit control: phase-locked loops, voltage regulators, and laser stabilization circuits use PID-like controllers tuned for their specific dynamics.

Frequently Asked Questions

What is PID control?

PID control is a feedback control algorithm that computes a control signal from three terms: proportional (K_p × error), integral (K_i × integral of error), and derivative (K_d × derivative of error). The proportional term provides base correction, integral eliminates steady-state error, and derivative adds damping. PID is effective on a wide range of processes and is the most common industrial control algorithm.

How does the Ziegler-Nichols method work?

Open-loop method: apply a step to the process, measure the dead time L and time constant T from the response, then set K_p = 1.2T/L, K_i = 2L (integral time), K_d = 0.5L (derivative time). Closed-loop method: increase K_p until sustained oscillation, measure K_u (ultimate gain) and P_u (oscillation period), then set K_p = 0.6K_u, K_i = P_u/2, K_d = P_u/8. Z-N gives aggressive tuning that may need refinement for less oscillatory response.

When should I use P, PI, or PID?

P (proportional only): simple processes where steady-state error is acceptable. PI: eliminates steady-state error; good for most process control (flow, level, temperature) without fast dynamics. PID: fast processes with significant overshoot concerns (motor control, servo positioning). Don't use derivative for noisy processes — it amplifies noise and causes erratic control.

What's a PID tuning safety rule?

Start with conservative gains: K_p = Z-N proportional × 0.5, K_i = Z-N integral × 2 (slower), K_d = 0 initially. Observe response, then gradually increase K_p and reduce integral time until you see the desired response. Add derivative only if overshoot is a problem. Never tune to the edge of instability — leave margin for process variations and disturbances.

What's integral windup?

Integral windup occurs when the integrator accumulates error during periods when the actuator is saturated (fully open or fully closed). This causes large overshoot when the error finally reverses because the integrator must first 'unwind' before the actuator can back off. Anti-windup techniques (integrator clamping, back-calculation, conditional integration) prevent this by stopping or limiting integration when saturation is detected.

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PID Controller Tuner

How to Use This Calculator

Formula Reference

When to Use This Calculator

About This Calculator

The Theory Behind It

Real-World Applications

Frequently Asked Questions

What is PID control?

How does the Ziegler-Nichols method work?

When should I use P, PI, or PID?

What's a PID tuning safety rule?

What's integral windup?

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References & Further Reading

Wikipedia